Updated on 2023/02/06

写真a

 
DOU, Xiaoling
 
Scopus Paper Info  
Paper Count: 0  Citation Count: 0  h-index: 5

Citation count denotes the number of citations in papers published for a particular year.

Affiliation
Affiliated organization, Center for Data Science
Job title
Associate Professor(tenure-track)
Profile

I came to Japan from Qingdao, China. As an international student, I spent my first 10 years in Japan learning Japanese at a Japanese language school, and studying statistics at Shiga and Osaka Universities. I conducted research in functional data analysis while at the Graduate School of Engineering Science, Osaka University, and in my doctoral course, I proposed functional subspace methods in functional discriminant analysis and investigated estimating derivatives of functional data. After graduating from Osaka University, I started working as a project researcher at the Institute Statistical Mathematics (ISM), Tokyo. At ISM, I was researching influence analysis in quantitative trait loci detection, Baker's distribution, and analysis of mouse ultrasonic vocalization data. Now, at Waseda University, I am teaching Mathematics and Statistics and doing research on copulas and functional data analysis. In addition to statistical research, I am also interested in travelling, cooking, and gardening.

Concurrent Post

  • Affiliated organization   Global Education Center

 

Research Areas

  • Applied mathematics and statistics

  • Statistical science

Papers

  • Bell Numbers in Matsunaga's and Arima's Genjikō Combinatorics: Modern Perspectives and Local Limit Theorems

    Xiaoling Dou, Hsien-Kuei Hwang, Chong-Yi Li

    The Electronic Journal of Combinatorics   29 ( 2 )  2022.04  [Refereed]

    　View Summary

    We examine and clarify in detail the contributions of Yoshisuke Matsunaga (1694?-1744) to the computation of Bell numbers in the eighteenth century (in the Edo period), providing modern perspectives to some unknown materials that are by far the earliest in the history of Bell numbers. Later clarification and developments by Yoriyuki Arima (1714-1783), and several new results such as the asymptotic distributions (notably the corresponding local limit theorems) of a few closely related sequences are also given.

    DOI

    Scopus

  • Causality for CHARN models

    Xiaoling Dou

    Scientiae Mathematicae Japanicae    2021.07  [Refereed]

  • An identity for two integral transforms applied to the uniqueness of a distribution via its Laplace–Stieltjes transform

    Gwo Dong Lin, Xiaoling Dou

    Statistics   55 ( 2 ) 367 - 385  2021.03  [Refereed]

    DOI

    Scopus

  • Dependence Properties of B-Spline Copulas

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

    Sankhya A    2019.11  [Refereed]

    Authorship：Lead author

  • Functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou, Shingo Shirahata, Hiroki Sugimoto

    PLoS ONE   13 ( 5 ) e0196834  2018.05  [Refereed]

  • The bivariate lack-of-memory distributions

    Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki

    Sankhya A: The Indian Journal of Statistics    2017.11  [Refereed]

  • An investigation of a generalized least squares estimator for non-linear time series model

    DOU, Xiaoling

    Scientiae Mathematicae Japonicae    2017.04  [Refereed]

  • Testing for Granger causality by use of Box-Cox transformations

    小池隆之介, Dou Xiaoling, 谷口正信, Xue Yujie

    ASTE Special Issue on the “Financial & Pension Mathematical Science”   13   17 - 23  2016.03  [Refereed]

  • EM algorithms for estimating the Bernstein copula

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

    COMPUTATIONAL STATISTICS & DATA ANALYSIS   93   228 - 245  2016.01  [Refereed]

    　View Summary

    A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent various distributions flexibly and that the proposed EM algorithms work well for such data. (C) 2014 Elsevier B.V. All rights reserved.

