Related papers: Mean Square Error bounds for parameter estimation …
The van Trees inequality relates the Ensemble Mean Squared Error of an estimator to a Bayesian version of the Fisher Information. The Ziv-Zakai inequality relates the Ensemble Mean Squared Error of an estimator to the Minimum Probability of…
We consider the problem of sequentially learning to estimate, in the mean squared error (MSE) sense, a Gaussian $K$-vector of unknown covariance by observing only $m < K$ of its entries in each round. We propose two MSE estimators, and…
We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…
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…
This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson…
In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown…
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…
We present novel lower bounds on the mean square error (MSE) of the location estimation of an emitting source via a network where the sensors are deployed randomly. The sensor locations are modeled as a homogenous Poisson point process. In…
This paper explores Bayesian lower bounds on the minimum mean squared error (MMSE) that belong to the Ziv-Zakai (ZZ) family. The ZZ technique relies on connecting the bound to an M-ary hypothesis testing problem. Three versions of the ZZ…
The multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional…
This article addresses the problem of estimating the population mean in the presence of auxiliary information when study variable itself is qualitative in nature. Bias and mean squared error (MSE) expressions of the class of estimators are…
Small area estimation has received enormous attention in recent years due to its wide range of application, particularly in policy making decisions. The variance based on direct sample size of small area estimator is unduly large and there…
Detailed derivations of two bounds of the minimum mean-square error (MMSE) of complex-valued multiple-input multiple-output (MIMO) systems are proposed for performance evaluation. Particularly, the lower bound is derived based on a…
Ensuring robust model performance in diverse real-world scenarios requires addressing generalizability across domains with covariate shifts. However, no formal procedure exists for statistically evaluating generalizability in machine…
Multilayer perceptrons (MLP) with one hidden layer have been used for a long time to deal with non-linear regression. However, in some task, MLP's are too powerful models and a small mean square error (MSE) may be more due to overfitting…
Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be…