Shingo Shirahata

Integrated squared error of kernel-type estimator of distribution function

Let X1,...,Xn be a random sample drawn from distribution function F(x) with density function f(x) and suppose we want to estimate X(x). It is already shown that kernel estimator of F(x) is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error.

An extension of the ranked set sampling theory

Abstract This paper is concerned with ranked set sampling theory which is useful to estimate the population mean when the order of a sample of small size can be found without measurements or with rough methods. Consider n sets of elements each set having size m. All elements of each set are ranked but only one is selected and quantified. The average of the quantified elements is adopted as the estimator. In this paper we introduce the notion of selective probability which is a generalization of a notion from Yanagawa and Shirahata (1976). Uniformly optimal unbiased procedures are found for some (n,m). Furthermore, procedures which are unbiased for all distributions and are good for symmetric distributions are studied for (n,m) which do not allow uniformly optimal unbiased procedures.

Rank tests for the k-sample problem with restricted alternatives

An asymptotically maximin most powerful rank test among somewhere asymptotically most powerful linear rank tests with scores generating function cf> is derived for each of the simple order alternative, the simple loop alternative and the simple tree alternative in the k-sample problem. The comparisons of the tests obtained with the rank analogues of the Bartholomews xv tests are made in terms of local asymptotic relative efficiency. It is found that our tests are better than the rank analogues of the xk tests. Furthermore, the asymptotic equivalence of the ranking by the pooled sample to the ranking in pairs are discuss¬ed and the tests which are asymptotically equivalent to ours are given.

Nonparametric measures of intraclass correlation

Three nonparametric measures of intraclass correlation based on the notion of concordance are considered. Their unbiased estimators and nonparametric tests based on the estimators are studied and it is shown that an analogue of the Kendalls tau provides small variance estimator and relatively powerful test. Furthermore, the approximate variance of the estimator is given when the correlation is small in the normal model.

Estimate of variance of u-statistics

Let g(x1,… , xk) be a symmetric function with k arguments. Let U be a U-statistic based on a random sample of size n with kernel function g . In this paper, the problem of estimating var(U) is considered. Several estimators are compared by computer simulations and we conclude that two estimators, one is constructed as a U-statistic and the other is the bootstrap estimator, give good estimates for many U-statistics.

Asymptotic properties of kruskal-wallis test and friedman test in the analysis of variance models with random effects

In this paper, asymptotic properties of the Kruskal-Wallis test in the one-way analysis of variance model and that of the Friedman test in the two-way classification model are investigated under alternatives when the treatment effects are random. It is shown that the asymptotic distribution of each statistic is the same as a mixture of central chi-squared variables. Asymptotic comparisons of the tests with respect to their parametric competitors are also performed

A nonparametric measure of interclass correlation

A nonparametric measure of interclass correlation is considered and its unbiased estimator and a test based on the estimator are studied. Hie measure is an analogue of the Kendalls measure of dependence. It is shown that the variance of the estimator is small and the information loss of the test based on the estimator is not serious relative to a standard parametric test in the sense of the Pitman asymptotic relative efficiency. Furthermore, the approximate variance of the estimator is given in the normal model.

A goodness of fit test based on some graphical representation when parameters are estimated

Abstract We consider a graphical representation of data and a goodness of fit test based on the representation when the family of hypothetical distributions includes unknown parameters. The graphical representation is given by a convex polygon which reflects the pattern of order statistics so that we can judge whether the null hypothesis is true or not by visual inspection. The area of our chart is adopted as the test statistic. Both the asymptotic and exact distributions of our test statistic cannot be derived and hence some computer simulations are performed in order to investigate the null distribution and the power properties.

Functional clustering of mouse ultrasonic vocalization data

Mouse ultrasonic vocalizations (USVs) are studied in many fields of science. However, various noise and varied USV patterns in observed signals make complete automatic analysis difficult. We improve several methods to reduce noise, detect USV calls and automatically cluster USV calls. After reduction of noise and detection of USV calls, we consider USV calls as functional data and characterize them as USV functions with B-spline basis functions. For discontinuous USV calls, breakpoints in the USV functions are defined using multiple knots in the construction of the B-spline basis functions, and a hierarchical method is used to cluster the USV functions by shape. We finally show the performance of the proposed methods with USV data recorded for laboratory mice.

Likelihood-based cross-validation score for selecting the smoothing parameter in maximum penalized likelihood estimation

Maximum penalized likelihood estimation is applied in non(semi)-para-metric regression problems, and enables us exploratory identification and diagnostics of nonlinear regression relationships. The smoothing parameter A controls trade-off between the smoothness and the goodness-of-fit of a function. The method of cross-validation is used for selecting A, but the generalized cross-validation, which is based on the squared error criterion, shows bad be¬havior in non-normal distribution and can not often select reasonable A. The purpose of this study is to propose a method which gives more suitable A and to evaluate the performance of it. A method of simple calculation for the delete-one estimates in the likeli¬hood-based cross-validation (LCV) score is described. A score of similar form to the Akaike information criterion (AIC) is also derived. The proposed scores are compared with the ones of standard procedures by using data sets in liter¬atures. Simulations are performed to compare the patterns of select...