    DOI

    Scopus

    15
    Citation
    (Scopus)

  • Noise reduction and classification of mouse ultrasonic vocalization data

    Xiaoling Dou, Shingo Shirahata, Hiroki Sugimoto, Tsuyoshi Koide

    ASTE Special Issue on the “Financial & Pension Mathematical Science”   12   71 - 79  2015.03  [Refereed]

    CiNii

  • Influence analysis in quantitative trait loci detection

    Xiaoling Dou, Satoshi Kuriki, Akiteru Maeno, Toyoyuki Takada, Toshihiko Shiroishi

    BIOMETRICAL JOURNAL   56 ( 4 ) 697 - 719  2014.07  [Refereed]

    　View Summary

    This paper presents systematic methods for the detection of influential individuals that affect the log odds (LOD) score curve. We derive general formulas of influence functions for profile likelihoods and introduce them into two standard quantitative trait locus detection methods-the interval mapping method and single marker analysis. Besides influence analysis on specific LOD scores, we also develop influence analysis methods on the shape of the LOD score curves. A simulation- based method is proposed to assess the significance of the influence of the individuals. These methods are shown useful in the influence analysis of a real dataset of an experimental population from an F 2 mouse cross. By receiver operating characteristic analysis, we confirm that the proposed methods show better performance than existing diagnostics.

    DOI

    Scopus

  • Recent developments on the construction of bivariate distributions with fixed marginals

    Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki, Jin-Sheng Huang

    Journal of Statistical Distributions and Applications   1 ( 14 )  2014.01  [Refereed]

  • Dependence structures and asymptotic properties of Baker's distributions with fixed marginals

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   143 ( 8 ) 1343 - 1354  2013.08  [Refereed]

    　View Summary

    We investigate the properties of Baker's (2008) bivariate distributions with fixed marginals and their multivariate extensions. The properties include the weak convergence to the Frechet-Hoeffding upper bound, the product-moment convergence, as well as the dependence structures TP2 (totally positive of order 2), or MTP2 (multivariate TP2). In proving the weak convergence, a generalized local limit theorem for binomial distribution is provided. (C) 2013 Elsevier B.V. All rights reserved.

    DOI

    Scopus

    8
    Citation
    (Scopus)

  • Dependence structure of bivariate order statistics with applications to bayramoglu's distributions

    J. S. Huang, Xiaoling Dou, Satoshi Kuriki, G. D. Lin

    Journal of Multivariate Analysis   114 ( 1 ) 201 - 208  2013  [Refereed]

    　View Summary

    We study the dependence structure of bivariate order statistics from bivariate distributions, and prove that if the underlying bivariate distribution H is positive quadrant dependent (PQD) then so is each pair of bivariate order statistics. As an application, we show that if H is PQD, the bivariate distribution K(n)+, recently proposed by Bairamov and Bayramoglu (2012) [1], is greater than or equal to Baker's (2008) [2] distribution H(n)+, and hence K(n)' attains a correlation higher than that of H(n)+. We give two explicit forms of the intractable K(n)+ and prove that for all n ≥ 2, K(n)+ is PQD regardless of H. We also show that if H is PQD, K(n)+ converges weakly to the Fréchet-Hoeffding upper bound as n tends to infinity. © 2012 Elsevier Inc.

    DOI

    Scopus

    14
    Citation
    (Scopus)

  • Statistical Inference for Baker's Distribution

    Dou Xiaoling, Kuriki Satoshi, Lin Gwo Dong

    Proceedings of the symposium of Japanese Society of Computational Statistics   24   121 - 124  2010

    DOI CiNii

  • Comparisons of B-spline procedures with kernel procedures in estimating regression functions and their derivatives

    Xiaoling Dou, Shingo Shirahata

    Journal of the Japanese Society of Computational Statistics   22 ( 1 ) 57 - 77  2009.12  [Refereed]

    　View Summary

    There are several methods to estimate regression functions and their derivatives. Among them, B-spline procedures and kernel procedures are known to be useful. However, at present, it is not determined which procedure is better than the others. In this paper, we investigate the performance of the procedures by computer simulations. Two B-spline procedures are considered. The first one is to estimate derivatives using a different roughness penalty for each degree of the derivative d. In this procedure, the smoothing parameters and the coefficients of the B-spline functions are different for each d. The second procedure is to estimate the dth derivative just by differentiating the estimated regression function d-times. In this case, the regression function and its derivatives have a common coefficient vector of B-spline functions. Two kernel procedures are also considered. The first kernel procedure used in our simulations is constructed with the Gasser-Muller estimator and a global plug-in bandwidth selector. The second one is a local polynomial fitting with a refined bandwidth selector. As a result of our simulations, we find that B-spline procedures can give better estimates than the kernel ones in estimating regression functions. For derivatives, we also find that in B-spline methods, it is necessary to choose a different smoothing parameter (or coefficient vector) for each degree of derivative; between the two kernel methods, the Gasser-Muller procedure gives better results than the local polynomial fitting in most cases. Furthermore, the first B-spline method can still work better than the Gasser-Muller procedure in the central area of the domain of the functions. But in the boundary areas, the Gasser-Muller procedure gives more stable derivative estimates than all the other methods.

