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Sat Gupta - One of the best experts on this subject based on the ideXlab platform.

  • A generalized class of difference type estimators for population median in survey sampling
    Hacettepe Journal of Mathematics and Statistics, 2017
    Co-Authors: Javid Shabbir, Sat Gupta
    Abstract:

    In this paper, we propose a generalized class of difference type estimators of nite population median in simple and stratied random sampling. The expressions for bias and mean square error are derived up to first order of approximation. Numerical comparisons reveal that the proposed class of estimators performs better than the unbiased sample median estimator, ratio estimator, exponential estimator, usual difference estimator, Rao [10] estimator and other difference type estimators.

  • improved family of estimators of population variance in simple random sampling
    Journal of statistical theory and practice, 2015
    Co-Authors: Subhash Kumar Yadav, Javid Shabbir, Cem Kadilar, Sat Gupta
    Abstract:

    In this article, we suggest a general procedure for estimating the population variance through a class of estimators. The bias and mean square error (MSE) of the proposed class of estimators are obtained to the first degree of approximation. The proposed class of estimators is more efficient than many other estimators, such as the usual variance estimator, ratio estimator, the Bahal and Tuteja (1991) exponential estimator, the traditional regression estimator, the Rao (1991) estimator, the Upadhyaya and Singh (1999) estimator, and the Kadilar and Cingi (2006) estimators. Four data sets are used for numerical comparison.

  • Estimation of Median in Two-Phase Sampling Using Two Auxiliary Variables
    Communications in Statistics - Theory and Methods, 2008
    Co-Authors: Sat Gupta, Javid Shabbir, Shabbir Ahmad
    Abstract:

    A general family of estimators for estimating the population median is proposed by making use of two auxiliary variables in two-phase sampling. Under simple random sampling without replacement (SRSWOR) scheme, the expressions for bias and mean square error (MSE) of the proposed estimators are given. The minimum MSE of the proposed estimator is equal to the minimum MSE of the Singh et al. (2006) estimator which is more efficient than many of the existing estimators. The proposed estimator, however, has less bias as compared to the Singh et al. (2006) estimator. An efficiency and bias comparison is provided using three data sets.

Michael Massmann - One of the best experts on this subject based on the ideXlab platform.

  • strong consistency of the least squares estimator in regression models with adaptive learning
    Electronic Journal of Statistics, 2019
    Co-Authors: Norbert Christopeit, Michael Massmann
    Abstract:

    This paper looks at the strong consistency of the ordinary least squares (OLS) estimator in a stereotypical macroeconomic model with adaptive learning. It is a companion to Christopeit & Massmann (2017, Econometric Theory) which considers the estimator’s convergence in distribution and its weak consistency in the same setting. Under constant gain learning, the model is closely related to stationary, (alternating) unit root or explosive autoregressive processes. Under decreasing gain learning, the regressors in the model are asymptotically collinear. The paper examines, first, the issue of strong convergence of the learning recursion: It is argued that, under constant gain learning, the recursion does not converge in any probabilistic sense, while for decreasing gain learning rates are derived at which the recursion converges almost surely to the rational expectations equilibrium. Secondly, the paper establishes the strong consistency of the OLS estimators, under both constant and decreasing gain learning, as well as rates at which the estimators converge almost surely. In the constant gain model, separate estimators for the intercept and slope parameters are juxtaposed to the joint estimator, drawing on the recent literature on explosive autoregressive models. Thirdly, it is emphasised that strong consistency is obtained in all models although the near-optimal condition for the strong consistency of OLS in linear regression models with stochastic regressors, established by Lai & Wei (1982), is not always met.

Jambulingam Subramani - One of the best experts on this subject based on the ideXlab platform.

George Orwa - One of the best experts on this subject based on the ideXlab platform.

  • estimation of population variance using the coefficient of kurtosis and median of an auxiliary variable under simple random sampling
    Open Journal of Statistics, 2017
    Co-Authors: Tonui Kiplangat Milton, Romanus Odhiambo, George Orwa
    Abstract:

    In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.

Gabriela F Nane - One of the best experts on this subject based on the ideXlab platform.

  • shape constrained non parametric estimators of the baseline distribution in cox proportional hazards model
    Scandinavian Journal of Statistics, 2013
    Co-Authors: Hendrik P Lopuhaa, Gabriela F Nane
    Abstract:

    We investigate nonparametric estimation of a monotone baseline hazard and a decreasing baseline density within the Cox model. Two estimators of a nondecreasing baseline hazard function are proposed. We derive the nonparametric maximum likelihood estimator and consider a Grenander type estimator, dened as the left-hand slope of the greatest convex minorant of the Breslow estimator [4]. We demonstrate that the two estimators are strong consistent and asymptotically equivalent and derive their common limit distribution at a xed point. Both estimators of a nonincreasing baseline hazard and their asymptotic properties are acquired in a similar manner. Furthermore, we introduce a Grenander type estimator for a nonincreasing baseline density, dened as the left-hand slope of the least concave majorant of an estimator of the baseline cumulative distribution function, derived from the Breslow estimator. We show that this estimator is strong consistent and derive its asymptotic distribution at a xed point.