# Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data

arXiv: https://arxiv.org/abs/2410.01008 · HTML: https://mlsanity.com/paper/2410.01008/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [A Bootstrap Lasso + Partial Ridge Method to Construct Confidence Intervals for Parameters in High-dimensional Sparse Linear Models](https://mlsanity.com/paper/1706.02150/) (2017)
- [Statistical Inference and Large-scale Multiple Testing for High-dimensional Regression Models](https://mlsanity.com/paper/2301.10392/) (2023)
- [A Revisit to De-biased Lasso for Generalized Linear Models](https://mlsanity.com/paper/2006.12778/) (2020)
- [Some Clustering-based Change-point Detection Methods Applicable to High Dimension, Low Sample Size Data](https://mlsanity.com/paper/2111.14012/) (2021)
- [Spatial Tweedie exponential dispersion models](https://mlsanity.com/paper/2003.06299/) (2020)
- [Bayesian Variable Selection in Double Generalized Linear Tweedie Spatial Process Models](https://mlsanity.com/paper/2306.11165/) (2023)

## Built on by (most cited first, 2 of 2)

- [Distribution-free inference for LightGBM and GLM with Tweedie loss](https://mlsanity.com/paper/2507.06921/) (2025)
- [Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting](https://mlsanity.com/paper/2508.10055/) (2025)

## Abstract (arXiv)

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.