K. R. Meena

Bio: K. R. Meena is an academic researcher from University of Delhi. The author has contributed to research in topics: Population & Selection (genetic algorithm). The author has an hindex of 2, co-authored 7 publications receiving 16 citations. Previous affiliations of K. R. Meena include Indian Institute of Technology Roorkee.

Estimation of the Mean of the Selected Population

Abstract: Two normal populations with different means and same variance are considered, where the variance is known. The population with the smaller sample mean is selected. Various estimators are constructed for the mean of the selected normal population. Finally, they are compared with respect to the bias and MSE risks by the mehod of Monte-Carlo simulation and their performances are analysed with the help of graphs. Keywords—Estimation after selection, Brewster-Zidek technique.

Estimating the parameter of selected uniform population under the squared log error loss function

Abstract: Let π1, …, πk be k (⩾ 2) independent populations, where πi denotes the uniform distribution over the interval (0, θi) and θi > 0 (i = 1, …, k) is an unknown scale parameter. The population associat...

On Estimating Scale Parameter of the Selected Pareto Population under the Generalized Stein Loss Function

Abstract: The problem of estimation after selection can be seen in numerous statistical applications. Let Xi1,…,Xin be a random sample drawn from the population Πi,i=1,…,k, where Πi follows Pareto distributi...

Estimating Volatility of the Selected Security

Abstract: SYNOPTIC ABSTRACTWe consider two competing pairs of random variables (X, Y1) and (X, Y2) satisfying linear regression models with equal intercepts. The model which connects the selection between two regression lines with the selection between two normal populations, proposed by Gangopadhyay et al. (2013) for estimating regression coefficients of the selected regression line, is described. This model is applied to a problem in finance which involves selecting security with lower risk. It is assumed that an investor being risk averse always chooses the security with lower risk (or, volatility) while choosing one of two securities available to him for investment, and further, is interested in estimating the risk of the chosen security. We construct several estimators and apply the theory to real data sets. Finally, graphical representation of the results is given.

Motion of the Infinitesimal Variable Mass in the Generalized Circular Restricted Three-Body Problem under the Effect of Asteroids Belt

Abstract: The present paper deals with the study of the motion’s properties of the infinitesimal variable mass body moving in the same orbital plan as two massive bodies (considered as primaries). It is assumed that the massive bodies have radiating effects, have oblate shapes, and are moving in circular orbits around their common center of mass. Using the procedures established by Singh and Abouelmagd, we determined the equations of motion of the infinitesimal body for which we assumed that under the effects of radiation and oblateness of the primaries, its mass varies following Jean’s law. We evaluated analytically and numerically the locations of equilibrium points and examined the stability of these equilibrium points. Finally, we found that all the points are unstable.

Estimation After Selection From Uniform Populations With Unequal Sample Sizes

Abstract: SYNOPTIC ABSTRACTConsider k (⩾ 2) independent uniform populations π1, …, πk, where πi ≡ U(0, θi), and θi > 0 (i = 1, …, k) is an unknown scale parameter. For selecting the unknown population having the largest scale parameter, we consider a class of selection rules based on the natural estimators of θi, i = 1, …, k. We consider the problem of estimating the scale parameter θS of the selected population, using a fixed selection rule from this class, under the scaled-squared error loss function. We derive the uniformly minimum variance unbiased estimator (UMVUE) of θS. We also consider three natural estimators ϕN, 1, ϕN, 2, and ϕN, 3 of θS which are, respectively, based on the maximum likelihood estimators, UMVUEs, and minimum risk equivariant estimators for component estimation problems. The natural estimator ϕN, 3 is shown to be a generalized Bayes estimator with respect to a non informative prior. Further, we derive a general result for improving a scale-invariant estimator of θS. Using this result, the ...

Estimation after Selection from Uniform Populations under an Asymmetric Loss Function

Abstract: SYNOPTIC ABSTRACTThe problem of estimation after selection arises in the situations where we wish to select a population among k available populations and estimate the parameter of the selected population. This paper considers estimation of the scale parameter θS of the selected uniform population, under the criterion of an asymmetric scale equivariant (ASE) loss function. For selecting the best uniform population, a class of selection rules proposed by Arshad and Misra (2015b) is used. Three natural estimators of θS based on the maximum likelihood estimators, uniformly minimum variance unbiased estimators, and minimum risk equivariant estimators are considered. The generalized Bayes estimator of θS with respect to a non-informative prior is derived. Under the ASE loss function, a general result for improving a scale-equivariant estimator of θS is provided. A consequence of this result, the estimators better than some of the natural estimators are obtained. Also, under the ASE loss function, a subclass of...

On Estimating Scale Parameter of the Selected Pareto Population under the Generalized Stein Loss Function

Abstract: The problem of estimation after selection can be seen in numerous statistical applications. Let Xi1,…,Xin be a random sample drawn from the population Πi,i=1,…,k, where Πi follows Pareto distributi...