Covariate classification by post–stratification

The plug–in Anderson's covariate classification statistic is constructed on the basis of an initially unclassified training sample by means of posty–stratification. The asymptotic efficiency relative to the discriminant based on an initially classified training sample is evaluated for the case where a covariate is present. Effect of post–stratification is examined.     

Bayesian credibility limits for small finite population proportions:stratified and cluster sampling

Bayes credibility limits for small proportions from stratified and fixed size cluster samples are discussed. Ericson’s (JRSS B (1969)) Beta Binomial and Dirichlet-Multinomial priors are used. Approximate limits that are appropriate for large samples and small proportions are derived in both cases. These allow asymptotic comparisons of the efficacy of stratified and cluster sampling relative to simple random sampling for estimating small proportions. Procedures for the selection of hyper parameters are also presented.     

A Bayesian Model for Markov Chains via Jeffrey's Prior

Abstract

This work deals with the problem of Bayesian estimation of the transition probabilities associated with multistate Markov chain. The model is based on the Jeffreys' noninformative prior. The Bayesian estimator is approximated by means of MCMC techniques. A numerical study by simulation is done in order to compare the Bayesian estimator with the maximum likelihood estimator.     

A Nonparametric Test for Deviation from Randomness with Applications to Stock Market Index Data

The proposed test detects deviations from randomness, without a priori distributional assumption, when observations are not independent and identically distributed (i.i.d.), which is suitable for our motivating stock market index data. Departures from i.i.d. are tested by subdividing data into subintervals and then using a conditional probability measure within intervals as a binomial test. This nonparametric test is designed to detect deviations of neighboring observations from randomness when the dataset consists of time series observations. Simulation results and a comparison with Lo and MacKinlay's (1988 Lo, A. W. and MacKinlay, A. C. 1988. Stock market prices do not follow random walks: Evidence from a simple specification test. The Review of Financial Studies, 1: 41–66. [Crossref], [Web of Science ®] , [Google Scholar]) variance ratio test showed that our proposed test is a competitive alternative.     

Accent on Teaching Materials: Notices and Reviews of Important Teaching Materials

This article examines the probabilities of outcomes from rolling dice with the dimension 1 × 1 × r for various values of r. Experiments were conducted by school students and university students. The results of the experiments are given and the probabilities examined using a generalized linear model. Notes are also made about the value of the experiment in teaching the groups of students.     

Bayesian Risk Ratio Analysis

The classical confidence interval approach has failed to find exact intervals, or even a consensus on the best approximate intervals, for the ratio of two binomial probabilities, the so-called risk ratio. The problem is reexamined from a Bayesian viewpoint, and a simple graphical presentation of the risk ratio assessment is given in such a way that sensitivity to the selected prior distribution can be readily examined.     

More Powerful Tests from Confidence Interval p Values

In this article the problem of comparing two independent binomial populations is considered. It is shown that the test based on the confidence interval p value of Berger and Boos often is uniformly more powerful than the standard unconditional test. This test also requires less computational time.     

Measure of departure from conditional marginal homogeneity for square contingency tables with ordered categories

For the analysis of square contingency tables with ordered categories, Tomizawa et al. (S. Tomizawa, N. Miyamoto, and N. Ashihara, Measure of departure from marginal homogeneity for square contingency tables having ordered categories, Behaviormetrika 30 (2003), pp. 173–193.) and Tahata et al. (K. Tahata, T. Iwashita, and S. Tomizawa, Measure of departure from symmetry of cumulative marginal probabilities for square contingency tables with ordered categories, SUT J. Math., 42 (2006), pp. 7–29.) considered the measures which represent the degree of departure from the marginal homogeneity (MH) model. The present paper proposes a measure that represents the degree of departure from the conditional MH, given that an observation will fall in one of the off-diagonal cells of the table. The measure proposed is expressed by using the Cressie–Read power-divergence or the Patil–Taillie diversity index, which is applied for the conditional cumulative marginal probabilities given that an observation will fall in one of the off-diagonal cells of the table. When the MH model does not hold, the measure is useful for seeing how far the conditional cumulative marginal probabilities are from those with an MH structure and for comparing the degree of departure from MH in several tables. Examples are given.