Online learning for network optimization under unknown models

A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates of vertical motion to the choice of estimator.

Large-scale channel matrices in massive multiple-input multiple-output (MIMO) systems increase the difficulty of channel estimation. Conventional best linear unbiased estimator (BLUE) algorithms include multiple inverse operations for large-scale matrices; however this typically reduces algorithm efficiency. Efficiency can be improved by converting inverse operations into a system of linear equations, which are more easily solved for large matrices. This approach is used in the conjugate gradient (CG) method, which exhibits higher efficiency and precision when solving for approximate optimal solutions. As such, we propose a hybrid conjugate gradient (CG BLUE) algorithm, an improved version of the conventional BLUE technique. This algorithm reduces the dimensions of the channel model through a vectorization transform and uses the CG method to improve algorithm process efficiency during channel estimation for massive MIMO systems. Simulated results of NMSE and algorithm processing time show the proposed CG-BLUE algorithm resulted in nearly one order of magnitude higher calculation efficiency while maintaining the same level of accuracy as conventional BLUE.

This paper tabulates: coefficients and relative s-efficiency of the best linear unbiased estimator (BLUE) of the scale parameter of the Rayleigh distribution for type II censored samples of size N=20(5)40, r=0(1)4 (number of observations censored from the left) and s=0(1)4 (number of observations censored from the right); and ranks, coefficients, variances, and relative s-efficiencies of the BLUE of a based on a selected few order statistics (k) for sample size N=20(1)40 and k=2(1)4. These estimators have the minimum variance among the BLUE of a based on the same number of order statistics. As compared to maximum likelihood estimators (MLE) and approximate MLE, the s-efficiency of BLUE of /spl rho/ is very high. When estimating the parameter using only a few observations, the k-optimum BLUE of /spl rho/ is the only choice, as the MLE of /spl rho/ is not available. Therefore, these tables for coefficients of BLUE of /spl rho/ based on censored samples and few observations for moderately large samples, have many applications. >

In this paper, an analysis of a target location estimation\nsystem using the best linear unbiased estimator (BLUE) for high\nperformance radar systems is presented. In synthetic environments,\nwe are here concerned with three key elements of radar system\nmodeling, which makes radar systems operates accurately in strategic\nsituation in virtual ground. Radar Cross Section (RCS) modeling\nis used to determine the actual amount of electromagnetic waves\nthat are reflected from a tactical object. Pattern Propagation Factor\n(PPF) is an attenuation coefficient of the radar equation that contains\nthe reflection from the surface of the earth, the diffraction, the\nrefraction and scattering by the atmospheric environment. Clutter is\nthe unwanted echoes of electronic systems. For the data fusion of\noutput results from radar detection in synthetic environment, BLUE\nis used and compared with the mean values of each simulation results.\nSimulation results demonstrate the performance of the radar system.

Seemingly unrelated regression models (SURMs) are extensions of linear regression models which allow correlated errors between regression equations. The purpose of this article is to reconsider some fundamental problems on the performance and connection of ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of parametric functions under an SURM. Motivated by a variety of known results and facts on the equivalence of OLSEs and BLUEs under general linear models, this article collects a list of necessary and sufficient conditions for OLSEs to be BLUEs under an SURM and presents a variety of statistical interpretations on the equivalence of OLSEs and BLUEs under the SURM.

In this paper, we study the energy-efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise-corrupted channels. We assume a Gaussian network model where (i) the data being sensed at different sensors are correlated and the correlation structure (in the form of a correlation matrix) is known at the fusion center, (ii) the links between the local sensors and the fusion center are subject to multipath fading plus AWGN, and the fading gains are available to the receiver node, and (iii) the central node uses the squared error distortion metric. We first determine the optimum power-distortion regions assuming (i) a multiple-letter, and (ii) a single-letter square distortion characterization. Next, for the two distortion characterization, we investigate the performance of an uncoded transmission approach where the noisy observations are only amplified-and-forwarded to the fusion center. At the fusion center, two different estimators are considered: (i) minimum mean-square error estimator (MMSE) that exploits the correlation, and (ii) best linear unbiased estimator (BLUE) that does not require or exploit the knowledge of the correlation matrix. For both estimators, we solve for the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate (for both multiple-letter and single-letter distortion metrics). The numerical comparisons between the two schemes indicate that the MMSE requires less power to attain the same distortion provided by the BLUE. Furthermore, comparisons between power-distortion region achieved by the theoretically optimum system and the uncoded system indicates that the performance gap between the two system becomes small for low level of correlation between the sensor observations. If observations at all sensor nodes are uncorrelated, the uncoded system attains the theoretically optimum system performance.

