Related papers: An Approximate MSE Expression for Maximum Likeliho…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…
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 have proposed an almost unbiased estimator using known value of some population parameter(s) with known population proportion of an auxiliary variable. A class of estimators is defined which includes [1], [2] and [3]…
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…
Maximum-a-posteriori (MAP) approaches are an effective framework for inverse problems with known forward operators, particularly when combined with expressive priors and careful parameter selection. In blind settings, however, their use…
Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…
The limit distribution of the nonparametric maximum likelihood estimator for interval censored data with more than one observation time per unobservable observation, is still unknown in general. For the so-called separated case, where one…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
This paper studies the minimum mean squared error (MMSE) of estimating $\mathbf{X} \in \mathbb{R}^d$ from the noisy observation $\mathbf{Y} \in \mathbb{R}^k$, under the assumption that the noise (i.e., $\mathbf{Y}|\mathbf{X}$) is a member…
We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
This two-part work considers the minimum means square error (MMSE) estimation problem for a high dimensional multi-layer generalized linear model (ML-GLM), which resembles a feed-forward fully connected deep learning network in that each of…
In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator…
The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…
In Ruckdeschel[10], we derive an asymptotic expansion of the maximal mean squared error (MSE) of location M-estimators on suitably thinned out, shrinking gross error neighborhoods. In this paper, we compile several consequences of this…
We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical…
Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…
In this article, we analyse the accuracy and computational complexity of estimators for expected functionals of the solution to multi-dimensional parabolic stochastic partial differential equations (SPDE) of Zakai-type. Here, we use the…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…