Sparse high-dimensional varying coefficient model: non-asymptotic\n minimax study

2013/12/14 by Olga Klopp, Klopp, Olga, Marianna Pensky +1
Economics, Econometrics and Finance · Mathematics · #62C20 #62H12 #62J05 #FOS: Mathematics #Spatial and Panel Data Analysis #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1312.4087

openalex publication_date 2013/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The objective of the present paper is to develop a minimax theory for the\nvarying coefficient model in a non-asymptotic setting.\n We consider a high-dimensional sparse varying coefficient model where only\nfew of the covariates are present and only some of those covariates are time\ndependent. Our analysis allows the time dependent covariates to have different\ndegrees of smoothness and to be spatially inhomogeneous. We develop the minimax\nlower bounds for the quadratic risk and construct an adaptive estimator which\nattains those lower bounds within a constant (if all time-dependent covariates\nare spatially homogeneous) or logarithmic factor of the number of observations.\n

Citations

• Statistical inference in compound functional models
• Consistency of the group Lasso and multiple kernel learning

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