A debiased distributed estimation for sparse partially linear models in diverging dimensions
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We consider a distributed estimation of the double-penalized least squares approach for high dimensional partial linear models, where the sample with a total of N data points is randomly distributed among m machines and the parameters of interest are calculated by merging their m individual estimators. This paper primarily focuses on the investigation of the high dimensional linear components in partial linear models, which is often of more interest. We propose a new debiased averaging estimator of parametric coefficients on the basis of each individual estimator, and establish new non-asymptotic oracle results in high dimensional and distributed settings, provided that m≤√(N/ p) and other mild conditions are satisfied, where p is the linear coefficient dimension. We also provide an experimental evaluation of the proposed method, indicating the numerical effectiveness on simulated data. Even under the classical non-distributed setting, we give the optimal rates of the parametric estimator with a looser tuning parameter limitation, which is required for our error analysis.
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