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Singh Housila P.,Singh Sarjinder,Kim, Jong-Min The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.4
In this paper we have suggested a family of chain estimators of the population mean $\bar{Y}$ of a study variate y using two auxiliary variates in two phase (double) sampling assuming that the coefficient of variation of the second auxiliary variable is known. It is well known that chain estimators are traditionally formulated when the population mean $\bar{X}_1$ of one of the two auxiliary variables, say $x_1$, is not known but the population mean $\bar{X}_2$ of the other auxiliary variate $x_2$ is available and $x_1$ has higher degree of positive correlation with the study variate y than $x_2$ has with y, $x_2$ being closely related to $x_1$. Here the classes are constructed when the population mean $\bar{X}_1\;of\;X_1$ is not known and the coefficient of variation $C_{x2}\;of\;X_2$ is known instead of population mean $\bar{X}_2$. Asymptotic expressions for the bias and mean square error (MSE) of the suggested family have been obtained. An asymptotic optimum estimator (AOE) is also identified with its MSE formula. The optimum sample sizes of the preliminary and final samples have been derived under a linear cost function. An empirical study has been carried out to show the superiority of the constructed estimator over others.
QUANTILE ESTIMATION IN SUCCESSIVE SAMPLING
Singh, Housila P.,Tailor, Ritesh,Singh, Sarjinder,Kim, Jong-Min The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.4
In successive sampling on two occasions the problem of estimating a finite population quantile has been considered. The theory developed aims at providing the optimum estimates by combining (i) three double sampling estimators viz. ratio-type, product-type and regression-type, from the matched portion of the sample and (ii) a simple quantile based on a random sample from the unmatched portion of the sample on the second occasion. The approximate variance formulae of the suggested estimators have been obtained. Optimal matching fraction is discussed. A simulation study is carried out in order to compare the three estimators and direct estimator. It is found that the performance of the regression-type estimator is the best among all the estimators discussed here.
Singh, Housila P.,Singh, Sarjinder,Kim, Jong-Min The Korean Statistical Society 2012 응용통계연구 Vol.25 No.2
This paper proposes some alternative classes of shrinkage estimators and analyzes their properties. In particular, some new shrinkage estimators are identified and compared with Pandey (1983), Pandey and Srivastav (1985) and Jani (1991) estimators. Numerical illustrations are also provided.
Estimation of Median in the Presence of Three Known Quartiles of an Auxiliary Variable
Singh, Housila P.,Shanmugam, Ramalingam,Singh, Sarjinder,Kim, Jong-Min The Korean Statistical Society 2014 Communications for statistical applications and me Vol.21 No.5
This paper has improved several ratio type estimators of the population median including their generalization in the presence of three known quartiles of an auxiliary variable. The properties of the improved estimators are discussed and applied. Both the empirical and simulation studies confirm that our new estimators perform efficiently.
Families of Estimators of Finite Population Variance using a Random Non-Response in Survey Sampling
Singh, Housila P.,Tailor, Rajesh,Kim, Jong-Min,Singh, Sarjinder The Korean Statistical Society 2012 응용통계연구 Vol.25 No.4
In this paper, a family of estimators for the finite population variance investigated by Srivastava and Jhajj (1980) is studied under two different situations of random non-response considered by Tracy and Osahan (1994). Asymptotic expressions for the biases and mean squared errors of members of the proposed family are obtained; in addition, an asymptotic optimum estimator(AOE) is also identified. Estimators suggested by Singh and Joarder (1998) are shown to be members of the proposed family. A correction to the Singh and Joarder (1998) results is also presented.
A Class of Estimators for Population Variance in Two Occasion Rotation Patterns
Singh, G.N.,Priyanka, Priyanka,Prasad, Shakti,Singh, Sarjinder,Kim, Jong-Min The Korean Statistical Society 2013 Communications for statistical applications and me Vol.20 No.4
A variety of practical problems can be addressed in the framework of rotation (successive) sampling. The present work presents a sample rotation pattern where sampling units are drawn on two successive occasions. The problem of estimation of population variance on current (second) occasion in two - occasion successive (rotation) sampling has been considered. A class of estimators has been proposed for population variance that includes many estimators as a particular case. Asymptotic properties of the proposed class of estimators are discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion. Optimum replacement policy is discussed. Results are supported with the empirical means of comparison.
Efficient Use of Auxiliary Variables in Estimating Finite Population Variance in Two-Phase Sampling
Singh, Housila P.,Singh, Sarjinder,Kim, Jong-Min The Korean Statistical Society 2010 Communications for statistical applications and me Vol.17 No.2
This paper presents some chain ratio-type estimators for estimating finite population variance using two auxiliary variables in two phase sampling set up. The expressions for biases and mean squared errors of the suggested c1asses of estimators are given. Asymptotic optimum estimators(AOE's) in each class are identified with their approximate mean squared error formulae. The theoretical and empirical properties of the suggested classes of estimators are investigated. In the simulation study, we took a real dataset related to pulmonary disease available on the CD with the book by Rosner, (2005).
Estimation of population mean using imputation techniques in sample surveys
G.N. Singh,Kumari Priyanka,Sarjinder Singh,Jong-Min Kim 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.1
To deal with the problems of non-response, one-parameter classes of imputation techniques have been suggested and their corresponding point estimators have been proposed. The proposed classes of estimators include several other estimators as a particular case for different values of the parameter. A design based approach is used to compare the proposed strategy with the existing strategies. Theoretical results have been verified through simulation studies handling real data examples.
Quantile Estimation in Successive Sampling
Housila P. Singh,Ritesh Tailor,Sarjinder Singh,김종민 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.4
In successive sampling on two ccasions the problem of estimating a -nite population quantile has been considered. The theory developed aimsat providing the optimum estimates by combining (i) three double sam-pling estimatorsviz.ratio-type, product-type and regression-type, from thematched portion of the sample and (ii) a simple quantile based on a randomsample from the unmatched portion of the sample on the second occasion.The approximate variance formulae of the suggested estimators have beenobtained. Optimal matching fraction is discussed. A simulation study iscarried out in order to compare the three estimators and direct estimator.It is found that the performance of the regression-type estimator is the bestamong all the estimators discussed here.
Housila P. Singh,Sarjinder Singh,김종민 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.4
In this paper we have suggested a family of chain estimators of the pop-ulation mean Y of a study variatey using two auxiliary variates in twophase (double) sampling assuming that the coecient of variation of thesecond auxiliary variable is known. It is well known that chain estimatorsare traditionally formulated when the population meanX1 of one of thetwo auxiliary variables, sayx1, is not known but the population mean X2of the other auxiliary variatex2 is available and x1 has higher degree ofpositive correlation with the study variatey than x2 has with y,x2 beingclosely related tox1. Here the classes are constructed when the populationmean X1 of x1 is not known and the coecient of variationCx 2 of x2 isknown instead of population mean X2 . Asymptotic expressions for the biasand mean square error (MSE) of the suggested family have been obtained.An asymptotic optimum estimator (AOE) is also identied with its MSEformula. The optimum sample sizes of the preliminary and nal sampleshave been derived under a linear cost function. An empirical study has beencarried out to show the superiority of the constructed estimator over others.AMS 2000 subject classications.Primary 65D05; Secondary 62J10.Keywords. Study variate, auxiliary variates, population mean, coecient of variation,bias, mean square error, double sampling.Received November 2005; accepted September 2006.1School of Studies in Statistics, Vikram University, Ujjain 456010, India (e-mail: hs-ingh@winedt.com)