Estimation of Ability with Reduced Asymptotic Mean Square Error in Item Response Theory

Optimization of Generalized Mean-Square Error in Noisy Linear Estimation

A class of least squares problems that arises in linear Bayesian estimation is analyzed. The data vector y is given by the model y = P(Hθ + η) +w, where H is a known matrix, while θ, η, and w are uncorrelated random vectors. The goal is to obtain the best estimate for θ from the measured data. Applications of this estimation problem arise in multisensor data fusion problems and in wireless comm...

Mean square error optimal weighting for multitaper cepstrum estimation

The aim of this paper is to find a multitaper-based spectrum estimator that is mean square error optimal for cepstrum coefficient estimation. The multitaper spectrum estimator consists of windowed periodograms which are weighted together, where the weights are optimized using the Taylor expansion of the log-spectrum variance and a novel approximation for the log-spectrum bias. A thorough discus...

Mean Square Error bounds for parameter estimation under model misspecification

In parameter estimation, assumptions about the model are typically considered which allow us to build optimal estimation methods under many statistical senses. However, it is usually the case where such models are inaccurately known or not capturing the complexity of the observed phenomenon. A natural question arises to whether we can find fundamental estimation bounds under model mismatches. T...

Rate-distortion function via minimum mean square error estimation

We derive a simple general parametric representation of the rate–distortion function of a memoryless source, where both the rate and the distortion are given by integrals whose integrands include the minimum mean square error (MMSE) of the distortion ∆ = d(X, Y ) based on the source symbol X , with respect to a certain joint distribution of these two random variables. At first glance, these rel...

NEW APPROACH TO MEAN SQUARE ERROR ESTIMATION OF RESPONSE SURFACES by Edward