We consider the variable selection problem in the nonlinear discriminant procedure using local likelihood. The local likelihood method is an effective technique for analyzing data with complex structure,and various bandwidth selection methods have been suggested in recent years. Variable selection in a nonlinear model,however, is more complex than bandwidth selection,since the optimal bandwidth depends on the combination of the variables. We propose a technique for variable selection using generalized information criteria in logistic discrimination based on local likelihood. We derive the logistic discrimination method with a sample covariance matrix to account for the correlation of the variables. Real data examples are given to examine the effectiveness of our technique.
{"title":"VARIABLE SELECTION IN LOGISTIC DISCRIMINATION BASED ON LOCAL LIKELIHOOD","authors":"Yoshisuke Nonaka, S. Konishi","doi":"10.14490/JJSS.38.431","DOIUrl":"https://doi.org/10.14490/JJSS.38.431","url":null,"abstract":"We consider the variable selection problem in the nonlinear discriminant procedure using local likelihood. The local likelihood method is an effective technique for analyzing data with complex structure,and various bandwidth selection methods have been suggested in recent years. Variable selection in a nonlinear model,however, is more complex than bandwidth selection,since the optimal bandwidth depends on the combination of the variables. We propose a technique for variable selection using generalized information criteria in logistic discrimination based on local likelihood. We derive the logistic discrimination method with a sample covariance matrix to account for the correlation of the variables. Real data examples are given to examine the effectiveness of our technique.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128171914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The (arbitrary) higher order asymptotic expansion for posterior distributions of a single parameter is derived by using posterior modes, and its validity is shown. An asymptotic expansion for the Bayes risk with squared error loss of a posterior mode is derived.
{"title":"HIGHER ORDER EXPANSIONS FOR POSTERIOR DISTRIBUTIONS USING POSTERIOR MODES","authors":"Y. Miyata","doi":"10.14490/JJSS.38.415","DOIUrl":"https://doi.org/10.14490/JJSS.38.415","url":null,"abstract":"The (arbitrary) higher order asymptotic expansion for posterior distributions of a single parameter is derived by using posterior modes, and its validity is shown. An asymptotic expansion for the Bayes risk with squared error loss of a posterior mode is derived.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114397978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump occurred from finite samples. The paper includes a discussion about the validity of the procedure.
{"title":"A PRACTICAL INFERENCE FOR DISCRETELY OBSERVED JUMP-DIFFUSIONS FROM FINITE SAMPLES","authors":"Y. Shimizu","doi":"10.14490/JJSS.38.391","DOIUrl":"https://doi.org/10.14490/JJSS.38.391","url":null,"abstract":"In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump occurred from finite samples. The paper includes a discussion about the validity of the procedure.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"187 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131711606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider smoothed version of the empirical distribution functions from the finite population and the asymptotic behavior of the statistical functionals defined on the class of smoothed empirical distribution functions. Main parts of our results correspond to those of Fernholz (1991, 1993) in I.I.D. case.
{"title":"Smoothed Versions of Statistical Functionals from a Finite Population","authors":"Hitoshi Motoyama, Hajime Takahashi","doi":"10.14490/JJSS.38.475","DOIUrl":"https://doi.org/10.14490/JJSS.38.475","url":null,"abstract":"We consider smoothed version of the empirical distribution functions from the finite population and the asymptotic behavior of the statistical functionals defined on the class of smoothed empirical distribution functions. Main parts of our results correspond to those of Fernholz (1991, 1993) in I.I.D. case.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"438 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123573497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An estimator of the number of components of a finite mixture of k-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of a k-dimensional independent random sample. Some properties of the estimator are given. Some simulation results also are given for the case of finite mixtures of two-dimensional normal distributions.
{"title":"An Estimator of the Number of Components of a Finite Mixture of Multivariate Distributions","authors":"J. Henna","doi":"10.14490/JJSS.38.379","DOIUrl":"https://doi.org/10.14490/JJSS.38.379","url":null,"abstract":"An estimator of the number of components of a finite mixture of k-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of a k-dimensional independent random sample. Some properties of the estimator are given. Some simulation results also are given for the case of finite mixtures of two-dimensional normal distributions.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134443100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We attempt to estimate a state space model of investment and borrowing in a Bayesian framework, and to extract the unobservable agency costs of Japanese firms, which we differentiate by firm size.Our estimates suggest that agency cost exhibited a declining trend in the late 1980s, which changed to an increasing trend in the 1990s. We pinned down the driving force of fluctuations in agency cost as the market value of land.Furthermore, we found that the investment and borrowing behavior of small firms was very much affected by their agency costs in the late 1980s and early 1990s. Our evidence suggests that imperfections in the capital market were important for small firms in Japan.
