An explicit third-order median bias-corrected estimator is proposed for smooth scalar focus parameters via Cornish-Fisher expansion of the MLE.
McCullagh.Tensor Methods in Statistics
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Proves total variation distance between finite neural network output laws and their order-(4m-1) Edgeworth approximations is O(n^{-m}) with matching lower bounds, under invertible covariance and polynomially bounded activations; extends to conditionally Gaussian sequences.
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Focused median bias reduction
An explicit third-order median bias-corrected estimator is proposed for smooth scalar focus parameters via Cornish-Fisher expansion of the MLE.
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Optimal Non-Asymptotic Edgeworth Expansions for Multivariate Neural Network Outputs
Proves total variation distance between finite neural network output laws and their order-(4m-1) Edgeworth approximations is O(n^{-m}) with matching lower bounds, under invertible covariance and polynomially bounded activations; extends to conditionally Gaussian sequences.