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December, 1992 Fixed Size Confidence Regions for Parameters of a Logistic Regression Model
Yuan-chin Ivan Chang, Adam T. Martinsek
Ann. Statist. 20(4): 1953-1969 (December, 1992). DOI: 10.1214/aos/1176348897

Abstract

Let $(\mathbf{X}_i, Y_i)$ be independent, identically distributed observations that satisfy a logistic regression model; that is, for each $i, \log \lbrack P(Y_i = 1 | \mathbf{X}_i)/P(Y_i = 0 |\mathbf{X}_i)\rbrack = \mathbf{X}^T_i \beta_0$, where $Y_i \in \{0, 1\}, \mathbf{X}_i \in \mathbf{R}^p$ and $\beta_0 \in \mathbf{B}^p$ is the unknown parameter vector of the model. The marginal distribution of the covariate vectors $\mathbf{X}_i$ is assumed to be unknown. Sequential procedures for constructing fixed size and fixed proportional accuracy confidence regions for $\beta_0$ are proposed and shown to be asymptotically efficient as the size of the region becomes small.

Citation

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Yuan-chin Ivan Chang. Adam T. Martinsek. "Fixed Size Confidence Regions for Parameters of a Logistic Regression Model." Ann. Statist. 20 (4) 1953 - 1969, December, 1992. https://doi.org/10.1214/aos/1176348897

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0765.62075
MathSciNet: MR1193320
Digital Object Identifier: 10.1214/aos/1176348897

Subjects:
Primary: 62L12
Secondary: 62F25, 62J12

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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