Confidence intervals in multiple linear regression conditioned on the selected model via the kick-one-out method Online publication date: Tue, 13-Dec-2022
by Kyohei Mochizuki; Hirokazu Yanagihara
International Journal of Knowledge Engineering and Soft Data Paradigms (IJKESDP), Vol. 7, No. 2, 2022
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 Cp criterion are employed.
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