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Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We propose a two parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai (1985) and Singh…
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based…
Ridge estimator is an alternative to ordinary least square estimator when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose new estimators which are modifications of the…
Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…
Bessel's correction adjusts the denominator in the sample variance formula from n to n-1 to ensure an unbiased estimator of the population variance. This paper provides rigorous algebraic derivations geometric interpretations and…
We propose small area estimators of general indicators in off-census years, which avoid the use of deprecated census microdata, but are nearly optimal in census years. The procedure is based on replacing the obsolete census file with a…
We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the…
Sample surveys are widely used to obtain information about totals, means, medians, and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific…
We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error…
This paper considers the Liu estimator in the multinomial logistic regression model. We propose some different estimators of the biasing parameter. The mean square error (MSE) is considered as the performance criterion. In order to compare…
Finite-sample upper bounds on the estimation error of a winsorized mean estimator of the population mean in the presence of heavy tails and adversarial contamination are established. In comparison to existing results, the winsorized mean…
Modified estimators for the contribution rates of population eigenvalues are given under an elliptically contoured distribution. These estimators decrease the bias of the classical estimator, i.e. the sample contribution rates. The…
We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…
We consider benchmarked empirical Bayes (EB) estimators under the basic area-level model of Fay and Herriot while requiring the standard benchmarking constraint. In this paper we determine the excess mean squared error (MSE) from…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…