Hayter and Tsui's test with double sampling for the vector mean of multivariate normal population

Abstract

In this paper, we introduce a version of Hayter and Tsui's statistical test with double sampling for the vector mean of a population under multivariate normal assumption. A study showed that this new test was more or as efficient than the well-known Hotelling's T² with double sampling. Some nice features of Hayter and Tsui's test are its simplicity of implementation and its capability of identifying the errant variables when the null hypothesis is rejected. Taking that into consideration, a new control chart called HTDS is also introduced as a tool to monitor multivariate process vector mean when using double sampling.     

Semiparametric inference on partially linear single-index model

ABSTRACT

We consider semiparametric inference on the partially linearsingle-index model (PLSIM). The generalized likelihood ratio (GLR) test is proposed to examine whether or not a family of new semiparametric models fits adequately our given data in the PLSIM. A new GLR statistic is established to deal with the testing of the index parameter α₀ in the PLSIM. The newly proposed statistic is shown to asymptotically follow a χ²-distribution with the scale constant and the degrees of freedom being independent of the nuisance parameters or function. Some finite sample simulations and a real example are used to illustrate our proposed methodology.     

Detection of outliers in mixed regressive-spatial autoregressive models

ABSTRACT

This article studies the outlier detection problem in mixed regressive-spatial autoregressive model. The formulae for testing outliers and their approximate distributions are derived under the mean-shift model and the variance-weight model, respectively. The simulation studies are conducted for examining the power and size of the test, as well as for the detection of outliers when a simulated data contains several outliers. A real data is analyzed to illustrate the proposed method, and modified models based on mean-shift and variance-weight models in which detected outliers are taken into account are suggested to deal with the outliers and confirm theconclusions.     

A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACT

In this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990 Nakamura, T. (1990). Corrected score function for errors in variables models: methodology and application to generalized linear models. Biometrika 77:127–137.[Crossref], [Web of Science ®] , [Google Scholar]). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.     

PMSE performance of two different types of preliminary test estimators under a multivariate t error term

Abstract

In this paper, assuming that the error terms follow a multivariate t distribution, we derive the exact formula for the predictive mean squared error (PMSE) of two different types of pretest estimators. It is shown analytically that one of the pretest estimator dominates the SR estimator if a critical value of the pretest is chosen appropriately. Also, we compare the PMSE of the pretest estimators with the MMSE, AMMSE, SR and PSR estimators by numerical evaluations. Our results show that the pretest estimators dominate the OLS estimator for all combinations when the degrees of freedom is not more than 5.     

Testing for abrupt breaks in variance structures with smooth changes

Abstract

We investigate the problem of testing for variance breaks in the case where the variance structure is assumed to be smoothly time-varying under the null. Since the classical tests are aimed to detect any change in the variance, they are not able to distinguish between smooth non constant variance and abrupt breaks. In this paper a new procedure for detecting variance breaks taking into account for smooth changes in the variance under the null is proposed. The finite sample properties of the test we introduce are investigated by Monte Carlo experiments. The theoretical outputs are illustrated using U.S. macroeconomic data.     

Notes on Test Homogeneity of the Odds Ratio in Matched Pairs Under Stratified Sampling: A Monte Carlo Evaluation

Using Monte Carlo simulation, we compare the performance of five asymptotic test procedures and a randomized permutation test procedure for testing the homogeneity of odds ratio under the stratified matched-pair design. We note that the weighted-least-square test procedure is liberal, while Pearson's goodness-of-fit (PGF) test procedure with the continuity correction is conservative. We note that PGF without the continuity correction, the conditional likelihood ratio test procedure, and the randomized permutation test procedure can generally perform well with respect to Type I error. We use the data taken from a case–control study regarding the endometrial cancer incidence published elsewhere to illustrate the use of these test procedures.     

Simulation Study on Improved Shapiro–Wilk Tests for Normality

The article concerns tests for normality based on the Shapiro–Wilk W statistic. The constants in the test statistic are recalculated as those given in Shapiro and Wilk are incorrect. The empirical significance levels and power of improved tests have been evaluated in simulation study and compared to original ones. The improved tests were also applied to the multivariate case. In this case, we consider two implementations of the W statistic, the first one proposed by Srivastava and Hui and the other by Hanusz and Tarasinska. Empirical size of tests and their power have been compared to the Henze–Zirkler test.     

Exponentiality test based on Renyi distance between equilibrium distributions

ABSTRACT

On the basis of Csiszar's φ-divergence discrimination information, we propose a measure of discrepancy between equilibriums associated with two distributions. Proving that a distribution can be characterized by associated equilibrium distribution, a Renyi distance of the equilibrium distributions is constructed that made us to propose an EDF-based goodness-of-fit test for exponential distribution. For comparing the performance of the proposed test, some well-known EDF-based tests and some entropy-based tests are considered. Based on the simulation results, the proposed test has better powers than those of competing entropy-based tests for the alternatives with decreasing hazard rate function. The use of the proposed test is evaluated in an illustrative example.