A Correction Note on Improvement in Variance Estimation Using Auxiliary Information

ABSTRACT

In this paper, the testing problem for homogeneity in the mixture exponential family is considered. The model is irregular in the sense that each interest parameter forms a part of the null hypothesis (sub-null hypothesis) and the null hypothesis is the union of the sub-null hypotheses. The generalized likelihood ratio test does not distinguish between the sub-null hypotheses. The Supplementary Score Test is proposed by combining two orthogonalized score tests obtained corresponding to the two sub-null hypotheses after proper reparameterization. The test is easy to design and performs better than the generalized likelihood ratio test and other alternative tests by numerical comparisons.     

Pseudo New Modified Latin Square (NML m (m)) Type PBIB Designs

A New Modified Latin square [NML _i (m)] association scheme with i constraints for v = m ² treatments was introduced by Garg (2008 Garg , D. K. ( 2008 ). New modified Latin square (NMLi) type PBIB designs . J. Math. Syst. Sci. 1 ( 4 ): 83 – 89 . [Google Scholar]). In this article, a new association scheme known as Pseudo New Modified Latin square [Pseudo NML _m (m)] type association scheme is defined. The parameters of Pseudo NML _m (m) association scheme turned out to be parameters of NML _i (m) association scheme by taking i = m in NML _i (m) association scheme. The Pseudo NML _m (m) association scheme will be the usual NML _m (m) association scheme when m is a prime or a prime power. The PBIB designs following Pseudo NML _m (m) association scheme will be called the Pseudo NML _m (m) type PBIB designs. Analysis of Pseudo NML _m (m) designs along with a construction method of these designs is also given in this article.     

Estimating Quantiles of Normal Populations with a Common Mean

Suppose independent random samples are available from two normal populations with a common mean and unequal variances. Estimation of a quantile of the first population is considered with respect to the quadratic loss. Some new estimators for the quantile are proposed using some previously known estimators of a common mean. Inadmissibility results are proved for estimators which are equivariant under affine and location groups of transformations. Risk values of various estimators of a quantile are compared numerically using a detailed simulation study.     

Testing for Upper Outliers in Gamma Sample

The problem of multiple upper outlier detection in gamma sample is considered. Balasooriya and Gadag (1994 Balasooriya , U. , Gadag , V. ( 1994 ). Tests for upper outliers in the two-parameter exponential distribution . J. Statist. Computat. Simul. 50 : 249 – 259 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a location and scale invariant test based on the test statistic Z _k for testing the k upper outliers in two-parameter exponential sample. In this article, the test statistic is extended for gamma sample and the null distribution of the statistic is obtained. A simulation study is carried out to compare the performance of the tests and is found that the test based on Z _k is more powerful than the test based on the test statistic proposed by Jabbari Nooghabi et al. (2010 Jabbari Nooghabi , M. , Jabbari Nooghabi , H. , Nasiri , P. ( 2010 ). Detecting outliers in gamma distribution . Commun. Statist. Theor. Meth. 39 : 698 – 706 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

Computer-Generated Change-Over Designs for Correlated Observations

Change-over designs with independently distributed errors in the model have been studied extensively in the literature. Martin and Eccleston (2001 Martin , R. J. , Eccleston , J. A. ( 2001 ). Optimal and near optimal designs for dependent observations . Statist. Applic. 3 : 101 – 116 . [Google Scholar]) gave an algorithm for the generation of efficient change-over designs when the errors are correlated. This article proposes an algorithm for the generation of efficient change-over designs for estimation of direct effects of treatments in the presence of first-order residual effects in the model and when the errors are correlated.     

Clustering large number of extragalactic spectra of galaxies and quasars through canopies

Abstract

Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike classification, in clustering one has to first decide the optimum number of clusters and then assign the objects into different clusters. Solution of such problems for a large number of high dimensional data points is quite complicated and most of the existing algorithms will not perform properly. In the present work a new clustering technique applicable to large data set has been used to cluster the spectra of 702248 galaxies and quasars having 1,540 points in wavelength range imposed by the instrument. The proposed technique has successfully discovered five clusters from this 702,248X1,540 data matrix.     

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.     

Progressively censored tests for clinical experiments and life testing problems based on weighted empirical distributions

In the context of time-sequential studies, progressively censored tests for a simple regression model based on weighted empirical distributions are considered for ungrouped as well as grouped data situations. Early decision rules based on such tests are formulated. The asymptotic theory of the proposed tests rests on a construction of suitable empirical processes and their convergence (in distribution) to appropriate Gaussian functions. Critical values of the proposed test statistics are obtained by simulation, For a hypothetical example (of practical interest), a comparative study is made for the empirical powers and stopping times for some rival tests.     

Use of multi-auxiliary variables as a condensed auxiliary variable in selecting a sample

Information on several auxiliary variables correlated with the variable under study is available in most of the sample survey studies. This paper attempts an optimal use of several auxiliary variables in the form of a single auxiliary variable obtained as a linear function of these variables. The performance of this condensed auxiliary variable has been studied in selecting the sample.