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In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not…
We consider logistic regression including two sets of discrete or categorical covariates that are missing at random (MAR) separately or simultaneously. We examine the asymptotic properties of two multiple imputation (MI) estimators, given…
The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via…
Biomedical researchers usually study the effects of certain exposures on disease risks among a well-defined population. To achieve this goal, the gold standard is to design a trial with an appropriate sample from that population. Due to the…
A new family of minimum distance estimators for binary logistic regression models based on $\phi$-divergence measures is introduced. The so called "pseudo minimum phi-divergence estimator"(PM$\phi$E) family is presented as an extension of…
In this article, we propose the Sample Information Optimal Estimator (SIOE) and the Stochastic Restricted Optimal Estimator (SROE) for misspecified linear regression model when multicollinearity exists among explanatory variables. Further,…
In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased…
A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We…
The linear minimum mean squared error (LMMSE) estimator is the best linear estimator for a Bayesian linear inverse problem with respect to the mean squared error. It arises as the solution operator to a Tikhonov-type regularized inverse…
Empirical Bayes estimators are based on minimizing the average risk with the hyper-parameters in the weighting function being estimated from observed data. The performance of an empirical Bayes estimator is typically evaluated by its mean…
The logistic regression model is one of the most powerful statistical methods for the analysis of binary data. The logistic regression allows to use a set of covariates to explain the binary responses. The mixture of logistic regression…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
Research in NLP is often supported by experimental results, and improved reporting of such results can lead to better understanding and more reproducible science. In this paper we analyze three statistical estimators for expected validation…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
In complex survey data, each sampled observation has assigned a sampling weight, indicating the number of units that it represents in the population. Whether sampling weights should or not be considered in the estimation process of model…
This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…
Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator…
We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
Bagging can significantly improve the generalization performance of unstable machine learning algorithms such as trees or neural networks. Though bagging is now widely used in practice and many empirical studies have explored its behavior,…