Polynomials of Parameters in the Regression Model — Estimation and Design

A. Pázman and J. Volaufová
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A. Pázman: Slovak Academy of Sciences, Mathematical Institute, Electro-Physical Research Centre
J. Volaufová: Slovak Academy of Sciences, Institute of Measurement and Measuring Technique Electro-Physical Research Centre

A chapter in Probability and Statistical Inference, 1982, pp 275-285 from Springer

Abstract: Abstract The regression model $$y({x_i}) = \sum {_{j = 1}^m} {f_j}({x_i}){\theta _j} + \varepsilon ({x_i})$$ is considered, with $$ (\varepsilon ({x_1}), \ldots ,\varepsilon ({x_N})) \sim N(0,K),K $$ K known. The aim of the paper is to consider unbiased estimates of polynomials in the variables θl,…,θm. An explicit expression for the minimum variance unbiased estimate is given and bounds for the variance of this estimate are given. A criterion of optimality of the design is considered and an algorithm for computing the optimum design in the case of uncorrelated observations is presented.

Keywords: Hilbert Space; Regression Model; Unbiased Estimate; Homogeneous Polynomial; Variance Vare (search for similar items in EconPapers)
Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-7840-9_26

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DOI: 10.1007/978-94-009-7840-9_26

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