Robust Correlation Structure for Multivariate Failure Time Data

When incomplete repeated failure times are collected from a large number of independent individuals, interest is focused primarily on the consistent and efficient estimation of the effects of the associated covariates on the failure times. Since repeated failure times are likely to be correlated, it is important to exploit the correlation structure of the failure data in order to obtain such consistent and efficient estimates. However, it may be difficult to specify an appropriate correlation structure for a real life data set. We propose a robust correlation structure that can be used irrespective of the true correlation structure. This structure is used in constructing an estimating equation for the hazard ratio parameter, under the assumption that the number of repeated failure times for an individual is random. The consistency and efficiency of the estimates is examined through a simulation study, where we consider failure times that marginally follow an exponential distribution and a Poisson distribution is assumed for the random number of repeated failure times. We conclude by using the proposed method to analyze a bladder cancer dataset.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.     

Kolmogorov-Smirnov Type Test-Statistics For The Gamma,Erlang-2 And The Inverse Gaussian Distributions When The Parameters Are Unknown.

Critical values are presented for the Kolmogorov-Smirnov type test statistics for the following three cases: (i) the gamma distribution when both the scale and the shape parameters are not known, (ii) the scale parameter of the gamma distribution is not known and (iii) the inverse Gaussian distribution when both the parameters are unknown. This study was motivated by the necessity to fit the gamma, the Erlang-2 and the inverse Gaussian distributions to the interpurchase times of individuals for coffee in marketing research.     

Testing of Suspected Observations in an Exponential Sample With Unknown Origin

The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.     

Quasi-maximum exponential likelihood estimation for a non stationary GARCH(1,1) model

ABSTRACT

This article investigates a quasi-maximum exponential likelihood estimator(QMELE) for a non stationary generalized autoregressive conditional heteroscedastic (GARCH(1,1)) model. Asymptotic normality of this estimator is derived under a non stationary condition. A simulation study and a real example are given to evaluate the performance of QMELE for this model.     

Bootstrap test of hypothesis for the multi-state models in survival analysis

Abstract

In the present paper we develop bootstrap tests of hypothesis, based on simulation, for the transition probability matrix arising in the context of a multi-state model. The bootstrap test statistic is based on the paper of Tattar and Vaman (2008 Tattar, P. N., Vaman, H. J. (2008). Testing transition probability matrix of a multi-state model with censored data. Lifetime Data Anal. 14(2):216–230.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which develops a statistic for the testing problems concerning the transition probability matrix of the non homogeneous Markov process.     

Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion

In this paper, we introduce the concept of the p-mean almost periodicity for stochastic processes in non linear expectation spaces. The existence and uniqueness of square-mean almost periodic solutions to some non linear stochastic differential equations driven by G-Brownian motion are established under some assumptions for the coefficients. The asymptotic stability of the unique square-mean almost periodic solution in the square-mean sense is also discussed.     

Exponential Inequalities in Stochastic Inverse Problems Using an Iterative Method

We consider an iterative method in order to solve linear inverse problems. We establish exponential inequalities for the probability of the distance between the approximated solution and the exact one for a calibration problem. The approximate is given by an iterative method with Gaussian errors. We treat an operator equation of the form Ax = u, where A is a compact operator.     

The non parametric regression estimate with dependent measurement errors

ABSTRACT

Non parametric regression estimation with measurement errors data has received great attention, and deconvolution local polynomial estimators can be used to deal with the problem that the errors are independent of other variables in the literature. In this article, the copula method is applied to tackle the case that the errors may depend on covariates, and the asymptotic properties of the resulting estimators are derived. Two simulations are conducted to illustrate the performance of the proposed estimators.     

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.