{"title":"DOES THE AGENCY COST MODEL EXPLAIN BUSINESS FLUCTUATIONS IN JAPAN? : A BAYESIAN APPROACH TO ESTIMATE AGENCY COST FOR FIRMS CLASSIFIED BY SIZE","authors":"K. Ogawa, Hirokuni Iiboshi","doi":"10.14490/JJSS.38.349","DOIUrl":"https://doi.org/10.14490/JJSS.38.349","url":null,"abstract":"We attempt to estimate a state space model of investment and borrowing in a Bayesian framework, and to extract the unobservable agency costs of Japanese firms, which we differentiate by firm size.Our estimates suggest that agency cost exhibited a declining trend in the late 1980s, which changed to an increasing trend in the 1990s. We pinned down the driving force of fluctuations in agency cost as the market value of land.Furthermore, we found that the investment and borrowing behavior of small firms was very much affected by their agency costs in the late 1980s and early 1990s. Our evidence suggests that imperfections in the capital market were important for small firms in Japan.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125340039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this article is to give an overview of the developments in the theory of the asymptotic expansion for stochastic processes of continuous time. Today we know two typical methods of asymptotic expansion: the martingale approach and the mixing approach. These methods are complementary to each other. The martingale approach was found first and applied to derive an asymptotic expansion for ergodic diffusion processes. However, if the diffusion process satisfies a sufficiently nice mixing condition, then the mixing approach is more effective. On the other hand, the martingale approach is still useful when the higher-order terms do not obey an asymptotic normal law, which makes it impossible to apply the mixing approach. Such examples are seen in a stochastic regression model with a long memory explanatory variable, and in estimation of a volatility parameter over a finite time interval. In the latter example, the data is strongly time dependent, so that it requires a global estimate of the smoothness of random variables. In this sense, the martingale approach is also called the global approach. Contrarily, the mixing approach is called the local approach since the regularity often comes from a local (in time) estimate of the characteristic function. We will focus our attention on the mixing approach in this article. In Section 2, we recall a stochastic process having the “� -Markovian” structure as an underlying stochastic process. The � -Markov model written in continuous time may seem to be complicated, however it has an advantage because nonlinear (Markovian) time series models are included in the present model by natural embedding. Section 3 gives an illustrative application. We demonstrate an ap
{"title":"ASYMPTOTIC EXPANSION FOR STOCHASTIC PROCESSES: AN OVERVIEW AND EXAMPLES","authors":"Yuji Sakamoto, N. Yoshida","doi":"10.14490/JJSS.38.173","DOIUrl":"https://doi.org/10.14490/JJSS.38.173","url":null,"abstract":"The aim of this article is to give an overview of the developments in the theory of the asymptotic expansion for stochastic processes of continuous time. Today we know two typical methods of asymptotic expansion: the martingale approach and the mixing approach. These methods are complementary to each other. The martingale approach was found first and applied to derive an asymptotic expansion for ergodic diffusion processes. However, if the diffusion process satisfies a sufficiently nice mixing condition, then the mixing approach is more effective. On the other hand, the martingale approach is still useful when the higher-order terms do not obey an asymptotic normal law, which makes it impossible to apply the mixing approach. Such examples are seen in a stochastic regression model with a long memory explanatory variable, and in estimation of a volatility parameter over a finite time interval. In the latter example, the data is strongly time dependent, so that it requires a global estimate of the smoothness of random variables. In this sense, the martingale approach is also called the global approach. Contrarily, the mixing approach is called the local approach since the regularity often comes from a local (in time) estimate of the characteristic function. We will focus our attention on the mixing approach in this article. In Section 2, we recall a stochastic process having the “� -Markovian” structure as an underlying stochastic process. The � -Markov model written in continuous time may seem to be complicated, however it has an advantage because nonlinear (Markovian) time series models are included in the present model by natural embedding. Section 3 gives an illustrative application. We demonstrate an ap","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124800129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with nonstationary autoregressive (AR) models with complex roots on the unit circle. We examine the asymptotic properties of the least squares estimators (LSEs) in the model. We also extend the model to the case where the error term follows a stationary linear process. We show that the limiting distribution of the LSE of the unit root parameter has a property comparable to that of the LSE in the standard nonstationary seasonal model with period two. Percent points and moments of the limiting distribution are computed by numerical integration.
{"title":"Analysis of Models with Complex Roots on the Unit Circle","authors":"Katsuto Tanaka","doi":"10.14490/JJSS.38.145","DOIUrl":"https://doi.org/10.14490/JJSS.38.145","url":null,"abstract":"This paper deals with nonstationary autoregressive (AR) models with complex roots on the unit circle. We examine the asymptotic properties of the least squares estimators (LSEs) in the model. We also extend the model to the case where the error term follows a stationary linear process. We show that the limiting distribution of the LSE of the unit root parameter has a property comparable to that of the LSE in the standard nonstationary seasonal model with period two. Percent points and moments of the limiting distribution are computed by numerical integration.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"223 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123241920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A general method for constructing pseudo-Gaussian tests—reducing to traditional Gaussian tests under Gaussian densities but remaining valid under nonGaussian ones—is proposed. This method provides a solution to several open problems in classical multivariate analysis. One of them is the test of the homogeneity of covariance matrices, an assumption that plays a crucial role in multivariate analysis of variance, under elliptical, and possibly heterokurtic densities with finite fourth-order moments.
{"title":"A General Method for Constructing Pseudo-Gaussian Tests","authors":"M. Hallin, D. Paindaveine","doi":"10.14490/JJSS.38.27","DOIUrl":"https://doi.org/10.14490/JJSS.38.27","url":null,"abstract":"A general method for constructing pseudo-Gaussian tests—reducing to traditional Gaussian tests under Gaussian densities but remaining valid under nonGaussian ones—is proposed. This method provides a solution to several open problems in classical multivariate analysis. One of them is the test of the homogeneity of covariance matrices, an assumption that plays a crucial role in multivariate analysis of variance, under elliptical, and possibly heterokurtic densities with finite fourth-order moments.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127653331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article analyses the relationship between unobserved component trend-cycle models and the Hodrick-Prescott filter. Consideration is given to the consequences of using an inappropriate smoothing constant and the effect of changing the observation interval.
{"title":"TREND ESTIMATION AND THE HODRICK-PRESCOTT FILTER","authors":"A. Harvey, T. Trimbur","doi":"10.14490/JJSS.38.41","DOIUrl":"https://doi.org/10.14490/JJSS.38.41","url":null,"abstract":"The article analyses the relationship between unobserved component trend-cycle models and the Hodrick-Prescott filter. Consideration is given to the consequences of using an inappropriate smoothing constant and the effect of changing the observation interval.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122788704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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