A0481
Title: Quadratic form estimation for moderate-dimensional logistic regression models
Authors: Lingfeng Lyu - University of Science and Technology of China (China) [presenting]
Xiao Guo - University of Science and Technology of China (China)
Abstract: Statistical inferences for quadratic forms of logistic regression parameters have found wide applications. Classical theory based on the maximum likelihood estimator works perfectly in the low-dimensional regime but fails when the parameter dimension $p_n$ grows proportionally to the sample size $n$. The focus is on moderate-dimensional logistic regression where $n$ and $p_n$ become increasingly large in a fixed ratio without imposing sparsity assumption on the regression parameter. A novel estimator is proposed for the quadratic forms of the regression parameter based on the MLE and the bias and variance corrected procedure. The performance of the proposed method is illustrated both theoretically and numerically.
