The Annals of Statistics

Fixed Size Confidence Regions for Parameters of a Logistic Regression Model

Yuan-chin Ivan Chang and Adam T. Martinsek

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 20, Number 4 (1992), 1953-1969.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348897

Digital Object Identifier
doi:10.1214/aos/1176348897

Mathematical Reviews number (MathSciNet)
MR1193320

Zentralblatt MATH identifier
0765.62075

JSTOR
links.jstor.org

Subjects
Primary: 62L12: Sequential estimation
Secondary: 62F25: Tolerance and confidence regions 62J12: Generalized linear models

Keywords
Logistic regression fixed size confidence set sequential estimation stopping rule last time uniform integrability asymptotic efficiency

Citation

Chang, Yuan-chin Ivan; Martinsek, Adam T. Fixed Size Confidence Regions for Parameters of a Logistic Regression Model. Ann. Statist. 20 (1992), no. 4, 1953--1969. doi:10.1214/aos/1176348897. https://projecteuclid.org/euclid.aos/1176348897


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