A new nonparametric bivariate test for two sample location problem

A strictly nonparametric bivariate test for two sample location problem is proposed. The proposed test is easy to apply and does not require the stringent condition of affine-symmetry or elliptical symmetry which is required by some of the major tests available for the same problem. The power function of the proposed test is calculated. The asymptotic distribution of the proposed test statistic is found to be normal. The power of proposed test is compared with some of the well-known tests under various distributions using Monte Carlo simulation technique. The power study shows that the proposed test statistic performs better than most of the test statistics for almost all the distributions considered here. As soon as the underlying population structure deviates from normality, the ability of the proposed test statistic to detect the smallest shift in location increases as compared to its competitors. The application of the test is shown by using a data set.     

On confidence intervals for the mean past lifetime function under random censorship

The mean past lifetime (MPL) function (also known as the expected inactivity time function) is of interest in many fields such as reliability theory and survival analysis, actuarial studies and forensic science. For estimation of the MPL function some procedures have been proposed in the literature. In this paper, we give a central limit theorem result for the estimator of MPL function based on a right-censored random sample from an unknown distribution. The limiting distribution is used to construct normal approximation-based confidence interval for MPL. Furthermore, we use the empirical likelihood ratio procedure to obtain confidence interval for the MPL function. These two intervals are compared with each other through simulation study in terms of coverage probability. Finally, a couple of numerical example illustrating the theory is also given.     

A study of quadratic inference functions with alternative weighting matrices

Quadratic inference function (QIF) is an alternative methodology to the popular generalized estimating equations (GEE) approach, it does not involve direct estimation of the correlation parameter, and thus remains optimal even if the working correlation structure is misspecified. The idea is to represent the inverse of the working correlation matrix by a linear combination of some basis matrices. In this article, we present a modification of QIF with a robust variance estimator of the extended score function. Theoretical and numerical results show that the modified QIF attains better efficiency and achieves better small sample performance than the original QIF method.     

Monitoring the coefficient of variation using a variable sample size and sampling interval control chart

This article proposes a CV chart by using the variable sample size and sampling interval (VSSI) feature to improve the performance of the basic CV chart, for detecting small and moderate shifts in the CV. The proposed VSSI CV chart is designed by allowing the sample size and the sampling interval to vary. The VSSI CV chart's statistical performance is measured by using the average time to signal (ATS) and expected average time to signal (EATS) criteria and is compared with that of existing CV charts. The Markov chain approach is employed in the design of the chart.     

A direct procedure for monitoring the coefficient of variation using a variable sample size scheme

A variable sample size (VSS) scheme directly monitoring the coefficient of variation (CV), instead of monitoring the transformed statistics, is proposed. Optimal chart parameters are computed based on two criteria: (i) minimizing the out-of-control ARL (ARL₁) and (ii) minimizing the out-of-control ASS (ASS₁). Then the performances are compared between these two criteria. The advantages of the proposed chart over the VSS chart based on the transformed statistics in the existing literature are: the former (i) provides an easier alternative as no transformation is involved and (ii) requires less number of observations to detect a shift when ASS₁ is minimized.     

Statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data

In this article, the statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is obtained using maximum likelihood method (MLE) and Bayesian method under three different loss functions. We also proved the existence and uniqueness of the MLE. The one-sample Bayesian prediction intervals are obtained. The work is done for different values of the parameters. We apply the Monto Carlo simulation to compare the proposed methods, also an example is discussed to construct the Prediction intervals.     

Bayesian prediction of order statistics with fixed and random sample sizes based on k-record values from Pareto distribution

In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here.     

Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman–Morgan test of homogeneity of two variances. The bias and mean square error of the estimator are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max–min criterion.     

Shrinkage estimation of proportion via logit penalty

By releasing the unbiasedness condition, we often obtain more accurate estimators due to the bias–variance trade-off. In this paper, we propose a class of shrinkage proportion estimators which show improved performance over the sample proportion. We provide the “optimal” amount of shrinkage. The advantage of the proposed estimators is given theoretically as well as explored empirically by simulation studies and real data analyses.     

Retrospective change detection in categorical time series

The aim of this paper is to propose methods of detecting change in the coefficients of a multinomial logistic regression model for categorical time series offline. The alternatives to the null hypothesis of stationarity can be either the hypothesis that it is not true, or that there is a temporary change in the sequence. We use the efficient score vector of the partial likelihood function. This has several advantages. First, the alternative value of the parameter does not have to be estimated; hence, we have a procedure that has a simple structure with only one parameter estimation using all available observations. This is in contrast with the generalized likelihood ratio-based change point tests. The efficient score vector is used in various ways. As a vector, its components correspond to the different components of the multinomial logistic regression model’s parameter vector. Using its quadratic form a test can be defined, where the presence of a change in any or all parameters is tested for. If there are too many parameters one can test for any subset while treating the rest as nuisance parameters. Our motivating example is a DNA sequence of four categories, and our test result shows that in the published data the distribution of the four categories is not stationary.