    DOI CiNii

  • 区間マッピング法における影響分析(セッション3A)

    Xiaoling Dou, 栗木 哲, 前野 哲輝, 高田 豊行, 城石 俊彦

    日本計算機統計学会シンポジウム論文集   23   151 - 154  2009

    DOI CiNii

  • Functional discriminant analysis--Linear method and functional subspace methods

    Xiaoling Dou, Shingo Shirahata, Wataru Sakamoto

    日本計算機統計学会   19 ( 1 ) 13 - 30  2007.07  [Refereed]

    　View Summary

    For discriminating functional data, several linear methods have been proposed, such as, filtering method, regularization method and functional linear discriminant analysis. However, if the size of training data is small or if it can not be assumed that the data in each class are sampled from multivariate normal populations with equal covariance matrices, there is no guarantee that linear methods are always available. In this paper, nonlinear discriminant analysis methods are introduced, based on principal component expansion of functional data. They are called functional subspace methods, which include functional subspace method and functional CLAFIC method. These procedures do not require the knowledge on the underlying distributions of populations, but linear discriminant analysis methods do. Furthermore, our procedures can be carried out more rapidly than the traditional subspace methods, because they require only small size of training data and they can be computed with lower dimensions. In order to show that the functional subspace methods are effective, they are compared with filtering method. As a result, the functional subspace methods produce good discrimination. Particularly, when the size of training data is small they can give more stable results than the filtering method.

    DOI CiNii

▼display all

Misc

Awards

  • e-Teaching Award 2019 (Good Practice)

    2019.05   Waseda University   Advanced Probability and Statistics, Ordinary Differential Equations, Exercise for Fundamental Mathematics

    Winner： Xiaoling Dou

Research Projects

  • B-splineコピュラの相関構造とその推定

    日本学術振興会  科学研究費助成事業 基盤研究(C)

    Project Year :

    2016.04
    -
    2020.03
     

    DOU XIAOLING

    　View Summary

    今まで、B-spline基底関数を用いて、B-splineコピュラを定義し、相関を最大にするB-splineコピュラがFrechet-Hoeffding upper bound に達することができることと任意のオーダーのtotal positivityの性質を持つことがわかった。コピュラの柔軟性をさらに詳しく調べるために、本年度はB-splineコピュラの相関性質、特にB-spline基底関数の次数が与えられた時に、原点周りの h（h >= 0）次モーメントについて研究してきた。B-spline基底関数はある初期条件の下で、再帰的に生成されるという性質を持つため、B-spline基底関数のモーメントも再帰的な性質を持つことがわかる。その具体的数式表現を導出した。また、Stirling numbers of the second kindもある初期条件の下で再帰性を持つことが知られている。この再帰性を用いて、B-spline基底関数のモーメントをStirling numbers of the second kindで書くことができた。これらについては、数学的帰納法で証明した。特に、B-spline基底関数の０次と１次のモーメントの明白な数式で与えた。このように得られたB-spline基底関数の０次と１次のモーメントが等間隔にB-spline基底関数のknotsを配置する時に、相関を最大にするB-splineコピュラの相関係数の計算に用いられる。

  • Estimate on Regression Functions and ProbabilityDensity Functions

  • EMアルゴリズムによるBernstein コピュラの推定

    科学研究費助成事業(大学共同利用機関法人情報・システム研究機構（新領域融合研究センター及びライフサイ)  科学研究費助成事業(若手研究(B))

Presentations

  • EM algorithms for estimating B-spline copulas

    Xiaoling Dou

    Computational and Financial Econometrics (CFE 2019) & 12th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2019) 

    Presentation date： 2019.12

    Event date：
    2019.12
    　
    　

  • EM algorithms for estimating B-spline copula

    Xiaoling Dou

    New Developments in Statistics and its Applications 

    Presentation date： 2019.12

  • Baker’s distribution, Bernstein copula and B-spline copulas

    Xiaoling Dou  [Invited]

