Document Type
Lecture
Publication Date
3-26-2026
Abstract
In this talk, we analyze uniform estimation of covariate-dependent copula parameters using local likelihood methods. Building on our recent preprint establishing uniform stochastic equicontinuity and convergence rates, we derive minimax lower bounds over Holder classes of calibration functions. Under mild regularity conditions on the copula family and the covariate design, we show that the minimax sup-norm risk over a compact covariate region is bounded below by the classical nonparametric rate for smooth functions on an s-dimensional domain. The proof combines a localized packing construction with a Fano–Le Cam testing argument, using second-order expansions of the conditional copula likelihood to control information distances. As a consequence, local polynomial likelihood estimators achieve the minimax rate up to the logarithmic factors inherent to uniform estimation, providing a sharp optimality justification for their use in conditional copula modeling.
Relational Format
presentation
Recommended Citation
Muia, Mathias, "Minimax Lower Bounds for Uniform Estimation of Covariate-Dependent Copula Parameters" (2026). Probability & Statistics Seminar. 76.
https://egrove.olemiss.edu/math_statistics/76
Accessibility Status
Searchable text