Nonparametric testing for simple regression under progressive censoring with stagering entry and random withdrawal

In the context of (multi-center) clinical trials and life testins problems, a general model incorporating both the staggering entry and random withdrawal and pertaining to a simple regression problem (including the two-sample location problem as a special case) is conceived, and, within this framework, a scheme allowing progressive censoring (continuous monitoring of experimentation from the beginning) is developed along with the proposal for and study of some nonparametric testing procedures, The proposed tests rest on the construction of certain two-dimensional time-parameter stochastic processes from a triangular array of progressively censored linear rank statistics and their weak convergence to appropriate Gaussian functions. Asymptotic properties of these procedures are studied. A computer program pertaining to the numerical computations and practical administrations of these testing procedures is also provided at the end.     

Invariance principles for jackknifing U-statistics for finite population sampling and some applications

For simple random sampling (without replacement) from a finite population, suitable stochastic processes are constructed from the entire sequence of jackknife estimators based on smooth functions of U-statistics and these are approximated (in distributions) by some Brownian bridge processes. Strong convergence of the Tukey estimator of the variance of a jackknife U-statistic has been interpreted suitably and established. Some applications of these results in sequential analysis relating to finite population sampling are also considered.     

Upper bounds for the variances of certain random variables

Jacobson (1969) proved that the variance of a unimodal distribution on the unit interval is bounded above by 1/9. This paper generalizes Jacobson's result by deriving sharp upper bounds for the variances of α-unimodal distributions and for the variances of S-shaped distributions.     

A bivariate signed rank test for two sample location problem

An affine-invariant signed rank test for the difference in location between two symmetric populations is proposed. The proposed test statistic is compared with Hotelling's T2 test statistic, Mardia's(1967)test statistic, Peters-Randles(1991) test statistic and Wilcoxon's rank sum test statistic using a Monte Carlo Study. It performs better than Mardia's test statistic under almost all populations considered. Under the bivariate normal distribution, it performs better than other test statistics compared for small differences in location between two populations except Hotelling's T2. It performs better than all statistics, including Hotelling's T , for sample size 15 when samples are drawn from Pearson type.     

A note on interpenetrating subsamples of unequal sizes drawn with and without replacement

In this article it is shown how one can gain in efficiency in selecting K interpenetrating subsamples of unequal sizes according to Chaudhuri and Adhikary's (1987) scheme rather than selecting them with replacement and considering the estimator based on distinct units as proposed by Bedi(1987).     

The Slippage Problem for the Circular Normal Distribution

The slippage problem occurs when an unspecified observation in a given random sample is from a distribution other than that for all the remaining observations. This paper studies the problem in terms of the 'slip' in the mean direction of a circular normal distribution. The slippage problem is first treated as a multiple decision problem with a prior which is invariant under the permutations of the hypotheses. The probabilities of accepting the various hypotheses for the Bayes rule with respect to this prior are explicitly obtained. The likelihood ratio tests for this slippage problem, for the cases when the mean directions are both known and unknown, are shown to be easily computable. The tests are illustrated through two well-known datasets. The performances of a range of tests are compared using extensive simulation.     

A two-stage unrelated randomized response model for estimating a rare sensitive attribute in probability proportional to size sampling using Poisson distribution

This paper describes the estimating procedures of mean number of entities that possess a rare sensitive attribute using the Mangat (1992) randomized device, when the population consists of some clusters and the population is again stratified with some clusters in each stratum. Unbiased estimation procedures for the mean number of individuals have been discussed and their properties are described when the parameter of a rare unrelated attribute is assumed to be known and unknown. An empirical study is carried out to show the dominance of the proposed estimator over Lee et al. (2013) estimator.     

Multiple imputation of censored survival data in the presence of missing covariates using restricted mean survival time

Missing covariates data with censored outcomes put a challenge in the analysis of clinical data especially in small sample settings. Multiple imputation (MI) techniques are popularly used to impute missing covariates and the data are then analyzed through methods that can handle censoring. However, techniques based on MI are available to impute censored data also but they are not much in practice. In the present study, we applied a method based on multiple imputation by chained equations to impute missing values of covariates and also to impute censored outcomes using restricted survival time in small sample settings. The complete data were then analyzed using linear regression models. Simulation studies and a real example of CHD data show that the present method produced better estimates and lower standard errors when applied on the data having missing covariate values and censored outcomes than the analysis of the data having censored outcome but excluding cases with missing covariates or the analysis when cases with missing covariate values and censored outcomes were excluded from the data (complete case analysis).     

Bayesian neural tree models for nonparametric regression

Frequentist and Bayesian methods differ in many aspects but share some basic optimal properties. In real-life prediction problems, situations exist in which a model based on one of the above paradigms is preferable depending on some subjective criteria. Nonparametric classification and regression techniques, such as decision trees and neural networks, have both frequentist (classification and regression trees (CARTs) and artificial neural networks) as well as Bayesian counterparts (Bayesian CART and Bayesian neural networks) to learning from data. In this paper, we present two hybrid models combining the Bayesian and frequentist versions of CART and neural networks, which we call the Bayesian neural tree (BNT) models. BNT models can simultaneously perform feature selection and prediction, are highly flexible, and generalise well in settings with limited training observations. We study the statistical consistency of the proposed approaches and derive the optimal value of a vital model parameter. The excellent performance of the newly proposed BNT models is shown using simulation studies. We also provide some illustrative examples using a wide variety of standard regression datasets from a public available machine learning repository to show the superiority of the proposed models in comparison to popularly used Bayesian CART and Bayesian neural network models.