Classification of High Dimensional Small Sample Genetic Data by Forward Maximum Likelihood Ratio Stepwise Logistic Regression

A Modern Maximum-Likelihood Theory for High-dimensional Logistic Regression

Every student in statistics or data science learns early on that when the sample size n largely exceeds the number p of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there are formulas to predict the variability of these estimates which are used for the purpose of statistical inference; for instance, to produce p-values fo...

High-dimensional classification by sparse logistic regression

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic bounds for the resulting misclassification excess risk. The bounds can be reduced under the additional low-noise condition. The proposed complexity penalty ...

Bayesian and Iterative Maximum Likelihood Estimation of the Coefficients in Logistic Regression Analysis with Linked Data

This paper considers logistic regression analysis with linked data. It is shown that, in logistic regression analysis with linked data, a finite mixture of Bernoulli distributions can be used for modeling the response variables. We proposed an iterative maximum likelihood estimator for the regression coefficients that takes the matching probabilities into account. Next, the Bayesian counterpart...

A MODERN MAXIMUM-LIKELIHOOD THEORY FOR HIGH-DIMENSIONAL LOGISTIC REGRESSION By

THE LIKELIHOOD RATIO TEST IN HIGH-DIMENSIONAL LOGISTIC REGRESSION IS ASYMPTOTICALLY A RESCALED CHI-SQUARE By

Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression coefficients by using an approximation to the distribution of the likelihood-ratio test. Indeed, Wilks’ theorem asserts that whenever we...