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 parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML ...

In this paper, we investigate a joint source and relay precoding design scheme for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with absence of the direct link. The joint optimization problem, which is to minimize an objective function based on the mean square error (MSE), is formulated as a nonconvex optimization problem in the AF MIMO relay system. Instead of...

The Wiener-Kolmogorov (WK) signal extraction filter, extended to handle nonstationary signal and noise, has minimum Mean Square Error (MSE) among filters that preserve the signal’s initial values; however, the stochastic dynamics of the signal estimate typically differ substantially from that of the target. The use of such filters, although widespread, is observed to produce dips in the spectru...

This module motivates and introduces the minimum variance unbiased estimator (MVUE). This is the primary criterion in the classical (frequentist) approach to parameter estimation. We introduce the concepts of mean squared error (MSE), variance, bias, unbiased estimators, and the bias-variance decomposition of the MSE. The Minimum Variance Unbiased Estimator 1 In Search of a Useful Criterion In ...

In this study, plant height and plant dry weight of five wheat varieties (namely Da da 94, K nac 97, Konya 2002, Karahan 99 and Ahmeta a), collected for 20 weeks, were modeled via fitting generalized logistic (GLC), logistic (LC) and Gompertz (GC) growth curves. Growth curve selection was based on residual sum of square (RSS) and mean square error (MSE). Following growth curve selection, growth...

In this paper we provide further results on the properties of the IV estimator in the presence of weak instruments.We begin by formalizing the notion of weak identi ̄cation within the local-to-zero asymptotic framework of Staiger and Stock (1997), and deriving explicit analytical formulae for the asymptotic bias and mean square error (MSE) of the IV estimator. These results generalize earlier ̄n...

This paper proposes a cumulant (higher-order statistics) based mean-square-error (MSE) criterion for the design of Wiener filters when both the given wide-sense stationary random signal x(n) and the desired signal d(n) are non-Gaussian and contaminated by Gaussian noise sources. It is theoretically shown that the designed Wiener filter associated with the proposed criterion is identical to the ...

Medium Neural Networks (MNN), Whale Optimization Algorithm (WAO), and Support Vector Machine (SVM) methods are frequently used in the literature for estimating electricity demand. The objective of this study was to make an estimation demand Turkey’s mainland with use mixed MNN, WAO, SVM. Imports, exports, gross domestic product (GDP), population data based on input from 1980 2019 Turkey, demand...

This paper studies the generalized spatial two stage least squares (GS2SLS) estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the ca...

In data-driven prognostic methods, autoregressive moving average(ARMA) model requires stationary time series, and grey model(GM) can achieve high prediction accuracy only for exponential increasingly data sequence. To compensate these shortcomings, a novel prognostic method based on the improved Verhulst model optimized by particle swarm optimization (PSO) is proposed. Firstly, the Verhulst mod...