Related papers: Convergence of Chao Unseen Species Estimator
Entropy estimation plays a significant role in biology, economics, physics, communication engineering and other disciplines. It is increasingly used in software engineering, e.g. in software confidentiality, software testing, predictive…
Given $n$ i.i.d. samples from an unknown discrete distribution over an unknown set, the unseen species problem is to predict how many new outcomes would be observed in $m$ additional samples. For small $m$ we show that the Good-Toulmin…
We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by…
Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…
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…
Given $n$ samples from a population of individuals belonging to different species, what is the number $U$ of hitherto unseen species that would be observed if $\lambda n$ new samples were collected? This is an important problem in many…
We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to…
While the ordinary least squares estimator (OLSE) is still the most used estimator in linear regression models, other estimators can be more efficient when the error distribution is not Gaussian. In this paper, our goal is to evaluate this…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
Traditional covariate selection methods for causal inference focus on achieving unbiasedness and asymptotic efficiency. In many practical scenarios, researchers must estimate causal effects from observational data with limited sample sizes…
We analyze the performance of the least absolute shrinkage and selection operator (Lasso) for the linear model when the number of regressors $N$ grows larger keeping the true support size $d$ finite, i.e., the ultra-sparse case. The result…
This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a…
Unbiased estimation for parameters of maximal distribution is a very fundamental problem in the statistical theory of sublinear expectation. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper…
In a recent paper, Nguyen, Kuhn, and Esfahani (2018) built a distributionally robust estimator for the precision matrix of the Gaussian distribution. The distributional uncertainty size is a key ingredient in the construction of this…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
The James-Stein estimator's dominance over maximum likelihood in terms of mean square error (MSE) has been one of the most celebrated results in modern statistics, suggesting that biased estimators can systematically outperform unbiased…
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,…
Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher, uses $n$ samples to predict the number $U$ of hitherto unseen species that would be observed…
This paper proposes a class of ratio type estimators of finite population variance, when the population variance of an auxiliary character is known. Asymptotic expression for mean square error (MSE) is derived and compared with the mean…