<title>Abstract</title>In the game of baseball, each pitcher throws various types of pitches, such as cutter, curve ball, slider, and splitter. Although the type of a given pitch may be inferred by audience and/or obtained from the TrackMan data, the actual pitch type (i.e., the pitch type declared by the pitcher) may not be known. Classification of pitch types is a challenging task, as pitched baseballs may have different kinematic characteristics across pitchers even if the self-declared pitch types are the same. In addition, there is a possibility that the kinematic characteristics of pitched baseballs are identical even if the self-declared pitch types are different. In this study, we aimed to classify TrackMan data of pitched baseballs into pitch types by applying the Variational Bayesian Gaussian Mixture Models technique. We also aimed to analyze the kinematic characteristics of the classified pitch types and indices related to batting performance while pitching each pitch type. The results showed that the pitch types could not be accurately classified solely by kinematic characteristics, but with consideration of the characteristics of the fastball the accuracy improves substantially. This study could provide a basis for the development of a more accurate automatic pitch type classification system.

Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change.
Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix.
Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change.
Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them.
Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.

&lt;p&gt;&lt;strong&gt;Purpose:&lt;/strong&gt; Condition-based maintenance requires an accurate detection of unknown yet-to-have-occurred anomalies and the establishment of anomaly detection procedure for sensor data is urgently needed. Sensor data are noisy, and a conventional analysis cannot always be conducted appropriately. An anomaly detection procedure for noisy data was therefore developed.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Methodology/Approach:&lt;/strong&gt; In a conventional Mahalanobis–Taguchi method, appropriate anomaly detection is difficult with noisy data. Herein, the following is applied: 1) estimation of a statistical model considering noise, 2) its application to anomaly detection, and 3) development of a corresponding analysis framework.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Findings:&lt;/strong&gt; Engineers can conduct anomaly detection through the measurement and accumulation, analysis, and feedback of data. Especially, the two-step estimation of the statistical model in the analysis stage helps because it bridges technical knowledge and advanced anomaly detection.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Research Limitation/implication:&lt;/strong&gt; A novel data-utilisation design regarding the acquired quality is provided. Sensor-collected big data are generally noisy. By contrast, data targeted through conventional statistical quality control are small but the noise is controlled. Thus various findings for quality acquisition can be obtained. A framework for data analysis using big and small data is provided.&lt;/p&gt;&lt;strong&gt;Originality/Value of paper:&lt;/strong&gt; The proposed statistical anomaly detection procedure for noisy data will improve of the feasibility of new services such as condition-based maintenance of equipment using sensor data.

Many sports, such as gymnastics and figure skating, can be classified as scoring competitions or as interpersonal competitions, such as soccer and baseball. Moreover, round robin tournaments and elimination tournaments are used prominently in tournament systems to rank participants in interpersonal competitions. In a round robin tournament, establishing an order for participant play is simple, but each player must be matched against all other players. Consequently, much time is required to complete a round robin tournament. On the other hand, when using an elimination tournament, it is possible to rank the top competitors by playing fewer games, although it is difficult to identify where participants who lose games fit in the final order. To compensate for these disadvantages, cyclic designs and Swiss system tournaments have been proposed recently. In this study, we propose a new tournament system that utilizes a paired-competition methodology, which is based on the concepts of cyclic designs and Swiss system tournament. Our aim is to eliminate the disadvantages of round robin and elimination tournaments. To this end, we simulate the tournament system proposed, doing so under various conditions. We are able to demonstrate the superiority of this system over conventional tournament systems by comparing the accuracy of the estimated rank order of each tournament system, as well as the number of games required to complete each tournament system.

<p>To derive useful information from complicated data, many hybrid modeling strategies that combine nonparametric and parametric methods have been proposed. In this study, we propose a new hybrid modeling strategy that combines the random forest and the x-means methods using linear regression analysis. This strategy is referred to as XR regression.This study has three purposes: to improve the performance of a strategy of hybrid modeling using the random forest method, to determine an optimal class automatically using the x-means method, and to compare the prediction accuracy of this method with that of other existing methods.To determine the characteristics of XR regression, we compare its prediction accuracy with that of the existing methods using Monte Carlo simulations.The simulation results show that XR regression has a high performance in any situation, especially in data sets that include interaction effects.</p>

