Test for the existence of moments

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K03656
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Economic statistics
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: Hitomi Kohtaro 京都工芸繊維大学, 基盤科学系, 教授 (00283680)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: optimal minimax rate / nearest neighour method / instrumental variables

Outline of Final Research Achievements

This study investigates optimal minimax rates for specification testing
when the alternative hypothesis is built on a set of non-smooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is -1/4 power of n, where n is the sample size. The rate is achieved by a simple test based on the difference between non-parametric and parametric variance estimators. Simulation studies illustrate that the test has reasonable power against various non-smooth alternatives. The empirical application to Engel curves specification emphasizes the good applicability of the test.

Free Research Field

計量経済学

Academic Significance and Societal Importance of the Research Achievements

既存の研究では 関数型の検定の minimax rate は対立仮説が滑らかな関数の集合に含まれる場合のみしかわかっていなかった。しかし、経済学の場合には流動性制約などによって需要関数やエンゲル曲線が微分不可能な点が存在することがあることが知られている。
未知の誤差分散構造を持つ操作変数回帰の設定では，対立仮設が滑らかでない関数である場合の最適な minimax rate はnをサンプルサイズとして nの(-1/4)乗 であることを発見し、簡単な検定を開発した。