ON TWO-STAGE SUCCESSIVE SAMPLING

In repeated sampling enquiries application of method of successive sampling with partial replacement of units is advantageous. In this paper use of successive sampling technique when the sampling design is multi-stage has been studied. Estimates of population mean and its variance have been obtained (a) on the second occasion, and (b) on the h-th occasion under two systems of replacement, namely (i) by retaining only a fraction p of psu's along with their sample of ssu's, and (ii) by retaining all the psu's on the second occasion, but from each psu only a fraction p of the ssu's within them is retained. A cost function suitable to the design has been illustrated, with the help of data collected from a sample survey conducted by the Indian Council of Agricultural Research.     

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]).     

On the Use of Superpopulation Model in Estimation of Population Mean in Two-Occasion Rotation Patterns

The present work is an attempt to study the estimation of the population mean on the current occasion in two-occasion successive (rotation) sampling under a superpopulation model. Six different estimators are proposed for estimating the current population mean in two-occasion successive (rotation) sampling. Optimum replacement policies and performances of the proposed estimators have been discussed. Results are interpreted via empirical studies.     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.     

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.     

Some Classes of Estimators for the Population Median Using Auxiliary Information

This article considers some classes of estimators of the population median of the study variable using information on an auxiliary variable with their properties under large sample approximation. Asymptotic optimum estimator (AOE) in each class of estimators has been investigated along with the approximate mean square error formulae. It has been shown that the proposed classes of estimators are better than these considered by Gross (1980 Gross , T. S. ( 1980 ). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Assoc. 181–184 . [Google Scholar]), Kuk and Mak (1989 Kuk , A. Y. C. , Mak , T. K. ( 1989 ). Median estimation in the presence of auxiliary information . J. Roy. Statist. Soc. Ser. B51 : 261 – 269 . [Google Scholar]), Singh et al. (2003a Singh , H. P. , Singh , S. , Joarder , A. H. ( 2003a ). Estimation of population median when mode of an auxiliary variable is known . J. Statist. Res. 37 ( 1 ): 57 – 63 . [Google Scholar]), and Al and Cingi (2009 Al , S. , Cingi , H. ( 2009 ). New estimators for the population median in simple random sampling. Tenth Islamic Countries Conference on Statistical Sciences, held in New Cairo, Egypt . [Google Scholar]). An empirical study is carried out to judge the merits of the suggested class of estimators over other existing estimators.     

Effective Rotation Patterns Under Non Response in Two-Occasion Successive Sampling

This article intends to develop some effective rotation patterns with the aid of attractive imputation methods when the problems of non response occur in two-occasion successive sampling. Utilizing the information on p (p ??1) auxiliary variables regression methods of imputation have been considered and subsequently multiple linear regression type estimators are proposed to estimate the current population mean in two-occasion successive sampling. Proposed estimators are compared with the estimator for same situations but in the absence of non-response. Optimum replacement strategies of the respective estimators have been discussed and results are interpreted with the help of empirical studies. Conclusions and suitable recommendations are made.