Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model

In this article we consider the partitioned fixed linear model F : y = X1β1 + X2β2 + ε" and the corresponding mixed model M : y =X1β1+X2u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β1 in the fixed model F remains BLUE in the mixed model M . In this paper we extend the results concerning further equalities arising from models F and M.

Visible Light Positioning with Multiple Transmitters and Multiple Receiving Sensors

Visible light communications (VLC) based positioning systems will form an important part of the future generation wireless communication systems because they offer higher accuracy for indoor positioning as compared to radio frequency based systems. In this paper, we have used non Bayesian statistical signal processing techniques for the hybrid time-of-arrival/received-signal-strength and hybrid time-difference-of-arrival/received-signal-strength based positioning. These hybrid measurements are combined with the following fusion algorithms: weighted least squares and the best linear unbiased estimator. These two fusion algorithms are compared in terms of the mean Euclidean error as a function of various parameters such as signal-to-noise ratio, transmitter arrangement and synchronization error. Even though the performance of the weighted least squares algorithm is better, the best linear unbiased estimator is still an attractive algorithm for systems that require a lower complexity.

Performance of stochastic restricted and unrestricted two-parameter estimators in linear mixed models

In this article, two parameter estimation using penalized likelihood method in the linear mixed model is proposed. In addition, by considering the stochastic linear restriction for the vector of fixed effects parameters we are introduced the stochastic restricted two parameter estimation. Methods are proposed for estimating variance parameters when unknown. Also, the superiority conditions of the two parameter estimator over the best linear unbiased estimator, and the stochastic restricted two parameter estimator over the stochastic restricted best linear unbiased estimator are obtained under the mean square error matrix sense. Methods are proposed for estimating of the biasing parameters. Finally, a simulation study and a numerical example are given to evaluate the proposed estimators

On exponential decay of the variance of BLUE for the mean of a stationary sequence

In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.