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This paper provides a new perspective for robust estimation and inference methods based on Huber regression. An efficient distributed learning with sparsity is proposed, in which the observations are randomly divided among different machines. We modify the proximal alternating direction method of multiplies (ADMM) algorithm to calculate the sparse penalized Huber regression. The convergence property of the algorithm is established. Computationally, our proposed approach requires only a central machine to solve a SCAD or adaptive lasso penalized M-estimation problem, and other node machines to calculate gradients based on local datasets. In terms of communication, the estimation error of our method decreases to that of the centralized method in several rounds of communication. Simulation studies are conducted to evaluate the finite-sample performance of our proposed method. The empirical study shows that our method has good practicability in the practice of a Communities and Crime analysis. [ABSTRACT FROM AUTHOR]

In this paper, we develop estimators of the finite population variance using the information on the study variable’s first and second raw moments under stratified random sampling. In addition, both combined and separate estimators are also developed for estimating the population variance using supplementary information on a study variable and one or two auxiliary variables. The proposed estimators are compared with the existing estimators in terms of absolute bias and relative efficiency. Based on simulated and empirical studies, it is found that the proposed estimators may outperform the existing estimators. [ABSTRACT FROM AUTHOR]

In this paper, we explore the k-class estimator in high-dimensional linear models with potential endogeneity issues which are very common in empirical economics studies. K-class estimator has the advantage of incorporating many popular estimators such as the OLS estimator, two stage least squares (2SLS) estimator, limited information maximum likelihood (LIML) estimator, etc., as k takes on different values. Our main innovations are: 1) In the newly proposed high-dimensional k-class estimator, we allow the value of k (hence the level of endogeneity) to be determined by the data. Therefore, our method is very useful in empirical studies where the researcher do not know the severity of endogeneity or the importance of variables in a very large pool of candidate covariates. 2) In this paper, the adaptive LASSO method is incorporated into the generalized k-class estimation for variable selection and coefficient estimation in both the structural and reduced form equations. We show that the adaptive LASSO type k-class estimator has oracle properties. In simulation studies, we show that our new estimator can choose the optimal k value as well as achieving the minimum MSE among a set of popular estimators in finite samples where the number of potential endogenous variable is large. [ABSTRACT FROM AUTHOR]

In the present paper, a general class of estimators has been proposed for estimating the population mean of the study variable using auxiliary variable when the population mean of the auxiliary variable is known in stratified random sampling. The bias and mean squared error of the proposed class of estimators are derived under stratified sampling to the first degree of approximation. Members of the proposed class of estimators are also obtained by giving suitable values to the constants used. Comparisons of the proposed strategy with the usual unbiased estimator and other estimators have been made. Empirical and simulation study is carried out to demonstrate the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

This paper studies the empirical likelihood method for a multivariate first-order random coefficient autoregressive (RCAR(1)) model. Based on the modified least square score equation, empirical likelihood method is used to test the randomness of coefficients and estimate the unknown parameters. First, the limiting distribution of the log empirical likelihood ratio statistic is established. Second, the maximum empirical likelihood estimator is derived and its asymptotic properties are established. Finally, the performances of the estimator are compared with the modified least square estimator via simulation. Furthermore, simulation result shows that the test has the correct size and very good power for all cases considered. [ABSTRACT FROM AUTHOR]

In this paper, a class of hybrid type estimators is proposed in estimating the finite population variance using single auxiliary variable in simple random sampling. Expressions for the bias and the mean square error (MSE) are derived up to the first order of approximation. Theoretically comparisons are provided to show that the proposed estimators perform more efficiently than various existing estimators. Empirical study and simulation results are carried out to confirm numerically that the proposed estimators are more efficient than the usual unbiased sample variance estimator, ratio and linear regression estimators by Isaki, Singh et al., and Shabbir and Gupta estimators. [ABSTRACT FROM AUTHOR]

In this paper, an efficient generalized estimation strategy has been proposed to present the problem of estimation of current population mean Y ¯ of study variable y in two-occasion rotation sampling. The properties of the proposed estimation procedure have been deeply examined and its optimum replacement strategy is formulated. Empirical studies are carried out to show the superiority of the proposed estimator over the sample mean estimator, natural successive sampling estimator (when no auxiliary information is used) and some well-known recent contemporary estimators under various situations. Numerical results are given in support of the study and recommendations are also made to the survey practitioners. [ABSTRACT FROM AUTHOR]

In the noncontractual setting of customer-base analysis, heterogeneity parameters in purchase model and lifetime model are usually assumed to follow some familiar parametric distribution such as gamma or log-normal distribution. But, in many applications, these assumptions may be questionable because the true distributions of heterogeneity parameters are usually unknown. To this end, this paper relaxes these assumptions imposed on heterogeneity parameters to develop a nonparametric approach to purchase model and lifetime model, in which unknown distributions of heterogeneity parameters are approximated by a truncated Dirichlet process prior. A nonparametric empirical Bayesian method is developed to obtain Bayesian estimations of unknown parameters in the proposed nonparametric models. The blocked Gibbs sampler is presented to draw observations required for Bayesian inference from the corresponding posterior distributions of the components of parameters. Extensive simulation studies and a CDNOW data set are presented to illustrate the newly developed methodologies. [ABSTRACT FROM AUTHOR]