    MSJ Autumn Meeting 2019 

    Presentation date： 2019.09

  • Dependence Properties of B-Spline Copulas

    Xiaoling Dou  [Invited]

    28th South Taiwan Statistics Conference 

    Presentation date： 2019.06

  • Testing for Granger Causality by Use of Box-Cox Transformations

    Xiaoling Dou, Ryunosuke Koike, Masanobu Taniguchi  [Invited]

    Workshop on causal inference in complex marine ecosystems 

    Presentation date： 2019.06

  • Dependence Structures of the B-spline Copulas including the Bernstein ones

    Xiaoling Dou  [Invited]

    Statistical Methods and Models for Complex Data (Benevento, Italy) 

    Presentation date： 2019.06

  • Dependence structures of the B-spline copulas

    Xiaoling Dou  [Invited]

    Mini Workshop on TDA, Time Series & Statistics 

    Presentation date： 2019.05

  • The Stirling and Eulerian numbers in the Edo Period

    Xiaoling Dou

    Kinosaki Seminar on Data Science & Causality 

    Presentation date： 2019.03

  • The Stirling and Eulerian numbers in the Edo Period

    Xiaoling Dou  [Invited]

    Presentation date： 2018.11

  • A nonparametric functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou  [Invited]

    EcoSta2018 

    Presentation date： 2018.06

  • The Stirling and Eulerian numbers: some historical notes

    Xiaoling Dou  [Invited]

    International Workshop at Waseda University 2018 (IWAWU2018) -- Topics in statistical inference and stochastics-- 

    Presentation date： 2018.03

  • A nonparametric functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou

    Kochi International Seminar 

    Presentation date： 2018.03

  • An investigation of a generalized least squares estimator for non-linear time series models

    Xiaoling Dou  [Invited]

    Computational and Methodological Statistics (CMStatistics 2017), 

    Presentation date： 2017.12

  • A nonparametric functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou

    ISI-ISM-ISSAS joint conference Tokyo 2017 

    Presentation date： 2017.12

  • A nonparametric functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou

    2017 Japanese Joint Statistical Meeting 

    Presentation date： 2017.09

  • An investigation of Ochi’s estimator

    Xiaoling Dou  [Invited]

    1st International Conference on Econometrics and Statistics (EcoSta 2017) 

    Presentation date： 2017.06

  • A functional nonparametric unsupervised classification of mouse ultrasonic vocalization data

    Xiaoling Dou

    Ise-Shima International Seminar 

    Presentation date： 2017.03

  • A generalized least squares estimator for non-linear time series model

    Xiaoling Dou  [Invited]

    Keio International Symposium 

    Presentation date： 2017.03

  • B-spline copula and its estimation

    Xiaoling Dou  [Invited]

    The 10th ICSA International Conference on Global Growth of Modern Statistics in the 21st Century, Shanghai Jiao Tong University 

    Presentation date： 2016.12

  • An investigation of the Ochi estimator in the first order of ARCH model

    Xiaoling Dou  [Invited]

    Waseda International Symposium 

    Presentation date： 2016.10

  • Baker distribution, Bernstein copula and B-spline copula

    Xiaoling Dou  [Invited]

    9th Seminar of Data Science, Shiga University 

    Presentation date： 2016.08

  • Functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou  [Invited]

    Statistics Seminar in University College London 

    Presentation date： 2016.08

  • Functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou  [Invited]

    The 4th Institute of Mathematical Statistics, Asia Pacific Rim Meeting, 

    Presentation date： 2016.06

  • Testing for Granger causality by use of Box-Cox transformations

    Xiaoling Dou, Ryunosuke Koike, Masanobu Taniguchi

    Ibusuki International Seminar--High Dimensional Statistical Analysis for Time Spatial Processes & Quantile Analysis for Time Series-- 

    Presentation date： 2016.03

  • EM algorithm for estimation of B-spline copula

    Xiaoling Dou  [Invited]

    Kumamoto International Symposium --High Dimensional Statistical Analysis & Quantile Analysis for Time Series-- 

    Presentation date： 2016.03

  • Noise cancelation and classification of mouse ultrasonic vocalization data

    Xiaoling Dou  [Invited]