<p></p><p>High-dimensional data sets have been used extensively in recent years. However, their use is computationally expensive, and model features are difficult to capture. Thus, it is necessary to construct a simple and appropriate model. The least absolute shrinkage and selection operator (Lasso) can estimate several regression coefficients as exactly zero, making it possible to estimate a model and select variables at the same time. However, several problems exist. The decision procedure for the tuning parameter, which is the coefficient of the penalty term, is not established, and it is difficult to determine the value of the estimated model.</p><p>In this paper, we consider a model evaluation method and a selection method for the tuning parameter. We investigate selection methods for the most appropriate tuning parameter and model evaluation methods using the model evaluation indexes RSS, AIC, BIC, and Mallows's Cp. Let several regression coefficients be zero and vary the number of zeroes. Then, we observe the performances of the evaluation indexes. Furthermore, we observe their performances when the values of the regression coefficients are close to zero and confirm them by simulation.</p>

<p></p><p>Panel data are a sort of multi-dimensional time-series data that consist of several sets of the observation unit as an identical community over time. Panel data include more information than time-series data or cross-section data. Using panel data, we are able to estimate more accurately, increase degrees of freedom, and avoid multi-collinearity.</p><p></p><p>In this paper, we consider a change point problem in panel data. Detection methods for change points in panel data have not been extensively proposed. This paper proposes a detection method for change points in panel data using the Mahalanobis–Taguchi (MT) method (Taguchi (2002)). As the MT method does not assume panel data or time-series data, we must extend the theory of the MT method. Furthermore, when the sample size is small, it is difficult to estimate the covariance matrix precisely (Miyakawa et al. (2007)). In this paper, the MT method is extended using Bayesian inference to resolve the above-mentioned difficulties. Conducting Monte Carlo simulations and a real data analysis, we show that our proposed method is useful.</p>

The intent of robust parameter design is to make a system insensitive to noise factors by choosing optimum levels for the controllable factors. This is conducted by finding the interactions between noise factors and control factors. In general, it is necessary to control the levels of noise factors; however, there are some that cannot be controlled. On the other hand, there are some which can be observed as covariates.<br/>Hirano and Miyakawa (2007) proposed a method based on linear regression to analyze the interactions between a single noise factor and the control factors, when the noise factor is observed as a covariate.<br/>This paper discusses robust parameter designs when multiple noise factors are observed as covariates. We propose two extensions of the Hirano and Miyakawa method: extended methods 1 and 2. We perform Monte Carlo simulations under several data models to estimate the accuracy of these methods. It is shown that the extended methods are able to analyze the interactions between each of the control factors and the noise factors, when multiple noise factors are observed as covariates. Since the noise factors are combined in extended method 1, it cannot detect which noise factor influences the control factors. On the other hand, extended method 2 distinguishes between noise factors, and thus it can detect the interactions between the control factors and each of the noise factors.

MT（Mahalanobis-Taguchi）法は，異常検知やパターン認識の問題を扱う基本的な多変量解析法である．しかし，十分なサンプル数が確保できなければ，MT法は大きな予測バイアスをもってしまう．そのため，小標本データのようなサンプル数が不足するデータの場合，良好な判定結果が得られるとは限らない．そこで本研究では，まず既存の対策方法には，未知データ検出力の問題があることを示す．次に，小標本データの場合に有効な新たな解析プロセスを2つ提案する．最後に，実データ解析およびシミュレーションの結果をもとに，提案プロセスにおける，多重共線性が発生した場合の適用方法とデータパターンに応じた使い分けについて考察する．

Taguchi's T-method is a part of the Mahalanobis-Taguchi (MT) system. The T-method is a technique for making predictions, and it has applications in various fields, including economic forecasting and predicting demand. The T-method can be summarized as follows: Prepare many weak learners that each predict one output value. Then, use the signal to noise ratio (S/N) to perform a weighted integration of these predictions and derive an overall estimate.<br/>If the accuracies of each of the individual estimates are increased, the accuracy of the integrated estimate will be increased. Therefore, in this paper, we propose a way to improve the accuracies of the individual estimates. Our method uses the concept of a generalized inverse regression estimator for each of the individual estimators.<br/>We use Monte Carlo simulations under various conditions to compare the prediction accuracies of the proposed method and that of the existing method. In many cases, our results show that the prediction accuracy of the proposal method is better than that of the original T-method. In particular, when the number of samples is small, the prediction accuracy of the proposal method is much better than that of the original T-method. Thus, we conclude that our proposed method is effective.

