New statistical method for minimax risk estimation in complex models

This paper delves into squared-error estimation within statistical models where a nuisance parameter is not fully identifiable but influences a target parameter that becomes negligible in that specific context. The research provides conditions under which the minimax risk, calculated along a critical path, accurately reflects the asymptotic minimax risk across the entire parameter space for models with higher-order profile expansions. An estimator is proposed that achieves this leading constant uniformly, even without knowledge of the profile coordinates, by utilizing calibration estimates, local feature means, and empirical recovery features. The paper verifies these conditions in two distinct models: a Gaussian logistic errors-in-variables regression and a degree-balanced replicated-network model, determining specific risk coefficients and constants for each. AI

IMPACT This research may lead to more robust statistical modeling techniques applicable in machine learning contexts.

RANK_REASON The item is an academic paper detailing a new statistical method. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv stat.ML →

• Errors-in-Variables Regression Using Stein Estimates
• Gaussian function
• logistics
• network model

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