    8th International Conference of the ERCIM WG on computational and Methodological Statistics (CMStatistics 2015) 

    Presentation date： 2015.12

  • Functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou, Shingo Shirahata

    60th World Statistics Congress- ISI2015 

    Presentation date： 2015.07

  • Dependence structure and estimation of B-spline copulas

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

    ISI-ISM-ISSAS Joint conference 2015 

    Presentation date： 2015.04

  • Dependence structure and estimation of B-spline copulas

    Xiaoling Dou  [Invited]

    International Workshop in Waseda University -- Recent Developments in Statistical Distribution Theory and its Applications-- 

    Presentation date： 2015.03

  • Functional Clustering of Mouse Ultrasonic Vocalization Data

    Xiaoling Dou  [Invited]

    Workshop on Statistical Methods for Large Complex Data (National Sun Yat-sen University) 

    Presentation date： 2015.03

  • Estimation of B-spline copulas

    Xiaoling Dou

    Miura Statistical Seminar 

    Presentation date： 2015.03

  • Baker's distribution and the B-spline copula

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

    Waseda International Symposium --Asymptotic Sufficiency, Asymptotic Efficiency and Semimartingale-- 

    Presentation date： 2015.03

  • Dependence structure of B-spline copulas

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

    Izu Seminar 

    Presentation date： 2015.01

  • A class of B-spline copulas: Dependence structure and estimation

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards  [Invited]

    7th International Conference of the ERCIM WG on Computational and Methodological Statistics (ERCIM 2014) 

    Presentation date： 2014.12

  • Functional Clustering of Mouse Ultrasonic Vocalization Data

    Xiaoling Dou, Shingo Shirahata, Hiroki Sugimoto, Tsuyoshi Koide

    ISI-ISM-ISSAS joint conference 2014 

    Presentation date： 2014.02

  • Expectation maximization algorithms for estimating Bernstein copula density

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

    59 ISI World Statistics Congress 2013 

    Presentation date： 2013.08

  • Dependence structure of bivariate order statistics and its applications

    Xiaoling Dou, J. S. Huang, Satoshi Kuriki, G. D. Lin

    ISI-ISM-ISSAS Joint Conference 2013 

    Presentation date： 2013.02

  • Functional clustering of mouse ultrasonic vocalization data

    Xiaoling Dou, Shingo Shirahata, Hiroki Sugimoto, Tsuyoshi Koide

    5th International Conference of the ERCIM Working Group on Computing & Statistics 

    Presentation date： 2012.12

  • Dependence structures and asymptotic properties of Baker’s distributions with fixed marginal

    Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin  [Invited]

    Ims-APRM2012 

    Presentation date： 2012.07

  • Cluster analysis of mouse ultrasonic vocalization data

    Xiaoling Dou, Shingo Shirahata, Hiroki Sugimoto, Tsuyosi Koide  [Invited]

    Workshop on Mouse Ultrasonic Communication 

    Presentation date： 2012.04

  • Influence analysis in QTL detection

    Xiaoling Dou, Satoshi Kuriki, Akiteru Maeno, Toshihiko Shiroishi

    The 57th Session of the International Statistical Institute 

    Presentation date： 2009.08

  • Estimating regression functions and their derivatives

    Xiaoling Dou, Shingo Shirahata  [Invited]

    Joint Meeting of 4th Conference of the IASC and 6th Conference of the Asian Regional Section of the IASC on Computational Statistics & Data Analysis 

    Presentation date： 2008.12

  • Functional Subspace Methods – A nonlinear discriminant analysis method for functional data

    Xiaoling Dou, Shingo Shirahata, Wataru Sakamoto

    The 56th Session of the International Statistical Institute 

    Presentation date： 2007.08

▼display all

Specific Research

  • A smoothed empirical beta copula

    2021  

    　View Summary

    In modeling multivariate distribution with the empirical beta copula, we find that it is difficult to do the computation when sample size is larger than 500, because the empirical beta distribution is constructed by Gamma functions. We try to use Stirling's approximation formula for the Gamma functions and translate them back by logarithm functions. This makes the calculation possible, however it still takes time when the sample size N is large. To solve this problem, we introduce a smaller integer K << N to separate the data set into K times K grids. We then calculate the means of data in each grid. The number of the means, say M, is smaller than or equal to K^2. Instead of the original N data, we use the M<<N means as the new data in the multivariate distribution modeling with the empirical beta copula. This method can dramatically reduce computation time and make the empirical beta copula applicable for large sample size. This method is presented at The Japanese Joint Statistical Meeting 2021 (September 2021) and Waseda International Symposium Topological Data Science, Causality, Analysis of Variance & Time Series 2022 (March 2022).