In sports, a wide variety of match systems have been adopted to rank the participants. Well-known systems include the tournament system and the league match system. In order to overcome faults in these systems, a system known as cyclic design has been proposed.<br/>A cyclic design is able to rank all of the participants and requires only one more game than those required by a tournament. We let the size of the block be 2, and we use an experimental design that compares v treatments. By calculating the observational equations that are derived from the design of the experiments, estimators (for example, estimations of an individuals strength) can be obtained.<br/>In this paper, we validated a cyclic design with an actual dataset. We analyzed all combinations of the actual data, and we showed that there were discrepancies between the estimated ranks and the real ranks. In a cyclic design, the accuracy of the estimated rankings (AER) depends on the initial design, and so it was necessary to improve this.<br/>We conducted a Monte Carlo simulation to compare the AER of a cyclic design to those of two common competitors: a tournament and a league match. In addition, we proposed a cyclic design combined with the Swiss system to compare the AER to other competitors. We found that the estimated ranking produced by the proposed cyclic design is more accurate than that produced by a tournament. Furthermore, we conducted a Monte Carlo simulation in which we used the similar model by adding interaction effects. We found that the AER of all methods were reduced compared to the previous results. In particular, interaction effects have a strong influence on the results of the cyclic designs. To improve performance, we proposed a further extended cyclic design that is robust to the interaction effects. We performed a Monte Carlo simulation that confirmed that the extended cyclic design is superior to the original cyclic design.

This article discusses the asymptotic theory of Taguchi's natural estimators of the signal to noise ratio (SNR) for dynamic robust parameter design. Three asymptotic properties are shown. First, two natural estimators of the population SNR are asymptotically equivalent. Second, both of these estimators are consistent. Finally, both of these estimators are asymptotically normally distributed.

タグチのRT法は,観測された個体の変数がすべて同一次元であるという仮定のもとで設計されている.そのため,同一次元でない連続量データに適用する場合,適切な分析ができるとは限らない.これはRT法の応用上,大きな課題となる.そこで,本論文では,RT法を同一次元でない連続量データに適用するための新たな方法を提示する.そして,未だ十分な議論がなされていない他の適用方法と合わせて,どの適用方法が有力となるのか検証する.まず,KDDCup99データの解析によって,すべての適用方法の性能を評価する.次に,良好な評価を得た適用方法の特徴を,シミュレーションによって詳細に比較・分析する.その結果,新たな適用方法は,KDDCup99データの解析で高い性能を示した.そして,他の適用方法よりも合理的に変数を評価することや,変数間の相関構造を考慮した計算方式を導入することが解析に役立つことがわかった.新たな適用方法は,有力な適用方法の一つであり,それを用いることで,RT法は高次元データを対象とした異常検知などに対する効果的な手法となりうると結論付ける.

タグチのT法は,田口玄一が開発した一連のMTシステムの手法の1つである.T法は,異常値やパターンを検出するMT(Mahalanobis-Taguchi)システムの他の手法とは異なり,予測を目的とした手法として活用されている.適用されるデータのタイプは重回帰分析と同じ場合が多いため,事例研究を通して,T法と重回帰分析との比較が検討されてきた.本稿では,まずT法の特徴を検討する.次に,T法に改良を加えた2つの方法を考察する.さらに,様々なモデルのもとでシミュレーションを用いて予測精度を計算することにより,T法,T法に対する2つの改良手法,重回帰分析の優劣の傾向と程度を検討する.その結果,改良手法はT法よりもほとんどいつも精度がよく,サンプル数が説明変数の個数と比較して十分に大きくない場合には重回帰分析よりも精度がよいことがわかった.

This paper discusses the principles of experimental design proposed by R.A. Fisher. They are consisted of three principles which are replication, randomization and local control. This paper investigates the book "The Design of Experiments" written by R.A. Fisher in order to grasp what he considered and how he intended to describe these principles.

