Title: Confidence intervals in multiple linear regression conditioned on the selected model via the kick-one-out method

Authors: Kyohei Mochizuki; Hirokazu Yanagihara

Addresses: Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan; Innovation Technology Laboratories, AGC Inc, 1-1 Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan ' Mathematics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan

Abstract: This paper deals with the construction of a post-selection confidence interval for a regression coefficient via the kick-one-out (KOO)method in multiple linear regression. We derive a confidence interval for a regression coefficient with 1 - α coverage conditioned on the selection event whereby the specific model is selected by the KOO method. In the KOO method, it is necessary to establish a discriminant function that is a difference of variable selection criteria when deciding whether to select a particular variable. In this paper, by deriving a general expression for the discriminant function, we systematically construct confidence intervals conditioned on the selection event via the KOO method when more than one variable selection criteria are used. Our results consider the case of the KOO method when various well-known variable selection criteria such as the Akaike's information criterion (AIC), Bayesian information criterion (BIC), and C_p criterion are employed.

Keywords: GIC; generalised information criterion; GC_p criterion; linear regression model; post-selection inference; variable selection.

DOI: 10.1504/IJKESDP.2022.127671

International Journal of Knowledge Engineering and Soft Data Paradigms, 2022 Vol.7 No.2, pp.95 - 114

Received: 05 Jun 2022
Accepted: 09 Jun 2022
Published online: 13 Dec 2022 *

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