This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three applications of minimum MSE shaping are considered, specifically matched filter detection, multiuser ...

Choosing the performance criterion to be mean squared error matrix, we have compared the least squares and Stein-rule estimators for coefficients in a linear regression model when the disturbances are not necessarily normally distributed. It is shown that none of the two estimators dominates the other, except in the trivial case of merely one regression coefficient where least squares is found ...

Diierent predictors and their approximators in nonlinear prediction regression models are studied. The minimal value of the mean squared error (MSE) is derived. Some approximate formulae for the MSE of ordinary and weighted least squares predictors are given.

A method of obtaining approximate redshifts and spectral types of galaxies using a photometric system of six broad-bandpass lters is developed. The technique utilizes a smallest maximum diierence approach rather than a least-squares approach, and does not consider a galaxy's apparent magnitude in the determination of its redshift. In an evalution of its accuracy using two distinct galaxy sample...

Neurophysiological changes in the brain associated with early dementia can disrupt articulatory timing and precision in speech production. Motivated by this observation, we address the hypothesis that speaking rate and articulatory coordination, as manifested through formant frequency tracks, can predict performance on an animal fluency task administerd to the elderly. Specifically, using phone...

The ability of texture models and red-edge to facilitate the detection of subtle structural vegetation traits could aid in discriminating and mapping grass quantity, a challenge that has been longstanding in the management of grasslands in southern Africa. Subsequently, this work sought to explore the robustness of integrating texture metrics and red-edge in predicting the above-ground biomass ...

Estimation problems with bounded, uniformly distributed noise arise naturally in reconstruction problems from over complete linear expansions with subtractive dithered quantization. We present a simple recursive algorithm for such bounded-noise estimation problems. The mean-square error (MSE) of the algorithm is “almost” (1 ), where is the number of samples. This rate is faster than the (1 ) MS...

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared differences of these paired observations on the squared distances between paired covariates via a simple least squares procedure, the resulting varianc...

An element being known quite nearly, to determine its correction by the collection of a great number of observations. Formation of the equations of condition. By disposing them in a manner that, in each of them, the coefficient of the correction of the element has the same sign, and adding them, we form a final equation which gives a mean correction. Expression of the probability that the error...

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We ...