Generalization of the robust bivariate t2 statistic to multivariate populations

The robust bivariate Hotelling–type T² statistics proposed by Tiku and Balakrishnan (1988) is extendend to p–variate (p ≧ 3) populations.     

Approximate maximum likelihood estimation of the mean and standard deviation of the normal distribution based on type ii censored samples

It is known that the maximum likelihood methods does not provide explicit estimators for the mean and standard deviation of the normal distribution based on Type II censored samples. In this paper we present a simple method of deriving explicit estimators by approximating the likelihood equations appropriately. We obtain the variances and covariance of these estimators. We also show that these estimators are almost as eficient as the maximum likelihood (ML) estimators and just as eficient as the best linear unbiased (BLU), and the modified maximum likelihood (MML) estimators. Finally, we illustrate this method of estimation by applying it to Gupta's and Darwin's data.     

On goodness of fit tests based on spacings for type ii censored samples

A class of tests based on spacings is obtained for milticensored samples. Their asymptotic null as well as alternative distributions are obtained.     

A robust procedure for testing the equality of mean vectors of two bivariate populations with unequal covariance matrices

A robust test is developed for testing equality of the mean vectors of two bivariate (multivariate) populations when the variance-covariance matrices are not necessarily equal. The test is an extension of the univariate robust test given by Tiku and Singh (1981).     

Testtesting for the equality of scale parameters of k(> 2) exponential populations based on complete and type ii censored samples

This paper is concerned with testing the equality of scale parameters of K(> 2) two-parameter exponential distributions in presence of unspecified location parameters based on complete and type II censored samples. We develop a marginal likelihood ratio statistic, a quadratic statistic (Qu) (Nelson, 1982) based on maximum marginal likelihood estimates of the scale parameters under the null and the alternative hypotheses, a C(a) statistic (CPL) (Neyman, 1959) based on the profile likelihood estimate of the scale parameter under the null hypothesis and an extremal scale parameter ratio statistic (ESP) (McCool, 1979). We show that the marginal likelihood ratio statistic is equivalent to the modified Bartlett test statistic. We use Bartlett's small sample correction to the marginal likelihood ratio statistic and call it the modified marginal likelihood ratio statistic (MLB). We then compare the four statistics, MLBi Qut CPL and ESP in terms of size and power by using Monte Carlo simulation experiments. For the variety of sample sizes and censoring combinations and nominal levels considered the statistic MLB holds nominal level most accurately and based on empirically calculated critical values, this statistic performs best or as good as others in most situations. Two examples are given.     

A new test for the mean vector in large dimension and small samples

In this article, we consider the problem of testing the mean vector in the multivariate normal distribution, where the dimension p is greater than the sample size N. We propose a new test T_Block and obtain its asymptotic distribution. We also compare the proposed test with other two tests. The simulation results suggest that the performance of the new test is comparable to the existing two tests, and under some circumstances it may have higher power. Therefore, the new statistic can be employed in practice as an alternative choice.     

A note on a parametric extension of rank tests to the analysis of multifactor experiments within blocks

A general rank test procedure based on an underlying multinomial distribution is suggested for randomized block experiments with multifactor treatment combinations within each block. The Wald statistic for the multinomial is used to test hypotheses about the within–block rankings. This statistic is shown to be related to the one–sample Hotellingt's T² statistic, suggesting a method for computing the test statistic using the standard statistical computer packages.     

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.     

A one-sample location test based on weighted averaging of two test statistics when the dimension and the sample size are large

We discuss a one-sample location test that can be used when the dimension and the sample size are large. It is well-known that the power of Hotelling’s test decreases when the dimension is close to the sample size. To address this loss of power, some non exact approaches were proposed, e.g., Dempster (1958 Dempster, A.P. (1958). A high dimensional two sample significance test. Ann. Math. Stat. 29:995–1010.[Crossref] , [Google Scholar], 1960 Dempster, A.P. (1960). A significance test for the separation of two highly multivariate small samples. Biometrics 16:41–50.[Crossref], [Web of Science ®] , [Google Scholar]), Bai and Saranadasa (1996 Bai, Z.D., Saranadasa, H. (1996). Effect of high dimension: by an example of a two sample problem. Stat. Sin. 6:311–329.[Web of Science ®] , [Google Scholar]), and Srivastava and Du (2008 Srivastava, M.S., Du, M. (2008). A test for the mean vector with fewer observations than the dimension. J. Multivariate Anal. 99:386–402.[Crossref], [Web of Science ®] , [Google Scholar]). In this article, we focus on Hotelling’s test and Dempster’s test. The comparative merits and demerits of these two tests vary according to the local parameters. In particular, we consider the situation where it is difficult to determine which test should be used, that is, where the two tests are asymptotically equivalent in terms of local power. We propose a new statistic based on the weighted averaging of Hotelling’s T²-statistic and Dempster’s statistic that can be applied in such a situation. Our weight is determined on the basis of the maximum local asymptotic power on a restricted parameter space that induces local asymptotic equivalence between Hotelling’s test and Dempster’s test. Numerical results show that our test is more stable than Hotelling’s T²-statistic and Dempster’s statistic in most parameter settings.