  • Bernsteinコピュラの推定に関する研究

    2020  

    　View Summary

    Bernstein コピュラのパラメータの各次元のサイズがデータのサイズと同じになるときに経験Betaコピュラになる。経験Betaコピュラはパラメータが必要としない、各次元でデータのランクを用いたノンパラメットリックな多次元分布の推定方法。本研究は経験Betaコピュラの推定を試みた。実データを使った実験では、サンプルサイズNに対してNの３乗の計算時間が必要。BernsteinコピュラはBernstein多項式の数のパラメータが必要だが、少ない計算量で済むメリットがある。また、経験Betaコピュラの計算には、Beta関数を用いるのでN=500までは計算できるが、それ以上はBeta関数が分母でゼロになるため, 不具合が生じることが分かった。

  • Stirling and Eulerian numbers in the Edo Period and their asymptotic distributions

    2019   Hwang, Hsien-Kuei

    　View Summary

    スターリン数とオイラー数は数学の組み合わせ理論や統計学におけるBスプライン・コピュラの相関構造の性質など, 幅広く利用されている. 西洋ではその歴史と発展は明らかにされているが, 東洋ではこれらの数に関しての研究は世界に知らされていないことが多い. 本研究は日本ではスターリン数とオイラー数の発見, 導出, 性質及び応用を詳しく研究し,特に, 第二種のオイラー数やベル数について日本は西洋より早く発見し応用していたことがわかった. さらに西洋よりも, 日本では多様に活用されてきた. これらの数の歴史, 性質を詳しく検討し, 生成関数によって, これらの数の確率変数を生成し,漸近分布とそれらの性質も研究している.<!-- /* Font Definitions */ @font-face {font-family:"ＭＳ 明朝"; panose-1:2 2 6 9 4 2 5 8 3 4; mso-font-alt:"MS Mincho"; mso-font-charset:128; mso-generic-font-family:modern; mso-font-pitch:fixed; mso-font-signature:-536870145 1791491579 134217746 0 131231 0;}@font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face {font-family:"ＭＳ Ｐゴシック"; panose-1:2 11 6 0 7 2 5 8 2 4; mso-font-alt:"MS PGothic"; mso-font-charset:128; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-536870145 1791491579 134217746 0 131231 0;}@font-face {font-family:"\@ＭＳ 明朝"; panose-1:2 2 6 9 4 2 5 8 3 4; mso-font-charset:128; mso-generic-font-family:modern; mso-font-pitch:fixed; mso-font-signature:-536870145 1791491579 134217746 0 131231 0;}@font-face {font-family:"\@ＭＳ Ｐゴシック"; mso-font-charset:128; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-536870145 1791491579 134217746 0 131231 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin:0mm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"ＭＳ Ｐゴシック",sans-serif; mso-bidi-font-family:"ＭＳ Ｐゴシック";}.MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-family:"游明朝",serif; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}size:612.0pt 792.0pt; margin:99.25pt 30.0mm 30.0mm 30.0mm; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;}div.WordSection1 {page:WordSection1;}

 

Syllabus

▼display all

Teaching Experience

  • Foundations of Analysis (Measure, Integral and Probability)

    Waseda University  

    2014.04
    -
    2019.03
     

  • Financial Econometrics

    Waseda University  

    2014.04
    -
    2019.03
     

  • Advanced Probability and Statistics

    Waseda University  

    2014.04
    -
    2019.03
     

  • Exercise for Fundamental Mathematics

    Waseda University  

    2014.04
    -
    2019.03
     

  • Probability and Statistics

    Waseda University  

    2013.09
    -
    2019.03
     

  • Ordinary Differential Equations

    Waseda University  

    2013.04
    -
    2019.03
     

  • Introduction to Probability and Statistics

    Waseda University  

    2018.04
    -
    2018.08
     

▼display all