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A general approach to heteroscedastic linear regression

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A general approach to heteroscedastic linear regression. / Leslie, David S.; Kohn, Robert; Nott, David J.
In: Statistics and Computing, Vol. 17, No. 2, 25.05.2007, p. 131-146.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Leslie, DS, Kohn, R & Nott, DJ 2007, 'A general approach to heteroscedastic linear regression', Statistics and Computing, vol. 17, no. 2, pp. 131-146. https://doi.org/10.1007/s11222-006-9013-8

APA

Leslie, D. S., Kohn, R., & Nott, D. J. (2007). A general approach to heteroscedastic linear regression. Statistics and Computing, 17(2), 131-146. https://doi.org/10.1007/s11222-006-9013-8

Vancouver

Leslie DS, Kohn R, Nott DJ. A general approach to heteroscedastic linear regression. Statistics and Computing. 2007 May 25;17(2):131-146. doi: 10.1007/s11222-006-9013-8

Author

Leslie, David S. ; Kohn, Robert ; Nott, David J. / A general approach to heteroscedastic linear regression. In: Statistics and Computing. 2007 ; Vol. 17, No. 2. pp. 131-146.

Bibtex

@article{1237971a237e45a689002bd9a8862c01,
title = "A general approach to heteroscedastic linear regression",
abstract = "Our article presents a general treatment of the linear regression model, in which the error distribution is modelled nonparametrically and the error variances may be heteroscedastic, thus eliminating the need to transform the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with parsimony achieved through variable selection and model averaging. A Bayesian approach is used for inference with priors that are data-based so that estimation can be carried out automatically with minimal input by the user. A Dirichlet process mixture prior is used to model the error distribution nonparametrically; when there are no regressors in the model, the method reduces to Bayesian density estimation, and we show that in this case the estimator compares favourably with a well-regarded plug-in density estimator. We also consider a method for checking the fit of the full model. The methodology is applied to a number of simulated and real examples and is shown to work well.",
keywords = "Density estimation, Dirichlet process mixture, Heteroscedasticity, Model checking, Nonparametric regression, Variable selection",
author = "Leslie, {David S.} and Robert Kohn and Nott, {David J.}",
year = "2007",
month = may,
day = "25",
doi = "10.1007/s11222-006-9013-8",
language = "English",
volume = "17",
pages = "131--146",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - A general approach to heteroscedastic linear regression

AU - Leslie, David S.

AU - Kohn, Robert

AU - Nott, David J.

PY - 2007/5/25

Y1 - 2007/5/25

N2 - Our article presents a general treatment of the linear regression model, in which the error distribution is modelled nonparametrically and the error variances may be heteroscedastic, thus eliminating the need to transform the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with parsimony achieved through variable selection and model averaging. A Bayesian approach is used for inference with priors that are data-based so that estimation can be carried out automatically with minimal input by the user. A Dirichlet process mixture prior is used to model the error distribution nonparametrically; when there are no regressors in the model, the method reduces to Bayesian density estimation, and we show that in this case the estimator compares favourably with a well-regarded plug-in density estimator. We also consider a method for checking the fit of the full model. The methodology is applied to a number of simulated and real examples and is shown to work well.

AB - Our article presents a general treatment of the linear regression model, in which the error distribution is modelled nonparametrically and the error variances may be heteroscedastic, thus eliminating the need to transform the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with parsimony achieved through variable selection and model averaging. A Bayesian approach is used for inference with priors that are data-based so that estimation can be carried out automatically with minimal input by the user. A Dirichlet process mixture prior is used to model the error distribution nonparametrically; when there are no regressors in the model, the method reduces to Bayesian density estimation, and we show that in this case the estimator compares favourably with a well-regarded plug-in density estimator. We also consider a method for checking the fit of the full model. The methodology is applied to a number of simulated and real examples and is shown to work well.

KW - Density estimation

KW - Dirichlet process mixture

KW - Heteroscedasticity

KW - Model checking

KW - Nonparametric regression

KW - Variable selection

U2 - 10.1007/s11222-006-9013-8

DO - 10.1007/s11222-006-9013-8

M3 - Journal article

VL - 17

SP - 131

EP - 146

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -