Titlebook: Applications of Linear and Nonlinear Models; Fixed Effects, Rando Erik W. Grafarend,Silvelyn Zwanzig,Joseph L. Awang Book 2022Latest editio

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The Third Problem of Probabilistic Regression,s Estimator (BLUMBE). The estimation of the variance by Best Invariant Quadratic Uniformly Unbiased Estimation (BIQUUE) is compared with the Best Invariant Quadratic Estimation (BIQE). The approach of Best Linear Estimation (hom BLE) for fixed effects is introduced. A key example is the treatment of

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The Fourth Problem of Probabilistic Regression,offered as (a) homogeneous best linear minimum mean square predictor (hom BLIP), (b) homogeneous .—weighted best linear minimum mean square predictor (hom .–BlIP) and (c) homogeneous α–weighted linear predictor (hom α–VIP). The A-optimal design is discussed. Three examples are presented related to:

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The Fifth Problem of Probabilistic Regression,v–Wiener Prediction in its general form. The best linear uniformly unbiased estimator (BLUUE) is derived. An explicit representation of the error budget in the general Gauss–Markov model with mixed effects is constructed under the restriction that the covariances and the correlations are known up to

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Special Problems of Algebraic Regression and Stochastic Estimation, with constraints is introduced and the complete solution is given. The n-way classification model with interaction is considered and the MINOLESS solution is given. Finally dynamic system equations are treated and the Kalman Filter (Kalman–Bucy Filter) is reviewed. Two examples are given: (a) track

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Systems of Equations: Hybrid Algebraic-Numeric Solutions,aic and numerical methods used to derive exact solutions is given. The algebraic algorithms needed to solve the nonlinear system of equations are presented, and enriched with examples to help the reader understand them. The algorithms are finally applied successfully to three real–time geodetic prob