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.
Publié le : 1992-12-14
Classification:
Logistic regression,
fixed size confidence set,
sequential estimation,
stopping rule,
last time,
uniform integrability,
asymptotic efficiency,
62L12,
62F25,
62J12
@article{1176348897,
author = {Chang, Yuan-chin Ivan and Martinsek, Adam T.},
title = {Fixed Size Confidence Regions for Parameters of a Logistic Regression Model},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1953-1969},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348897}
}
Chang, Yuan-chin Ivan; Martinsek, Adam T. Fixed Size Confidence Regions for Parameters of a Logistic Regression Model. Ann. Statist., Tome 20 (1992) no. 1, pp. 1953-1969. http://gdmltest.u-ga.fr/item/1176348897/