This paper applies weighted least square method to estimate the three-parameter power function equation of the fatigue life curve, and uses comprehensive fatigue life coefficient to correct the equation, and at the same time combines probability statistics method to bring out the prediction method of structure's three-parameter power function P-S-N curve, finally applies the prediction method to a ship's frame-type elevate, based on the fatigue test data of it's material-5A06 aluminium alloy, to obtain it's structure's three-parameter power function P-S-N curve. Compared with the conventional least square method, the presented method can give a rational estimation due to it's a best linear unbiased estimator, and this method has stronger practicality in engineering, and can be used in many structures of different materials, for achieving their three-parameter power function P-S-N curve.

In this work, we developed the distribution theory of concomitants of record values arising from the Morgenstern type bivariate Lindley distribution and derived best linear unbiased estimator (BLUE) of parameter associated with the study variate involved in it are generated. The efficiencies of the BLUE with respect to the unbiased estimator are also evaluated in this work.

This study analyzes the factors influencing Indonesia’s import value during the period 2021–2025 using the Ordinary Least Squares (OLS) method. To ensure the validity of the model, a series of classical assumption tests were conducted in accordance with the Best Linear Unbiased Estimator (BLUE) criteria, including tests for normality, multicollinearity, heteroscedasticity, and autocorrelation. The data were obtained from official publications of the Central Statistics Agency (BPS) and other relevant sources. The estimation results demonstrate that the independent variables, namely the exchange rate (X₁), national income (X₂), foreign exchange reserves (X₃), inflation rate (X₄), and interest rate (X₅), exert varying effects on Indonesia’s import value, with certain variables exhibiting significant influence while others remain insignificant. The model is free from violations of the classical assumptions, thereby meeting the criteria of the Best Linear Unbiased Estimator (BLUE). Keywords: Import Value, OLS, Classical Assumption Tests, Macroeconomics

Wu et al. [Computational comparison for weighted moments estimators and BLUE of the scale parameter of a Pareto distribution with known shape parameter under type II multiply censored sample, Appl. Math. Comput. 181 (2006), pp. 1462–1470] proposed the weighted moments estimators (WMEs) of the scale parameter of a Pareto distribution with known shape parameter on a multiply type II-censored sample. They claimed that some WMEs are better than the best linear unbiased estimator (BLUE) based on the exact mean-squared error (MSE). In this paper, the general WME (GWME) is proposed and the computational comparison of the proposed estimator with the WMEs and BLUE is done on the basis of the exact MSE for given sample sizes and different censoring schemes. As a result, the GWME is performing better than the best estimator among 12 WMEs and BLUE for all cases. Therefore, GWME is recommended for use. At last, one example is given to demonstrate the proposed GWME.

Ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE), and best linear unbiased predictor (BLUP) in the general linear model with new observations are generalized to the general multivariate linear model. The fundamental equations of BLUE and BLUP in the multivariate linear model are derived by two methods, including the vectorization method and projection method. By using the matrix rank method, some new results of linear BLUE-sufficiency, linear BLUP-sufficiency, and the equality of OLSE, BLUE, and BLUP are given in the multivariate linear model.

Online learning is a machine learning paradigm that is useful when data is not available all at once. In this paper we focus in real time applications for which data is being collected as the algorithm executes. The forgetron Algorithm [1] is an online learning algorithm that works under a limited memory constraint while guaranteeing a bound on the number of total mistakes. We have proposed a specific architecture for the forgetron algorithm using hardware/software based design in order to improve computation time in the training process. Experiments on real world data show the advantages of this implementation compared to an exclusive software implementation using a Xilinx Virtex II Pro FPGA with an embedded Power PC. These experiments validate the performance of the proposed architecture.

This paper develops an econometric model for estimating the amount of operational waste delivered at garbage reception facility (GRF). The multiple regression with ordinary least squares technique (OLS) was used to analyze the relationship between the amount of operational waste per month and two explanatory variables – size of ship and travelling distance from the last port of discharge. The data from 2008 to 2014 was obtained from Port Authority of Thailand. Overall, the model fits quite well with the dataset (Adjusted R 2 =0.79). The size of ship has a positive relationship with the amount of operational waste. However, the autocorrelation assumption was violated in the original model causing the estimated partial regression coefficients not the best linear unbiased estimator (BLUE). To remedy this problem, the adjusted model was created by adding 1-period lag of y into the model as the regressor. Besides, the irrelevant explanatory variable was excluded from an analysis in order to reduce model specification bias. An improvement was explored in the adjusted model. The Durbin-Watson of 2.072 indicates that autocorrelationwas solved whereas the rest assumptions of multiple regression were still satisfied. Hence, the partial regression coefficients in the adjusted model are BLUE making the estimated more practicable.

How herd best linear unbiased estimates affect the progress achievable from gains in additive and nonadditive genetic merit

Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction. Explicitly computing the BLUE usually requires the prior knowledge of the noise covariance matrix and the subspace to which the true signal belongs. However, such prior knowledge is often unavailable in reality, which prevents us from applying the BLUE to real-world problems. To cope with this problem, we give a practical procedure for approximating the BLUE without such prior knowledge. Our additional assumption is that the true signal follows a non-Gaussian distribution while the noise is Gaussian.