Nonparametric density estimation in high-dimensions

Chong Gu, Yongho Jeon, Yi Lin

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Penalized likelihood density estimation provides an effective approach to the nonparametric fitting of graphical models, with conditional independence structures characterized via selective term elimination in functional ANOVA decompositions of the log density. A bottleneck in the approach has been the cost of numerical integration, which has limited its application to low-dimensional problems. In Jeon and Lin (2006), a reformulation was proposed to replace multi-dimensional integrals by sums of products of univariate integrals, greatly reducing the numerical burden in high-dimensional problems. In this article, we derive a cross-validation score for use with the reformulation that delivers effective smoothing parameter selection at a manageable computational cost, introduce a geometric inference tool for the "testing" of model terms, and calculate the asymptotic convergence rates of the estimates. An assortment of practical issues are investigated through empirical studies, and open-source software is illustrated with data examples.

Original languageEnglish
Pages (from-to)1131-1153
Number of pages23
JournalStatistica Sinica
Volume23
Issue number3
DOIs
Publication statusPublished - 2013 Jul 1

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Nonparametric Density Estimation
Reformulation
Higher Dimensions
Penalized Likelihood
Conditional Independence
Asymptotic Convergence
Open Source Software
Parameter Selection
Smoothing Parameter
Density Estimation
Graphical Models
Term
Cross-validation
Empirical Study
Numerical integration
Univariate
Elimination
Convergence Rate
Computational Cost
High-dimensional

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Gu, Chong ; Jeon, Yongho ; Lin, Yi. / Nonparametric density estimation in high-dimensions. In: Statistica Sinica. 2013 ; Vol. 23, No. 3. pp. 1131-1153.
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Nonparametric density estimation in high-dimensions. / Gu, Chong; Jeon, Yongho; Lin, Yi.

In: Statistica Sinica, Vol. 23, No. 3, 01.07.2013, p. 1131-1153.

Research output: Contribution to journalArticle

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