工程能力指数は製造業の品質管理活動で頻繁に用いられている指標である.<br>本稿では,母集団分布として正規分布を想定した場合の4つの基本的な工程能力指数C_p,C_pL,C_pU,C_pKの自然な点推定量の改良を検討する.<br>2乗損失関数を用いた統計的決定理論の枠組みにおいて,Nagata(1995)は,C_pの自然な推定量がその定数倍で一様に改良できることを示し,改良度を数値計算している.また,数値計算により,C_pKの自然な推定量がその定数倍した推定量では一様に改良できないことを考察している.<br>本稿では,C_pL;とC_pUの自然な推定量がその定数倍により一様に改良できることを示し,改良度を数値的に示す.さらに,サンプルサイズが7以上のとき,C_pKの自然な推定量がその定数倍した推定量では一様に改良できないことを数学的に示す.

MTシステム(マハラノビス・タグチ・システム)の様々な発展形の中の1つとしてRT法(Recognition Taguchi System)がある.RT法は,MTシステムの中で一番新しい方法であるため,数理的な性質や適用上の注意点についてほとんど議論されていない.RT法は,計算の簡便さとアイデアに満ちた魅力的な方法のように見えるが,連続型のデータへの適用にあたっては注意が必要である.<BR> 本論文では次の3点を議論する.(1)RT法を適用するには各項目の単位が同じ,ないしは各項目が無次元数でなければならない.そうでないなら,各項目の無次元化を行う必要がある.(2)RT法で用いられる距離には単位空間の中心位置で大きめの値を取り,中心から離れたところでゼロになるという不適切な性質がある.このことは,新たに採取したデータが単位空間の中心に近い場合,それを単位空間外と判定する可能性が高くなり,ミスリーディングである.(3)(2)で述べた不適切な性質を改良する距離を提案する.この距離は,単位空間の中心位置でゼロとなり,中心位置から離れるに従って比例的に増加する.

It is discussed how to educate the practically useful SQC (statistical quality control). When a company holds an in-house training of SQC, there possibly exist several problems, which are the problem of selecting trainees, the problem of preparing adequate homework and examinations, the problem of engaging practical applications, the problem of evaluating the results and the problem of promoting a thoughtful secretary. In order to overcome these problems, a passionate support by the top is necessary and the existence of stars on SQC in the company is desired. As a guidepost for training a star, one particular topic is introduced, which is the way that one interprets the partial regression coefficients in regression equations. Furthermore, several topics which should be considered to use both the Taguchi methods and the SQC effectively are presented.

項目間に線形制約がある場合ないしはサンプル数nが項目数p以下の場合には多重共線性が発生し,マハラノビスの距離を求めることができない.MTシステムの多重共線性対策として宮川・永田(「品質」,Vo1.33)は2種類の距離の併用を提案した.本稿では,p≧nの場合には,正常空間の初期データに対する第1種の距離がすべて同じ値となることを示す.その結果,距離の標本分布に基づいて閾値を決めることができなくなる.本稿で考える多重共線性は,項目間に線形制約式が成り立つ場合の多重共線性と比較して本質的に困難な状況であり,情報を捨て去る必要がある.そのときの情報の捨て方の可能性を今後の課題として整理する.また,p=n-1の場合には,多重共線性は生じていないにもかかわらず,正常空間の初期データに対するマハラノビスの距離がすべて同じ値となることも示す.

In this paper the optimality of the Stein type confidence interval of the disturbance variance among the class of pre-test confidence interval after the pre-test for a linear hypothesis on coefficients is considered. The Stein type confidence interval is a member in the class with a critical value, say c. It is known that the Stein type confidence interval is the best in the subclass which consists of the pre-test confidence intervals with a smaller critical value than c. It is shown that an extension of the optimality to a larger class is not possible.

This paper considers the interval estimation of the disturbance variance in a linear regression model with multivariate Student-t errors. The distribution function of the Stein type estimator under multivariate Student-t errors is derived, and the coverage probability of the Stein type confidence interval which is constructed under the normality assumption is numerically calculated under the multivariate Student-t distribution. It is shown that the coverage probability of the Stein type confidence interval is sometimes much smaller than the nominal level, and that it is larger than that of the usual confidence interval in almost all cases. For the case when it is known that errors have a multivariate Student-t distribution, sufficient conditions under which the Stein type confidence interval improves on the usual confidence interval are given, and the coverage probability of the Stein type confidence interval is numerically evaluated.

