A Multiscale Ball Test for Conditional Mean Independence

2026-08-21

AI Summary

为解决多尺度条件下均值独立性检验失效问题，提出了一种基于球体的多尺度条件均值独立性(MBCMI)检验方法。

Abstract

Tests of conditional mean independence can lose power when departures are confined to a bounded part of a multivariate predictor space and the relevant spatial scale is unknown. We propose a Multiscale Ball Conditional Mean Independence (MBCMI) test that aggregates support-weighted local mean contrasts in an outcome variable across balls centered on each data point in a predictor set. Fixed-grid theory identifies the population target, establishes consistency for grid-visible alternatives, and derives a Pitman local-power limit governed by the ball-smoothed mean departure. For serial data, feasible recursive-sign-bootstrap validity for stable finite-order autoregressions with conditionally sign-symmetric innovations is established. Application-aligned serial null experiments reject 4.25% of the time. MBCI is demonstrated to be strongest for local and radial signals. Predictor-law experiments show that these conclusions are not an artefact of independent Gaussian covariates. In monthly U.S. finance data, cross-fitted residual MBCMI tests remove every full-sample rejection, suggesting contemporaneous conditional-mean dependence rather than evidence of distinctive nonlinear structure.

Problem

• conditional mean independence
• multivariate predictor space
• spatial scale

Innovation

• Multiscale Ball Conditional Mean Independence (MBCMI)
• support-weighted local mean contrasts
• fixed-grid theory
• recursive sign-bootstrap
• local and radial signals