用于条件均值独立性的多尺度球检验
A Multiscale Ball Test for Conditional Mean Independence
AI总结：
针对条件均值独立性检验功效不足的问题，提出多尺度球条件均值独立性（MBCMI）检验，经理论推导和实验验证，该检验在金融数据中可消除全样本拒绝，揭示同期条件均值依赖性。
AI中文摘要：
当偏离仅局限于多元预测空间的有界部分且相关空间尺度未知时，条件均值独立性检验会丧失功效。我们提出多尺度球条件均值独立性（MBCMI）检验，该检验在预测集的每个数据点为中心的球上聚合结果变量中经支撑加权的局部均值对比。固定网格理论确定总体目标，建立对网格可见备择假设的一致性，并推导由球平滑均值偏离控制的Pitman局部功效极限。对于序列数据，确立了具有条件符号对称创新的稳定有限阶自回归的可行递归符号自助法有效性。应用对齐的序列零假设实验以4.25%的比例拒绝原假设，MBCMI被证明对局部和径向信号最强。预测者定律实验表明，这些结论并非独立高斯协变量的人为结果。在月度美国金融数据中，交叉拟合残差MBCMI检验消除了所有全样本拒绝，表明存在同期条件均值依赖性，而非独特非线性结构的证据。
英文摘要：
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.
