Smoothing spline estimation of variance functions

Anna Liu; Tiejun Tong; Yuedong Wang

doi:10.1198/106186007X204528

Smoothing spline estimation of variance functions

Anna Liu
, Tiejun Tong
, Yuedong Wang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

19 Citations (Scopus)

Abstract

This article considers spline smoothing of variance functions. We focus on selection of the smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross-validation (GACV), and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, generalized cross-validation (GCV), and GML methods. The direct UBR and GML methods perform better than the GACV method. An application to array-based comparative genomic hybridization data illustrates the usefulness of the proposed methods.

Original language	English
Pages (from-to)	312-329
Number of pages	18
Journal	Journal of Computational and Graphical Statistics
Volume	16
Issue number	2
DOIs	https://doi.org/10.1198/106186007X204528
Publication status	Published - Jun 2007

User-Defined Keywords

Array-based comparative genomic hybridization
Generalized approximate cross-validation
Generalized maximum likelihood
Heteroscedasticity
Smoothing parameter
Unbiased risk

Access to Document

10.1198/106186007X204528

Cite this

@article{da13e8bd0f1f4a00b9b5b2e7f8d432ca,

title = "Smoothing spline estimation of variance functions",

abstract = "This article considers spline smoothing of variance functions. We focus on selection of the smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross-validation (GACV), and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, generalized cross-validation (GCV), and GML methods. The direct UBR and GML methods perform better than the GACV method. An application to array-based comparative genomic hybridization data illustrates the usefulness of the proposed methods. ",

keywords = "Array-based comparative genomic hybridization, Generalized approximate cross-validation, Generalized maximum likelihood, Heteroscedasticity, Smoothing parameter, Unbiased risk",

author = "Anna Liu and Tiejun Tong and Yuedong Wang",

note = "Funding information: This research was supported by NIH Grant R01 GM58533. The authors thank the editor, the associate editor and two referees for their constructive comments and suggestions that have led to a substantial improvement in the article. Publisher copyright: {\textcopyright} 2007 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America",

year = "2007",

month = jun,

doi = "10.1198/106186007X204528",

language = "English",

volume = "16",

pages = "312--329",

journal = "Journal of Computational and Graphical Statistics",

issn = "1061-8600",

publisher = "Taylor and Francis Ltd.",

number = "2",

}

TY - JOUR

T1 - Smoothing spline estimation of variance functions

AU - Liu, Anna

AU - Tong, Tiejun

AU - Wang, Yuedong

N1 - Funding information: This research was supported by NIH Grant R01 GM58533. The authors thank the editor, the associate editor and two referees for their constructive comments and suggestions that have led to a substantial improvement in the article. Publisher copyright: © 2007 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America

PY - 2007/6

Y1 - 2007/6

N2 - This article considers spline smoothing of variance functions. We focus on selection of the smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross-validation (GACV), and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, generalized cross-validation (GCV), and GML methods. The direct UBR and GML methods perform better than the GACV method. An application to array-based comparative genomic hybridization data illustrates the usefulness of the proposed methods.

AB - This article considers spline smoothing of variance functions. We focus on selection of the smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross-validation (GACV), and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, generalized cross-validation (GCV), and GML methods. The direct UBR and GML methods perform better than the GACV method. An application to array-based comparative genomic hybridization data illustrates the usefulness of the proposed methods.

KW - Array-based comparative genomic hybridization

KW - Generalized approximate cross-validation

KW - Generalized maximum likelihood

KW - Heteroscedasticity

KW - Smoothing parameter

KW - Unbiased risk

UR - https://www.scopus.com/pages/publications/34250738972

U2 - 10.1198/106186007X204528

DO - 10.1198/106186007X204528

M3 - Journal article

SN - 1061-8600

VL - 16

SP - 312

EP - 329

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

IS - 2

ER -

Smoothing spline estimation of variance functions

Abstract

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this