Workshops

2010年4月23日（金 Friday） 11:00-12:00　※時間にご注意下さい。

Jinook Jeong (School of Economics, Yonsei University)

The Breusch-Godfrey's LM test is one of the most popular tests for autocorrelation. However, it has been shown that the LM test may be erroneous when there exist heteroskedastic errors in regression model. Some remedies recently have been proposed by Godfrey and Tremayne (2005) and Shim et al. (2006). This paper suggests wild-bootstrapped variance ratio test for autocorrelation in the presence of heteroskedasticity. We show through a Monte Carlo simulation that our wildbootstrapped VR test has better small sample properties and is robust to the structure of heteroskedasticity.

2010年4月30日（金 Friday） 4:50-6:10

Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies)

This paper develops methods of Bayesian inference in a cointegrating panel data model. This model involves each cross-sectional unit having a vector error correction representation. It is flexible in the sense that different cross-sectional units can have different cointegration ranks and cointegration spaces. Furthermore, the parameters which characterize short-run dynamics and deter-ministic components are allowed to vary over cross-sectional units. In addition to a noninformative prior, we introduce an informative prior which allows for information about the likely location of the cointegration space and about the degree of similarity in coefficients in different cross sectional units. A collapsed Gibbs sampling algorithm is developed which allows for efficient posterior inference. Our methods are illustrated using real and artificial data.

特別講義
2010年5月19日（水 Wednesday） 1:50-4:30
2010年5月20日(木 Thursday）1:10-3:50
※開始時間が異なりますのでご注意下さい。

北村祐一 (Yale University)

This short lecture deals with empirical likelihood (EL) and other nonparametric maximum likelihood methods (NPMLE). EL and NPMLE is a direct application of the maximum likelihood estimation (MLE) method to nonparametric and semiparametric models. We focus on the rapidly growing literature on EL, though other applications of NPMLE will be also discussed. Applications to be covered include (conditional) moment restriction models, semiparametric discrete choice models, stratified/biased samples, mixtures, and missing data models.

2010年5月21日（金 Friday） 4:50-6:10

柿沢佳秀 (北海道大学大学院経済学研究科)

ベルンシュタイン確率密度推定法はVitale(1975)に提案され、境界バイアスがない 利点をもち、種々の漸近的性質が調べられてきた。報告者の２論文(2004,2006)、及び、 それらの１つの一般化について議論する。

2010年5月28日（金 Friday） 4:50-6:10

古澄英男 (神戸大学大学院経営学研究科)

Ramberg and Schmeiser (1974) によって提案された一般化ラムダ分布は，さまざまな 尖度や歪度を持つ柔軟な確率分布である．しかし，確率密度関数を明示的に導出 することができないため，ベイズ推定を行うことが困難である．そこで本研究で は，Approximate Bayesian computationを利用した推定方法を提案する．

2010年6月18日（金 Friday） 4:50-6:10

奥井　亮 (京都大学経済研究所)

This paper proposes asymptotically unbiased estimators of autocovariances and autocorrelations for panel data with both individual and time effects. We show that the conventional autocovariance estimators suffer from the bias caused by the elimination of individual and time effects. The bias related to individual effects is proportional to the long-run variance, and that related to time effects is proportional to the value of the estimated autocovariance. On the other hand, the elimination of time effects does not cause a bias for the conventional autocorrelation estimators while the elimination of individual effects does. We develop methods to estimate the long-run variance and propose bias- corrected estimators based on the proposed long-run variance estimator. The theoretical results are given by employing double asymptotics under which both the number of observations and the length of the time series tend to infinity. Monte Carlo simulations show that the asymptotic theory provides a good approximation to the actual bias and that the proposed bias correction works.

2010年6月25日（金 Friday） 11:00-12:00
※時間にご注意下さい。

真木 和彦 （Department of Mathematics, Wayne State University）

Consistency and Asymptotic normality of quasi-maximum likelihood estimators (QMLEs) for fractionally integrated asymmetric power ARCH (FIAPARCH) process are proved. The moment conditions are assumed only for standardized errors. We show the properties for a wide range of QMLEs by using an argument similar to Berkes and Horvath (2004).

