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Research on the Admissible Quadratic Error Variance Estimations in Growth Curve Model, and on the Admissibility of Quadratic Estimations with Restricted Parameter Sets

Author: LiuLiZhen
Tutor: ZhangLiZhen
School: Ocean University of China
Course: Applied Mathematics
Keywords: Growth Curve Model Error variance Quadratic Estimate Admissibility Constraints
CLC: O212.1
Type: Master's thesis
Year: 2010
Downloads: 13
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Abstract

The Admissibility estimated be more attention since the 1940s. For the linear model, it is important Admissibility of unknown regression coefficients and error variance estimation. Quadratic Admissible linear model error variance estimation problems after years of study by Wu Qiguang into a flat, Li Guoying, SPACE AND [3] gives a complete conclusion. This study has many applications in growth curve model error variance Sigma 2 Quadratic Admissible estimation problem. Growth curve model as follows: where, vec (?) Denote the matrix Kronecker product by column straightening and two matrices. Y and epsilon are n × p random matrix. An × m, Cq × p is a known non-zero matrix Gn × n gt; known positive definite matrix, IP is the identity matrix of order p. BM × q and Sigma 2 for the matrix and the parameters of the unknown parameters. It also assumes that the ε of the columns of the random vector independent of each other and with the n-dimensional normal distribution N (0, G) have the same first four moments. When p = 1, the model (1) is the linear model, the growth curve model is a direct extension of the linear model, it is a concept introduced in the plants and animals of the different groups of Wishart1938 research. For this model, XINYANG NORMAL assumed H0: G = In, rank (A) = r LT; the n derived tr (Y'MY) in D = {tr (Y'MY), Sigma 2: Mn × n ≥ 0} allowed to estimate the necessary conditions. In practical applications, the unknown parameters are often subject to some constraints limit. The rest of this article the growth curve model of unfettered conditions, have come to a complete conclusion, when the unknown parameters to be ellipsoidal constraints limit, research Admissibility of the quadratic estimate of the error variance. The first chapter of a linear model (growth curve model is a special linear model) unknown regression coefficients and error variance estimates Admissibility of the background and progress in research, and describes some of the concepts. Chapter II for the growth curve model (1), on the assumption that H1: G = In, rank (A) = r lt; continue the discussion Sigma 2 quadratic estimate for tr (Y'MY n Rak (C) = p) in D = {tr (Y'MY),: Mn × n ≥ 0} in the Admissibility tr (Y '[alpha (IP) PNP] Y} is admissible estimate Sigma 2 in D necessary and sufficient conditions. three chapters for the growth curve model (1), in the oval constraints: F s {(B, Sigma 2) │ B ∈ Rm × q, Sigma 2 gt; 0, tr [(ABC) '(ABC)] ≤ Sigma 2}, respectively. the assumptions H2: G = In, rank (A) = r lt; n, rank (C) = p and assumptions H3: G = IN, A = 1n, C '= 1p (1n and 1p, respectively, which means that component is 1 n-dimensional and p-dimensional column vector) the quadratic estimate tr (Y'MY) discussion of the error variance Sigma 2 in estimated class D = {tr (Y'MY): Mn × n ≥ 0} in the Admissibility. and came to the constraints of the ellipsoid, tr {Y '[a (IP) PNP] Y} is a necessary and sufficient condition Sigma 2 in D admissible estimate.

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