# Nonparametric Regression with Multiple Thresholds: Estimation and Inference

## TL;DR

This paper develops methods for estimating and testing the number and values of multiple thresholds in nonparametric regression models with an exogenous threshold variable, supported by simulations and an empirical application.

## Contribution

It introduces a testing procedure to determine the unknown number of thresholds and derives their asymptotic properties, advancing nonparametric regression analysis.

## Key findings

- The proposed test accurately identifies the number of thresholds.
- Sequential estimation of threshold values is precise.
- Monte Carlo simulations confirm the test's effectiveness.

## Abstract

This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties of the local constant estimator for a nonparametric regression with multiple thresholds. However, the number of thresholds and corresponding threshold values are typically unknown in practice. We then use our testing procedure to determine the unknown number of thresholds and derive the limiting distribution of the proposed test. The Monte Carlo simulation results indicate the adequacy of the modified test and accuracy of the sequential estimation of the threshold values. We apply our testing procedure to an empirical study of the 401(k) retirement savings plan with income thresholds.