Selective Confidence Intervals for Martingale Regression Model

TL;DR

This paper develops a method for constructing valid confidence intervals for coefficients in martingale regression models, accounting for variable selection, dependence, and heteroskedasticity, with demonstrated superior performance in simulations.

Contribution

It introduces consistent estimators and a resampling-based approach for confidence intervals in martingale regression models with variable selection.

Findings

Outperforms existing methods in simulation studies.

Handles dependent data and heteroskedastic errors effectively.

Provides reliable confidence intervals post-variable selection.

Abstract

In this paper we consider the problem of constructing confidence intervals for coefficients of martingale regression models (in particular, time series models) after variable selection. Although constructing confidence intervals are common practice in statistical analysis, it is challenging in our framework due to the data-dependence of the selected model and the correlation among the variables being selected and not selected. We first introduce estimators for the selected coefficients and show that it is consistent under martingale regression model, in which the observations can be dependent and the errors can be heteroskedastic. Then we use the estimators together with a resampling approach to construct confidence intervals. Our simulation results show that our approach outperforms other existing approaches in various data structures.