×

A mathematical-statistics approach to the least squares method. (English. Russian original) Zbl 1387.62083

Comput. Math. Model. 29, No. 1, 30-41 (2018); translation from Prikl. Mat. Inf. 54, 35-49 (2017).
Summary: We consider a mathematical-statistics approach to least-squares parameter estimation in a linear multiple regression model. This approach has led to a detailed description of the basic premises for the emergence and application of the least-squares method, produced a number of general distributional and statistical formulas for the estimation of model parameters independently of a specific joint distribution of the random variables, provided a deeper understanding of the parameter estimation risks associated with model specification errors, and made it possible to identify the place and role of knowledge of the theoretical and empirical distributions of observation errors.

MSC:

62J05 Linear regression; mixed models
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] H. Cramer, Mathematical Methods of Statistics [Russian translation], Mir, Moscow (1976).
[2] F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).
[3] G. I. Ivchenko and Yu. I. Medvedev, An Introduction to Mathematical Statistics [in Russian], Izd. LKI, Moscow (2010).
[4] M. Kendall and A. Stuart, Statistical Inference and Relationship [Russian translation], Nauka, Moscow (1973).
[5] G. Seber, Linear Regression Analysis [Russian translation], Mir, Moscow (1980). · Zbl 0447.62065
[6] S. M. Ermakov and G. A. Mikhailov, Statistical Modeling [in Russian], Nauka, Moscow (1982). · Zbl 0599.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.