p-Generalized Probit Regression and Scalable Maximum Likelihood Estimation via Sketching and Coresets

03/25/2022
by   Alexander Munteanu, et al.
0

We study the p-generalized probit regression model, which is a generalized linear model for binary responses. It extends the standard probit model by replacing its link function, the standard normal cdf, by a p-generalized normal distribution for p∈[1, ∞). The p-generalized normal distributions <cit.> are of special interest in statistical modeling because they fit much more flexibly to data. Their tail behavior can be controlled by choice of the parameter p, which influences the model's sensitivity to outliers. Special cases include the Laplace, the Gaussian, and the uniform distributions. We further show how the maximum likelihood estimator for p-generalized probit regression can be approximated efficiently up to a factor of (1+ε) on large data by combining sketching techniques with importance subsampling to obtain a small data summary called coreset.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

03/09/2021

Multivariate tail covariance for generalized skew-elliptical distributions

In this paper, the multivariate tail covariance (MTCov) for generalized ...
06/01/2022

The McDonald Normal Distribution

A five-parameter distribution called the McDonald normal distribution is...
06/03/2022

Beta Generalized Normal Distribution with an Application for SAR Image Processing

We introduce the beta generalized normal distribution which is obtained ...
05/02/2021

Asymptotic properties in the Probit-Zero-inflated Binomial regression model

Zero-inflated regression models have had wide application recently and h...
05/06/2022

A Flexible Quasi-Copula Distribution for Statistical Modeling

Copulas, generalized estimating equations, and generalized linear mixed ...
08/14/2020

Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution

The three-parameter generalized extreme value distribution arises from c...
05/16/2020

Transforming variables to central normality

Many real data sets contain features (variables) whose distribution is f...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.