Designs for estimating the difference between two responses

In this paper the problem of designing experiments for estimating the difference between responses at two arbitrary points in the region of interest is considered. Under the average mean squared error criterion the design moment conditions have been worked out. The results have been applied to the class of central composite designs.     

Linear filter model representations for integrated process control with repeated adjustments and monitoring

An integrated process control (IPC) procedure is a scheme which combines the engineering process control (EPC) and the statistical process control (SPC) procedures for the process where the noise and a special cause are present. The most efficient way of reducing the effect of the noise is to adjust the process by its forecast, which is done by the EPC procedure. The special cause, which produces significant deviations of the process level from the target, can be detected by the monitoring scheme, which is done by the SPC procedure. The effects of special causes can be eliminated by a rectifying action. The performance of the IPC procedure is evaluated in terms of the average run length (ARL) or the expected cost per unit time (ECU). In designing the IPC procedure for practical use, it is essential to derive its properties constituting the ARL or ECU based on the proposed process model. The process is usually assumed as it starts only with noise, and special causes occur at random times afterwards. The special cause is assumed to change the mean as well as all the parameters of the in-control model. The linear filter models for the process level as well as the controller and the observed deviations for the IPC procedure are developed here.     

The estimation of treatment effect for the censored bivariate data under the univariate censoring

This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given     

Testing lack of symmetry in spatial–temporal processes

Symmetry and separability of a covariance function are common assumptions to simplify the modeling effort of spatial–temporal processes. However, many studies in environmental sciences show that real data have complex spatial–temporal dependency structures resulting from lack of symmetry or violation of other standard assumptions of the covariance function. In this study, we propose new formal tests for lack of symmetry by using spectral representations of the spatial–temporal covariance functions of regularly spaced spatial–temporal data. The advantage of the proposed tests is that classical analysis of variance (ANOVA) models can be used for detecting lack of symmetry inherent in spatial–temporal processes. We evaluate the performance of the tests with simulation studies and we apply them to air pollution data.     

Likelihood ratio tests for multivariate normality

This paper presents some powerful omnibus tests for multivariate normality based on the likelihood ratio and the characterizations of the multivariate normal distribution. The power of the proposed tests is studied against various alternatives via Monte Carlo simulations. Simulation studies show our tests compare well with other powerful tests including multivariate versions of the Shapiro–Wilk test and the Anderson–Darling test.     

On nonparametric variogram estimation

A critical step for geostatistical prediction is estimation of variogram from the data. One of the popular methods estimating variogram is a smoothed version of classical nonparametric variogram estimator. In this paper we investigate its theoretical and empirical properties to provide useful information for using it. The main results are based on asymptotic theories (i.e., risk and central limit theorem) under nearly infill domain sampling. Simulation is also employed to make our points.     

The Representation of Hypergeometric Random Variables using Independent Bernoulli Random Variables

In this paper, we show that a hypergeometric random variable can be represented as a sum of independent Bernoulli random variables that are, except in degenerate cases, not identically distributed. In the proof, we use the factorial moment generating function. An asymptotic result on the probabilities of the Bernoulli random variables in the sum is also presented. Numerical examples are used to illustrate the results.