2010年6月25日（金 Friday） 4:50-6:10

高橋倫也 (神戸大学大学院海事科学研究科)

極値データのトレンドとしては種々のモノが存在すると考えられる。そこで、極値データの スムージングを行い、パラメトリックモデルによる解析結果と比較することを考 える。ここではスムージング法について説明し、年最大降水量の解析例について 紹介する。

2010年7月2日（金 Friday） 4:50-6:10

Omiros Papaspiliopoulos (Universitat Pompeu Fabra)

The statistical estimation of the unknown drift and diffusion coefficient of a diffusion process based on discrete-time data has long been identified as a challenging problem. We focus on the implementation of likelihood-based approaches, and we aim at providing a unifying framework for the wide range of data augmentation Monte Carlo schemes which have been proposed for this task. At the core of this methodology are different representations and simulation schemes for the diffusion bridge, i.e the process obtained by conditioning the diffusion process on its end-points.

2010年7月9日（金 Friday） 4:50-6:10

In-Kwon Yeo (Department of Statistics, Sookmyung Women's University)

Yeo and Johnson (2000) introduced a family of power transformations which is defined on whole real numbers. According to the definition of relative skewness by van Zwet(1964), Yeo-Johnson transformation reduces the skewness of the data. In this talk, I investigate two types of applications of Yeo-Johnson transformation to capture the asymmetry in volatility. One is that the GARCH model is applied to Yeo-Johnson transformed time series. In this application, the transformation and back-transformation approach is proposed to estimate the forecast interval on the original scale. This approach improves the coverage probability of the forecast interval and is used to compute a proper VaR(value at risk). Also I introduce the bootstrapping approach to reduce the bias of the forecast value obtained by the transformation and back-transformation approach. The other is asymmetric GARCH model via Yeo-Johnson transformation. In this application, we assume that the conditional variance equation can be described by a linear combination of quadratic forms of lagged Yeo-Johnson transformed shocks. The MCMC approach is employed to perform the inference of parameters in the model. In order to verify the validity of proposed approaches, KOSPI(Korea composite stock price index) and NIKKEI are analyzed.

2010年10月15日（金 Friday） 4:50-6:10

下津克巳（一橋大学）

This article analyzes the identifiability of k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components and the component distributions from the distribution function of the observed data. We reveal an important link between the number of variables (k), the number of values each variable can take, and the number of identifiable components. A lower bound on the number of components (M) is nonparametrically identifiable if k>=2, and the maximum identifiable number of components is determined by the number of different values each variable takes. When M is known, the mixing proportions and the component distributions are nonparametrically identified from matrices constructed from the distribution function of the data if (i) k>=3, (ii) two of k variables take at least M different values, and (iii) these matrices satisfy some rank and eigenvalue conditions. For the unknown M case, we propose an algorithm that possibly identifies M and the component distributions from data. We discuss a condition for nonparametric identification and its observable implications. In case M cannot be identified, we use our identification condition to develop a procedure that consistently estimates a lower bound on the number of components by estimating the rank of a matrix constructed from the distribution function of observed variables.

2010年10月29日（金 Friday） 4:50-6:10

江口真透（統計数理研究所）

Maximum likelihood has been established as the most popular method in statistics since R. Fisher gave the theoretical foundations in 1910's. If the model is correct, then maximum likelihood is supported by elegant properties including asymptotical consistency and efficiency. However, the excellent performance is broken down in the presence of model departure from distributional misspecification because of outlying, informative missing, hidden confounder and so forth. Such model uncertainty is frequently problematic in real data analysis. A new statistical method is proposed to have reasonable performance even under a situations with a substantial degree of model departure. For this we consider a class of entropy and divergence, called U-entropy and U-divergence which leads to another type of statistical method rather than maximum likelihood. In particular, the power entropy and divergence with the power index beta defines the statistical estimator which overperforms the maximum likelihood on a misspecified model. We discuss a unified framework such that U-entropy uniquely associates with the family of maximum entropy distributions, called U-model, in which the information geometric viewpoint is built with orthogonal foliation and minimax game. Finally we will discuss the reason why the maximum likelihood estimator can be improved by another estimation method on the misspec

