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.     

On Nonparametric Estimation of a Reliability Function

This article considers the properties of a nonparametric estimator developed for a reliability function which is used in many reliability problems. Properties such as asymptotic unbiasedness and consistency are proven for the estimator and using U-statistics, weak convergence of the estimator to a normal distribution is shown. Finally, numerical examples based on an extensive simulation study are presented to illustrate the theory and compare the estimator developed in this article with another based directly on the ratio of two empirical distributions studied in Zardasht and Asadi (2010 Zardasht , V. , Asadi , M. ( 2010 ). Evaluation of P(X _t  > Y _t ) when both X _t and Y _t are residual lifetimes of two systems . Statistica Neerlandica 64 : 460 – 481 .[Crossref], [Web of Science ®] , [Google Scholar]).     

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.     

A Numerical Method for Estimating the Variance of Age at Maximum Growth Rate in Growth Models

Studies on maturation and body composition mention age at peak height velocity (PHV) as an important measure that could predict adulthood outcome. The age at PHV is often derived from growth models such as the triple logistic fitted to the stature (height) data. Theoretically, for a well-behaved growth function, age at PHV could be obtained by setting the second derivative of the growth function to zero and solving for age. Such a solution obviously depends on the parameters of the growth function. Therefore, the uncertainty in the estimation of age at PHV resulting from the uncertainty in the estimation of the growth model, need to be accounted for in the models in which it is used as a predictor. Explicit expressions for the age at PHV and, consequently the variance of the estimate of the age at PHV, do not exist for some of the commonly used nonlinear growth functions, such as the triple logistic function. Once an estimate of this variance is obtained, it could be incorporated in subsequent modeling either through measurement error models or by using the inverse variances as weights. A numerical method for estimating the variance is implemented. The accuracy of this method is demonstrated through comparisons in models where explicit solution for the variance exists. The method of estimating the variance is illustrated by applying to growth data from the Fels study and subsequently used as weights in modeling two adulthood outcomes from the same study.     

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.     

On the Nonparametric Mean Residual Life Estimator in Length-biased Sampling

In this article, we discuss nonparametric estimation of a mean residual life function from length-biased data. Precisely, we prove strong uniform consistency and weak converge of the nonparametric mean residual life estimator in length-biased setting.     

An Improved Procedure of Estimating the Finite Population Mean Using Auxiliary Information in the Presence of Random Non Response

This article deals with the problem of estimation of the finite population mean using auxiliary information in the presence of random non response. Three different situations where random non response occurs either in study variate, or in auxiliary variate, or in both the variates, have been discussed. The asymptotically optimum estimators (AOEs) for each strategy are also identified. Expressions of biases and mean squared errors of the proposed estimators have been derived up to the first degree of approximation. Proposed estimators have been compared with the usual unbiased estimator, ratio estimator, and product estimator in the presence of random non response. Empirical studies are also carried out to show the performance of the proposed estimators over other 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.