Paper gives exact global minimax risk near nonidentification
Original title: Exact Global Minimax Risk near Nonidentification
Conditions let one estimator match the leading constant uniformly; two models fix fifth- and sixth-order risk constants.
The paper studies squared-error estimation when a nuisance parameter is unidentified on a submodel but still affects a vanishing target. For higher-order profile expansions, it states conditions under which the largest critical-path minimax risk is the exact asymptotic minimax risk over the full parameter space. An estimator using calibration estimates, a local feature mean and an empirical recovery feature attains the leading constant with profile coordinates unknown. The conditions are checked in Gaussian logistic errors-in-variables regression and a replicated-network model.
- The constant is expressed through a bounded-normal decision problem.
- The logistic errors-in-variables model uses one surrogate and two unknown variances.
- That model yields a fifth-order global coefficient risk and its exact constant.
- A degree-balanced network model yields sixth-order edge-contrast risk with unknown block proportions.
From the original article
1 min read at arxiv.orgWe study squared-error estimation when a nuisance parameter is unidentified on a submodel but affects a target that vanishes there. For models with higher-order profile expansions, we give sufficient conditions under which the largest critical-path minimax risk is the exact asymptotic minimax risk over the full parameter space.
By Kaiyue Yang · arxiv.org
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