Modified minimax estimation of regression coefficients
作者:
Josef Kozák,
期刊:
Statistics
(Taylor Available online 1985)
卷期:
Volume 16,
issue 3
页码: 363-371
ISSN:0233-1888
年代: 1985
DOI:10.1080/02331888508801866
出版商: Akademie-Verlag
关键词: Primary 62J05;Secondary 90A20;Minimax estimation;modified minimax estimation;partially interpretable estimators
数据来源: Taylor
摘要:
Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).
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