
A fast subsampling method for estimating the distribution of signaltonoise ratio statistics in nonparametric time series regression models
Signaltonoise ratio (SNR) statistics play a central role in many appli...
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Robust Inference Under Heteroskedasticity via the Hadamard Estimator
Drawing statistical inferences from large datasets in a modelrobust way...
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Quadratic Discriminant Analysis under Moderate Dimension
Quadratic discriminant analysis (QDA) is a simple method to classify a s...
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Sharp Biasvariance Tradeoffs of Hard Parameter Sharing in Highdimensional Linear Regression
Hard parameter sharing for multitask learning is widely used in empiric...
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Exploitation of error correlation in a large analysis validation: GlobCurrent case study
An assessment of variance in ocean current signal and noise shared by in...
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Generalized Power Method for Generalized Orthogonal Procrustes Problem: Global Convergence and Optimization Landscape Analysis
Given a set of multiple point clouds, how to find the rigid transformati...
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Inference and Computation for Sparsely Sampled Random Surfaces
Nonparametric inference for functional data over twodimensional domain...
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ModerateDimensional Inferences on Quadratic Functionals in Ordinary Least Squares
Statistical inferences on quadratic functionals of linear regression parameter have found wide applications including signal detection, one/twosample global testing, inference of fraction of variance explained and genetic coheritability. Conventional theory based on ordinary least squares estimator works perfectly in the fixeddimensional regime, but fails when the parameter dimension p_n grows proportionally to the sample size n. In some cases, its performance is not satisfactory even when n≥ 5p_n. The main contribution of this paper is to illustrate that signaltonoise ratio (SNR) plays a crucial role in the moderatedimensional inferences where _n→∞ p_n/n = τ∈ (0, 1). In the case of weak SNR, as often occurred in the moderatedimensional regime, both bias and variance need to be corrected in the traditional inference procedures. The amount of correction mainly depends on SNR and τ, and could be fairly large as τ→1. However, the classical fixeddimensional results continue to hold if and only if SNR is large enough, say when p_n diverges but slower than n. Our general theory holds, in particular, without Gaussian design/error or structural parameter assumption, and apply to a broad class of quadratical functionals, covering all aforementioned applications. The mathematical arguments are based on random matrix theory and leaveoneout method. Extensive numerical results demonstrate the satisfactory performances of the proposed methodology even when p_n≥ 0.9n in some extreme case.
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