Degenerate degree-two U-statistics have non-Gaussian limits, making sequential inference substantially more difficult than in the nondegenerate case. However, row normalization preserves the target parameter and makes the centered numerator a martingale on a harmonic variance clock, at the cost of logarithmic variance...
It is determined that sharp minimax rates for distribution estimation under pure local differential privacy at critical query smoothness are determined, and matching lower bounds allow finite public blackboard interaction and repeated participation under each user's total privacy budget.
Sequential quantile inference is difficult under local differential privacy because every record is randomized before reaching the analyst and the limiting quantile variance depends on an unknown density. We develop an online procedure that combines randomized response with dynamically chained parallel stochastic gradi...
In high-dimensional settings, multicollinearity is a pervasive issue that can substantially impair the performance of feature screening methods based on marginal Fr\'echet regression. Feature screening for non-Euclidean responses becomes unreliable when ultrahigh-dimensional predictors suffer from multicollinearity, be...
Mo-Shu Xu, Le-Heng Cai, Yan-Mei Shi et al.· 0 citations
The central limit theorem and consistency of the fully transcript-based sandwich covariance and intrinsic Wald region under local differential privacy are proved and the predicted decrease in estimation error and near-nominal coverage under moderate privacy is supported.
We consider nonparametric tangent vector field regression on a Riemannian manifold without boundary. Because responses at different points lie in different tangent spaces, the proposed kernel estimator first parallel transports nearby responses to the target tangent space and then forms a volume-corrected local average...
We study simultaneous inference for maxima of canonical order-two $U$-statistics in high dimension. Degeneracy makes quadratic fluctuations leading, so ordinary Gaussian calibration can fail even after exact variance normalization. We show that the appropriate general target is a joint signed Gaussian quadratic chaos a...
Le-Heng Cai, Qi-Rui Hu· 0 citations
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