Semiparametric Bernstein–von Mises for the error standard deviation

R. Jonge, de, J.H. Zanten, van

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

2 Citaties (Scopus)

Uittreksel

We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein–von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a hierarchical spline-based prior on the regression function and an independent prior on the error variance, can simultaneously achieve adaptive, rate-optimal estimation of a smooth, multivariate regression function and efficient, n-v-consistent estimation of the error standard deviation.
TaalEngels
Pagina's217-243
TijdschriftElectronic Journal of Statistics
Volume7
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 2013

Vingerafdruk

Standard deviation
Bayes Procedures
Regression Function
Consistent Estimation
Optimal Estimation
Multivariate Functions
Multivariate Regression
Nonparametric Regression
Marginal Distribution
Posterior distribution
Spline

Citeer dit

Jonge, de, R. ; Zanten, van, J.H./ Semiparametric Bernstein–von Mises for the error standard deviation. In: Electronic Journal of Statistics. 2013 ; Vol. 7, Nr. 1. blz. 217-243
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Jonge, de, R & Zanten, van, JH 2013, 'Semiparametric Bernstein–von Mises for the error standard deviation' Electronic Journal of Statistics, vol. 7, nr. 1, blz. 217-243. DOI: 10.1214/13-EJS768

Semiparametric Bernstein–von Mises for the error standard deviation. / Jonge, de, R.; Zanten, van, J.H.

In: Electronic Journal of Statistics, Vol. 7, Nr. 1, 2013, blz. 217-243.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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AB - We study Bayes procedures for nonparametric regression problems with Gaussian errors, giving conditions under which a Bernstein–von Mises result holds for the marginal posterior distribution of the error standard deviation. We apply our general results to show that a single Bayes procedure using a hierarchical spline-based prior on the regression function and an independent prior on the error variance, can simultaneously achieve adaptive, rate-optimal estimation of a smooth, multivariate regression function and efficient, n-v-consistent estimation of the error standard deviation.

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Jonge, de R, Zanten, van JH. Semiparametric Bernstein–von Mises for the error standard deviation. Electronic Journal of Statistics. 2013;7(1):217-243. Beschikbaar vanaf, DOI: 10.1214/13-EJS768

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