Testing Conditional Independence: Martingale Transforms and Bootstrap 1

• 영문명: Testing Conditional Independence: Martingale Transforms and Bootstrap 1
• 발행기관: 한국계량경제학회
• 저자명: Kyungchul Song
• 간행물 정보: 『한국계량경제학회 학술대회 논문집』2007년 하계학술대회, 1~71쪽, 전체 71쪽
• 주제분류: 경제경영 > 경제학
• 파일형태: PDF
• 발행일자: 2007.08.30

영문 초록

This paper investigates the problem of testing conditional independence of Y and Z given (X) for some 2 R d ; for a parametric function ( ): First, this paper proposes several classes of asymptotic pivotal tests that are based on Rosenblatt transforms and establishes that against certain alternatives of generic nature, a martingale transform can be employed to improve the asymptotic power of the tests in terms of limiting Pitman e¢ ciency. The martingale transform applied here is extremely simple, causing almost zero additional computational cost. Second, this paper proposes wild bootstrap procedures applied to Rosenblatt transform-based tests and Rosenblatt-martingale transform-based tests. Third, this paper …nds that even when one knows exactly the conditional distribution functions used in the test statistics, using their nonparametric estimators improves the asymptotic power in terms of limiting Pitman e¢ ciency. Lastly, the …nite sample performances of the proposed tests are compared via a Monte Carlo simulation study.

목차

1 Introduction

2 Testing Conditional Independence

3 Asymptotic Representation of a Semiparametric Empirical Process

4 When Z i is a Binary Variable

5 Bootstrap Tests

6 Asymptotic Power Comparison of Tests

7 Simulation Studies

8 Conclusion

키워드

Conditional independence asymptotic pivotal tests martingale transforms wild bootstrap limiting Pitman e¢ ciency