Paper
Minimax estimation for Varying Coefficient Model via Laguerre Series
Authors
Rida Benhaddou, Khalid Chokri, Jackson Pinschenat
Abstract
We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal convergence rates in the minimax sense. These rates are derived for functional coefficients that belong to Laguerre-Sobolev space. The method is based on approximating the functional coefficients using truncated Laguerre series and choosing empirical Laguerre coefficients that minimize the least squares criterion. In addition, we establish the asymptotic normality of the estimator for the functional coefficients, construct their confidence intervals, and establish point-wise hypothesis tests about their true values. A simulations study is carried out to examine the finite-sample properties of the proposed methodology. A real data set is considered as well, and results based on the proposed methodology are compared to those based on selected existing approaches.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.08538v1</id>\n <title>Minimax estimation for Varying Coefficient Model via Laguerre Series</title>\n <updated>2026-03-09T16:06:47Z</updated>\n <link href='https://arxiv.org/abs/2603.08538v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.08538v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>We delve into the estimation of the functional coefficients and inference for varying coefficient model. Applying Laguerre series, we develop an estimator for the vector of functional coefficients that attains asymptotically optimal convergence rates in the minimax sense. These rates are derived for functional coefficients that belong to Laguerre-Sobolev space. The method is based on approximating the functional coefficients using truncated Laguerre series and choosing empirical Laguerre coefficients that minimize the least squares criterion. In addition, we establish the asymptotic normality of the estimator for the functional coefficients, construct their confidence intervals, and establish point-wise hypothesis tests about their true values. A simulations study is carried out to examine the finite-sample properties of the proposed methodology. A real data set is considered as well, and results based on the proposed methodology are compared to those based on selected existing approaches.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.ST'/>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ME'/>\n <published>2026-03-09T16:06:47Z</published>\n <arxiv:comment>27 pages, 6 figures</arxiv:comment>\n <arxiv:primary_category term='math.ST'/>\n <author>\n <name>Rida Benhaddou</name>\n </author>\n <author>\n <name>Khalid Chokri</name>\n </author>\n <author>\n <name>Jackson Pinschenat</name>\n </author>\n </entry>"
}