A pilot Monte Carlo study of two sequential estimation procedures based on generalized U-statistics

Recently two sequential estimation procedures based on generalized U-statistics have appeared in the statistical literature [Williams and Sen (1973, 1974)]. One of these procedures concerns the multi-sample problem of estimating a vector of parameters when the total sample size is fixed. The other procedure concerns the multi-sample problem of constructing a confidence ellipsoid of bounded maximum width for a vector of parameters. To supplement the asymptotic theory discussed in these earlier papers, a Monte Carlo study investigating the efficiency of these procedures for moderate sample sizes would be useful. This paper describes a preliminary Monte Carlo study utilizing a small number of replications and performed to provide information for the design of a more extensive study.     

On the construction of nonparametric density function estimators using the bootstrap

The derivation of a new class of nonparametric density function estimators, the so-called bootstrap functional estimators (BFE's), is given. These estimators are shown to be strongly consistent under fairly nonrestrictive conditions. Some small-sample properties are discussed and a number of graphs are presented.     

A test for the variance residual life

In this paper we develop a test based on the empirical distribution function for the alternative representing 'decreasing variance residual life1 property. The test is consistent with asymptotically normal test statistic and is shown to perform well in the Pitman's asymptotic relative efficiency sense.     

Consistency of jackknife estimators of the variances of simple quantiles

Let σ² be the asymptotic variance of the sample p-quantile (0<p<1). Consistency of the delete-d jackknife estimators of σ² with d being a fraction of n is proved under very weak conditions. Some other results, such as the asymptotic orders of the moments of the jackknife histograms and an analog of the generalized Helly's theorem, are also established.     

Nonlinear regression analysis for complex surveys 1

In a clustered finite population, it is assumed that a given function depending on an unknown parameter may be adopted to reveal the relationship among the variables of interest. The finite population parameter corresponding to this unknown parameter is defined as a solution of an estimating equation defined by a properly chosen population loss function. An estimation procedure that takes sample weights into account is considered. Use of this function in estimating the population mean per cluster is discussed. Large sample properties of estimators are investigated.     

Consistency of l 1 estimates in censored linear regression models

In this paper, the regression model with a nonnegativity constraint on the dependent variable is considered. Under weak conditions, L ₁ estimates of the regression coefficients are shown to be consistent.     

Information theoretic criterion approach to dimensionality reduction in multinomial logistic regression models. part i: theory

We discuss the issue of dimensionality reduction in multinomial logistic models as problems arising in variable selection, collapsibility of responses and linear restrictions in the parameter matrix. A method using the information theoretic criterion suggested by Bai, Krishnaiah and Zhao, a variation of Akaike information criterion, is used to estimate the rank of the parameter matrix. The same procedure is used for the selection of variables and collapsibility of response categories. The strong consistency of this procedure is established in all the problems.     

Amplitude modulated model for analyzing non-stationary speech signals

Recently amplitude modulated (AM) model in presence of additive white noise was used to analyze certain non-stationary speech data. It is observed that the assumption of white noise may not be proper in many cases. In this article, we consider the AM signal model in presence of stationary noise. We consider the least squares estimators and the estimators obtained by maximizing the Periodogram function. The two estimators are asymptotically equivalent. We study the theoretical properties of both estimators and observe their performances through numerical simulations. One speech data is analyzed and it is observed that the performance of the proposed estimators is quite satisfactory.     

Testing for markov process vs semi-markov process

Here we have obtained a non-parametric test for testing the null hypothesis H₀ that the given realization is from a Markov process against the alternative hypothesis H₁ that it is from a semi-Markov process with the transition rate monotone increasing (or decreasing). We have shown that the test criterion has normal distribution asymptotically, and the test is consistent and unbiased.     

A control in stratified sampling

A new expression of the variance of the units from a stratified finite population wit L strata, is obtained in funcions of the means L–1 strata, and in conseqeuence we obtained formulae which relates the mean of a stratum in a statistical study with the population mean and the ones of the remaining strate. As an application, we obtained a useful checking of the estimation consistency by stratified sampling in any precies survey