2010年11月12日（金 Friday） 4:50-6:10

福水健次（統計数理研究所）

サポートベクターマシンの成功以来，正定値カーネル及び それの定める再生核ヒルベルト空間を用いたデータ解析の方法論が 発展している．この方法論では，データないしは確率変数を標準的 方法で高次元の関数空間（再生核ヒルベルト空間）に写像する ことによって，データの非線形性や高次統計量を取り出す． 再生核ヒルベルト空間の特殊な内積のおかげで，さまざまな古典的 データ解析手法を容易に非線形拡張することが可能であり，かつ， 計算量がサンプルサイズの行列計算に還元される点に長所がある． 　最近，再生核ヒルベルト空間に写像された確率変数の平均や分散 を用いると，分布の均一性や独立性といった，分布に関する ノンパラメトリックな統計的推論が可能となることが明らかとなり， このアイデアに基づく二標本検定や独立性検定などが提案されている． その際に重要となるは，ある種の正定値カーネルを用いると，再生核 ヒルベルト空間での平均がその確率変数の分布を一意に定めるという， 分布に対する特性的な性質である．この性質によって，分布に関する 推論の問題を再生核ヒルベルト空間上での平均に対する操作によって 解くことが可能となる． 　本講演では，特性的な正定値カーネルを用いたベイズ推論の新しい 方法論を述べる．そのために，ベイズルールを正定値カーネルの言葉 で表現する．すなわち，事後確率の再生核ヒルベルト空間における 平均を，事前確率と条件付き確率の再生核ヒルベルト空間における 表現を用いて求める方法を導く．この方法では，事前確率 \pi(x)と 条件付き確率 p(y|x)に関する情報が，それぞれ \pi と p(x,y) に 従うサンプルによって与えられれば十分であり，事前確率や条件付き 確率の陽な式は必要でない点が，他のベイズ推論の方法と異なる． 事後確率の再生核ヒルベルト値平均は，x のサンプルの重み付き和 として与えられる．このカーネル版ベイズルールに基づいて， さまざまなベイズ推論の方法をノンパラメトリックに拡張することが 可能である．本講演では，ノンパラメトリックな隠れマルコフモデル に対する逐次的フィルタリングの例とその数値例を示す．

2010年11月26日（金 Friday） 12:10-13:10 ※臨時ワークショップ※
※時間と場所にご注意ください※

Sokbae Simon Lee（University College of London）

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of L_p-type functionals of kernel estimators. Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. Furthermore, the tests have nontrivial local power against a certain class of local alternatives converging to the null at the rate of n^-1/2. Some results from Monte Carlo simulations are presented.

2010年11月26日（金 Friday） 4:50-6:10

大津泰介（Yale University）

This paper develops a Bayes procedure for moment restriction models. A nonparametric prior is employed to carry out Bayesian analysis without imposing parametric distributional assumptions. An information theoretic projection is used to deal with problems that stem from possible overidentification. A semiparametric Bernstein-von Mises theorem is proved for the finite dimensional parameters. An algorithm based on Gibbs sampling to implement the procedure is discussed.

2010年12月17日（金 Friday） 4:50-6:10

川崎能典（統計数理研究所）

To increase the predictive accuracy of a discrete choice model, it is often helpful to introduce interactions terms in addition to main effect. However, a simple-minded generation of interactions suffers from combinatorial explosion, and the mixture of continuous and categorical variables even makes it difficult to define interaction itself. This paper starts with presenting a reasonable way to choose the promising interactions based on contingency table analysis. The proposed method is illustrated with an application to a medical data. In an application to credit scoring, we compare the performance of competing methods with other data mining tools such as CART-logit. If time allows, we will introduce a method to group explanatory variables in our framework.

2011年1月14日（金 Friday） 4:50-6:10 　※日程が変更いたしましたのでご注意下さい。

Edward Vytlacil (Yale University)

We consider the identification and estimation of latent-index, threshold crossing models of loan approval when the econometrician observes all information observed by the decision maker for the approved loans, but observes no information on the loans that were not approved. For example, in our application to mortgage lending, we have all information collected by the bank at the time of loan origination for all loans originated by the bank, so that the bank's decision to approve the loan is a deterministic function of covariates observed by the econometrician, while we have no information on loans that were not approved by the bank. Under smoothness conditions, we use the boundary of the support the covariates in the approved sample and whether the density of the covariates at this boundary is strictly positive to infer a level set for the approval process We then use that level set to identify and estimate the parameters of the loan approval process. We consider identification and estimation of both nonparametric and semiparametric models of loan approval. We apply our results to study the mortgage loan approval process for a major national bank, using a data set comprised of all information collected by the bank at the time of loan origination on all 721,767 loans funded by the bank between January 2004 and February 2008.

2011年2月4日（金 Friday） 3:30-4:40, 4:50-6:10

ミクロデータはしばしばセンシティブな情報を含み、これを保護するため のデータ変換を「匿名化」と呼ぶ。匿名化は官庁がミクロデータを提供するために 研究されてきたが、近年 この枠組みにとらわれず、計算機科学で多様な発展が見られる。そしてその一部は、官庁にとっても有益である。 本講演ではそのような発展を、統計学の匿名化理論の立場から概観する。 その上で、公的統計の匿名化実務を理論と対応させて説明する。

4:50-6:10　Dale J. Poirier (University of California, Irvine)