# Bias Correction and Robust Inference in Semiparametric Models

## TL;DR

This paper investigates biases in semiparametric models caused by low-precision nonparametric components and proposes two bias-robust inference methods, demonstrating their effectiveness through simulations.

## Contribution

It introduces two novel bias correction procedures for semiparametric models that are effective under weaker conditions than previous methods.

## Key findings

- Both bias correction methods perform well in finite samples.
- The framework extends to discontinuous functionals of nonparametric components.
- Biases from variance and bias parts can significantly affect estimators.

## Abstract

This paper analyzes several different biases that emerge from the (possibly) low-precision nonparametric ingredient in a semiparametric model. We show that both the variance part and the bias part of the nonparametric ingredient can lead to some biases in the semiparametric estimator, under conditions weaker than typically required in the literature. We then propose two bias-robust inference procedures, based on multi-scale jackknife and analytical bias correction, respectively. We also extend our framework to the case where the semiparametric estimator is constructed by some discontinuous functionals of the nonparametric ingredient. Simulation study shows that both bias-correction methods have good finite-sample performance.