Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data

TL;DR

This paper discusses methods for constructing valid confidence intervals for coefficients in penalized regression models, specifically in the context of insurance data modeled with Tweedie distributions, addressing bias correction and post-selection inference.

Contribution

It introduces methodologies for accurate post-selection inference and confidence interval construction in penalized GLMs applied to insurance data, accounting for bias in lasso estimates.

Findings

Proposes bias correction techniques for lasso estimates in insurance models.

Demonstrates improved confidence interval accuracy post feature selection.

Applicable to Tweedie GLMs in insurance loss modeling.

Abstract

The Tweedie exponential dispersion family is a popular choice among many to model insurance losses that consist of zero-inflated semicontinuous data. In such data, it is often important to obtain credibility (inference) of the most important features that describe the endogenous variables. Post-selection inference is the standard procedure in statistics to obtain confidence intervals of model parameters after performing a feature extraction procedure. For a linear model, the lasso estimate often has non-negligible estimation bias for large coefficients corresponding to exogenous variables. To have valid inference on those coefficients, it is necessary to correct the bias of the lasso estimate. Traditional statistical methods, such as hypothesis testing or standard confidence interval construction might lead to incorrect conclusions during post-selection, as they are generally too optimistic. Here we discuss a few methodologies for constructing confidence intervals of the coefficients after feature selection in the Generalized Linear Model (GLM) family with application to insurance data.