Minimax Bounds for Estimation of Normal Location Mixtures

This thesis deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the application of standard minimax lower bound techniques. The...

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Main Author Kim, Kyoung Hee
Format Dissertation
LanguageEnglish
Published ProQuest Dissertations & Theses 01.01.2012
Subjects
Statistics
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Abstract This thesis deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the application of standard minimax lower bound techniques. The subtlety is reflected in the lower bounds under various loss functions, which are shown to be slower than the parametric rate inflated by only logarithmic factors. The sharpest results are obtained for squared error loss where the optimal inflation factor is the square root of the logarithm of the sample size. All the lower bounds are developed using novel Fourier and orthogonal polynomial methods.
AbstractList This thesis deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the application of standard minimax lower bound techniques. The subtlety is reflected in the lower bounds under various loss functions, which are shown to be slower than the parametric rate inflated by only logarithmic factors. The sharpest results are obtained for squared error loss where the optimal inflation factor is the square root of the logarithm of the sample size. All the lower bounds are developed using novel Fourier and orthogonal polynomial methods.
Author Kim, Kyoung Hee
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Title Minimax Bounds for Estimation of Normal Location Mixtures
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