In this paper the interval estimation of the disturbance variance in a linear regression model is discussed from several view points. Firstly, a brief summary ofthe Stein type point estimation theory and the Stein type interval estimation theory is given. Then, the relationship between the improvement on the point estimation and the improvement on the interval estimation is discussed. It is shown that substituting the Stein type estimator for the usual estimator in the confidence interval leads to the improvement on the interval estimation. Secondly, the Neyman accuracy of the Stein type confidence intervalis considered. The Neyman accuracy is a measure related to the unbiasedness of a confidence interval. It is shown that the Stein type confidence interval is not unbiased. Thirdly, the Wolfowitz accuracy of the Stein type confidence interval is considered. The Wolfowitz accuracy is related to the closeness of the endpoints to. the true parameter. The sufficient condition for the Stein type confidence interval to improve on the usual confidence interval is derived. Finally, the Stein type confidence interval is discussed under the multivariate Student-t distribution. It is shown that so far as the coverage probability and the multivariate Student-t distributions are concerned, the Stein type confidence interval is not robust against nonnormality, but that the superiority over the usual confidence interval still holds against nonnormality. Furthermore, for the case when it is known that error terms have a multivariate Student-t distribution, a Stein type confidence interval which improves on the usual confidence interval is presented.

This paper considers the optimality of the Stein-type estimator of the disturbance variance among the class of pre-test estimators after the pre-test for a linear hypothesis on coefficients. The Stein-type estimator is a member in this class with a critical value, say cs. It is known that the Stein-type estimator is the best in the subclass which consists of the pre-test estimators with smaller critical values than cs. It is analytically shown that an extension of the optimality to a larger class is not possible.

In this paper we consider the Neyman accuracy and the Wolfowitz accuracy of the Stein type improved confidence interval I-s* for the disturbance variance in a linear regression model. The Neyman accuracy is a measure related to the unbiasedness of a confidence interval, and the Wolfowitz accuracy is related to the closeness of the endpoints to the true parameter. We show that I-s* is not unbiased and give some numerical results for the Neyman accuracy. As for the Wolfowitz accuracy we derive the sufficient condition for I-s* to improve on the usual confidence interval under this criterion and show numerically that a large degree of improvement can be obtainted.

This paper considers a sequential procedure for setting a fixed-width confidence interval for the mean of a gamma distribution. Instead of a coverage probability, an average coverage probability is considered and its asymptotic expansion is obtained, from which it turns out that the interval with bias correction performs better than that with no bias correction.

In this paper the relationship between the improvement on the point estimation and the improvement on the interval estimation for the disturbance variance in a linear regression model is discussed. It is shown that substituting the Stein-type estimator for the usual estimator in the confidence interval leads to the improvement on the interval estimation. The equal-tailed and the shortest unbiased intervals are dealt with. Some appealing relationship is also found in the unbiased case.

Normal approximation to the distribution of the estimated process capability index _??__pk is discussed. The direct normal approximation to _??__pk and an alternative approach are compared in terms of skewness and kurtosis. It is shown that the latter approach improves on the former one.

Let x(1), x(2), …, x(n) be the order statistics of a sample of size n from the exponential distribution with an unknown location-scale parameter (μ,σ). It is shown that usual confidence intervals for σ based on the only statistic Σ^^^n__<i=1>(x(i)-x(1)) can be improved by using the statistic x(1). Further the degree of the improvement is computed numerically.

The process capability indices (CPI) are often used to obtain the information about the production process capability and there are some criteria in determining it, the criteria which are designed for the true values of CPI's. However, since the true values of CPI's are unknown in practice, they are estimated from several data. So the criteria might not be applied to these (point-) estimated values. Confidence intervals for CPI's should be constructed and these results should be taken into consideration. In this paper some useful and practical methods for the interval estimation are given.

1元配置モデルで対比較を行う多重比較の手法は古くから数多く提案されている.それらの検出力の相互比較は標本サイズの等しい場合についてEinot and Gabriel(1975)やRamsey(1978)などで行われているが,取り上げられた検出力の種類や比較対象の面でまだまだ不十分である.本稿では新しい検出力を提案し,標本サイズがアンバランスの場合も含めてより多角的な比較を行うとともに,まだ比較されたことのない手法との比較を試みる.比較を行った手法はTukeyの方法(Tukey-Kramerの方法),Tukey-Welschの方法,Peritzの方法,Holland-Copenhaverの方法である.