Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data

• URL: http://arxiv.org/abs/2410.01008v1
• Date: Tue, 1 Oct 2024 18:57:18 GMT
• Title: Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data
• Authors: Alokesh Manna, Zijian Huang, Dipak K. Dey, Yuwen Gu,
• Abstract summary: Tweedie exponential dispersion family is a popular choice among many to model insurance losses. It is often important to obtain credibility (inference) of the most important features that describe the endogenous variables.
• Score: 3.5637073151604093
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Inference at the data's edge: Gaussian processes for modeling and inference under model-dependency, poor overlap, and extrapolation [0.0]
  The Gaussian Process (GP) is a flexible non-linear regression approach. It provides a principled approach to handling our uncertainty over predicted (counterfactual) values. This is especially valuable under conditions of extrapolation or weak overlap.
  arXiv  Detail & Related papers  (2024-07-15T05:09:50Z)
• Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise [51.87307904567702]
  Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the distribution of outputs. We propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities.
  arXiv  Detail & Related papers  (2024-06-05T13:36:38Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• The Implicit Delta Method [61.36121543728134]
  In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of uncertainty. We show that the change in the evaluation due to regularization is consistent for the variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference.
  arXiv  Detail & Related papers  (2022-11-11T19:34:17Z)
• Two-Stage Robust and Sparse Distributed Statistical Inference for Large-Scale Data [18.34490939288318]
  We address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. We propose a two-stage distributed and robust statistical inference procedures coping with high-dimensional models by promoting sparsity.
  arXiv  Detail & Related papers  (2022-08-17T11:17:47Z)
• Modeling High-Dimensional Data with Unknown Cut Points: A Fusion Penalized Logistic Threshold Regression [2.520538806201793]
  In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. We consider a threshold model that all continuous features are discretized into ordinal levels, which further determine the binary responses. We find the lasso model is well suited in the problem of early detection and prediction for chronic disease like diabetes.
  arXiv  Detail & Related papers  (2022-02-17T04:16:40Z)
• Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression [14.493176427999028]
  We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE) with linear regression models. We show that the T-learner fails to achieve the consistency except the random assignment, while the IPW-learner converges the risk to zero if the propensity score is known.
  arXiv  Detail & Related papers  (2022-02-10T18:51:52Z)
• Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data [13.48481978963297]
  Blockwise missing data occurs when we integrate multisource or multimodality data where different sources or modalities contain complementary information. We propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods.
  arXiv  Detail & Related papers  (2021-06-07T05:12:42Z)
• Quantifying Uncertainty in Deep Spatiotemporal Forecasting [67.77102283276409]
  We describe two types of forecasting problems: regular grid-based and graph-based. We analyze UQ methods from both the Bayesian and the frequentist point view, casting in a unified framework via statistical decision theory. Through extensive experiments on real-world road network traffic, epidemics, and air quality forecasting tasks, we reveal the statistical computational trade-offs for different UQ methods.
  arXiv  Detail & Related papers  (2021-05-25T14:35:46Z)
• Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression [91.3373131262391]
  Uncertainty is the only certainty there is. Traditionally, the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. How to model the uncertainty within the present-day technologies for regression remains an open issue.
  arXiv  Detail & Related papers  (2021-03-25T06:56:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.