Robust durbin's and portmanteau goodness-of-fit test statistics and their limit distributions

Robust analogue of Durbin's(1970)statistic is derived and its limiting distribution is obtained under both null and alternative hypotheses. Also, robust version of the portmanteau goodness-of-fit test statistic for AR(p)model is given and the asymptotic distribution is derived.     

Two stage fixed width confidence intervals for the common location parameter of several exponential distributins

Two stage sampling schemes are introduced for use in estimating the common location parameter (guarantee time) of two or more exponential distributions with a confidence interval of prespecified width whose coverage probability is at least a given nominal value. Exact expressions for all moments of order r ≥ 1 of the associated two stage sample sizes and for the actual coverage probabilities are derived. The performance of the procedures in a variety of two population, moderate fixed sample size cases is examined via numerical studies involving both exact calculations and Monte Carlo simulations. No new tables are needed to implement any of the proposed methods. A modified two stage procedure is recommended for practical use     

A NONPARAMETRIC TEST OF SYMMETRY VERSUS ASYMMETRY FOR RANKED-SET SAMPLES

This paper introduces a nonparametric test of symmetry for ranked-set samples to test the asymmetry of the underlying distribution. The test statistic is constructed from the Cramér-von Mises distance function which measures the distance between two probability models. The null distribution of the test statistic is established by constructing symmetric bootstrap samples from a given ranked-set sample. It is shown that the type I error probabilities are stable across all practical symmetric distributions and the test has high power for asymmetric distributions.     

On Erlang(2) Risk Process Perturbed by Diffusion

ABSTRACT

In this article, we consider an Erlang(2) risk process perturbed by diffusion. From the extreme value distribution of Brownian motion with drift and the renewal theory, we show that the survival probability satisfies an integral equation. We then give the bounds for the ultimate ruin probability and the ruin probability caused by claim. By introducing a random walk associated with the proposed risk process, we define an adjustment-coefficient. The relation between the adjustment-coefficient and the bound is given and the Lundberg-type inequality for the bound is obtained. Also, a formula of Pollaczek–Khinchin type for the bound is derived. Using these results, the bound can be calculated when claim sizes are exponentially distributed.     

ON THE ECONOMIC DESIGN OF MULTIVARIATE CONTROL CHARTS

ABSTRACT

It is an increasingly common practice to monitor several related quality characteristics of a product or process using a multivariate control chart procedure. Several types of multivariate control charts, including Hotelling's χ ² and T ² control charts, have been developed in attempts to improve monitoring by using the correlation structure that exists between quality characteristics. The purpose of this paper is to summarize the assumptions made regarding the out-of-control process shift in the economic design of multivariate control charts and to address their consequences. We study the average run length (ARL) properties of the χ ² control chart using a numerical example and show that this chart can perform ineffectively under the assumed out-of-control conditions when designed using the economic approach. Following Healy,[1] Healy, J.D. 1987. A Note on the Multivariate CUSUM Procedures. Technometrics, 29: 409–412. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] we offer an alternative procedure that has improved ARL properties and overall performance. These results can be important to researchers and practitioners who are interested in using the economic design of multivariate control procedures.     

Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices

We propose a new test procedure for testing linear hypothesis on the mean vectors of normal populations with unequal covariance matrices when the dimensionality, p exceeds the sample size N  , i.e. p/N→c<∞$p/N\to c<\infty$. Our procedure is based on the Dempster trace criterion and is shown to be consistent in high dimensions.     

Testing for Heteroscedasticity and/or Autocorrelation in Longitudinal Mixed Effect Nonlinear Models with AR(1) Errors

The effect of influental observation son the parameter estimates of ordinary least squares regression models has received considerable a t t e n t i o n fn the last decade. However, very little attention has been given to the problem of influential observation sinthea naysis of variace . The purpose of this paper is to show by way of examples that in fluential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagno stics for identifying both extreme points and out liers can be used toreveal potential data and design problems.     

ℒ1-Limit of Trimmed Sums of Order Statistics from Location-Scale Distributions with Applications to Type II Censored Data Analysis

We derive the ?¹-limit of trimmed sums of order statistics from location-scale distributions satisfying certain assumptions. Based on this limit, an approximation to the asymptotic variance of a Best-Asymptotic-Normal (BAN) estimator for the location parameter is developed. Associated formulae are derived for four location-scale distributions commonly used in lifetime data analysis. The approximation is analyzed via the properties of the approximating function and by comparison to the exact values for a special case. Applications are illustrated by applying the approximation to comparing location parameters and to selecting the population with the largest location parameter, using censored samples from location-scale populations.     

Limit Theory for Random Coefficient First-Order Autoregressive Process

Random coefficient AR(1) processes are investigated where the random coefficient satisfies some suitable conditions. Conditional least squares estimator is shown to be consistent and to be asymptotically normality distributed. This extends the limit theory for stationary and near-stationary cases. Only second moments are assumed, as in the case of stationary autoregression models with fixed coefficient |ρ| < 1.     

Power-Law Adjusted Survival Models

A simple adjustment to parametric failure-time distributions, which allows for much greater flexibility in the shape of the hazard-rate function, is considered. Analytical expressions for the distributions of the power-law adjusted Weibull, gamma, log-gamma, generalized gamma, lognormal, and Pareto distributions are given. Most of these allow for bathtub-shaped and other multi-modal forms of the hazard rate. The new distributions are fitted to real failure-time data which exhibit a multi-modal hazard-rate function and the fits are compared.