zbMATH — the first resource for mathematics

A semiparametric Bayesian approach to joint mean and variance models. (English) Zbl 1281.62074
Summary: We propose a fully Bayesian inference for semiparametric joint mean and variance models on the basis of B-spline approximations of nonparametric components. An efficient MCMC method which combines the Gibbs sampler and Metropolis-Hastings algorithm is suggested for the inference, and the methodology is illustrated through a simulation study and a real example.

62F15 Bayesian inference
62G08 Nonparametric regression and quantile regression
65C40 Numerical analysis or methods applied to Markov chains
65C60 Computational problems in statistics (MSC2010)
GLIM; SemiPar
Full Text: DOI
[1] Aitkin, M., Modelling variance heterogeneity in normal regression using GLIM, Appl. Stat., 36, 332-339, (1987)
[2] Cepeda, E.; Gamerman, D., Bayesian modeling of variance heterogeneity in normal regression models, Braz. J. Probab. Stat., 14, 207-221, (2001) · Zbl 0983.62013
[3] Chen, X. D., Bayesian analysis of semiparametric mixed-effects models for zero-inflated count data, Comm. Statist. Theory Methods, 38, 1815-1833, (2009) · Zbl 1167.62025
[4] Chen, X. D.; Tang, N. S., Bayesian analysis of semiparametric reproductive dispersion mixed-effects models, Comput. Statist. Data Anal., 54, 2145-2158, (2010) · Zbl 1284.62168
[5] Fan, J.; Gijbels, I., Local polynomial modelling and its application, (1996), Chapman and Hall New York · Zbl 0873.62037
[6] Gelman, A., Inference and monitoring convergence in Markov chain Monte Carlo in practice, (1996), Chapman and Hall London
[7] Gelman, A.; Roberts, G. O.; Gilks, W. R., Efficient metropolis jumping rules, (Bernardo, J. M.; Berger, J. O.; Dawid, A. P.; Smith, A. F.M., Bayesian Statistics, Vol. 5, (1995), Oxford University Press Oxford), 599-607
[8] Geyer, C. J., Practical Markov chain Monte Carlo, Statist. Sci., 7, 473-511, (1992)
[9] Harvey, A. C., Estimating regression models with multiplicative heteroscedasticity, Econometrica, 44, 460-465, (1976) · Zbl 0333.62040
[10] He, X.; Fung, W. K.; Zhu, Z. Y., Robust estimation in a generalized partial linear model for clustered data, J. Amer. Statist. Assoc., 100, 1176-1184, (2005) · Zbl 1117.62351
[11] Lee, S. Y.; Zhu, H. T., Statistical analysis of nonlinear structural equation models with continuous and polytomous data, British J. Math. Statist. Psych., 53, 209-232, (2000)
[12] Li, A. P.; Chen, Z. X.; Xie, F. C., Diagnostic analysis for heterogeneous log-birnbaum – saunders regression models, Statist. Probab. Lett., 82, 1690-1698, (2012) · Zbl 1334.62174
[13] Lin, T. I.; Wang, W. L., Bayesian inference in joint modelling of location and scale parameters of the t distribution for longitudinal data, J. Statist. Plann. Inference, 141, 1543-1553, (2011) · Zbl 1204.62040
[14] Lin, J. G.; Wei, B. C., Testing for heteroscedasticity in nonlinear regression models, Comm. Statist. Theory Methods, 32, 171-192, (2003) · Zbl 1183.62112
[15] Park, R. E., Estimation with heteroscedastic error terms, Econometrica, 34, 888, (1966)
[16] Roberts, G., Markov chain concepts related to sampling algorithm, (1996), Chapman and Hall London · Zbl 0839.62078
[17] Ruppert, D.; Wand, M. P.; Carroll, R. J., Semiparametric regression, (2003), Cambridge University Press Cambridge, New York · Zbl 1038.62042
[18] Schumaker, L. L., Spline function, (1981), Wiley New York · Zbl 0449.41004
[19] Wu, L. C.; Li, H. Q., Variable selection for joint mean and dispersion models of the inverse Gaussian distribution, Metrika, 75, 795-808, (2012) · Zbl 1410.62132
[20] Xie, F. C.; Wei, B. C.; Lin, J. G., Homogeneity diagnostics for skew-normal nonlinear regression models, Statist. Probab. Lett., 79, 821-827, (2009) · Zbl 1157.62044
[21] Xu, D. K.; Zhang, Z. Z., Regularized REML for estimation in heteroscedastic regression models, (Li, S., Nonlinear Maths for Uncertainty and its Application, AISC, vol. 100, (2011), Springer Press Berlin, Heidelberg), 495-502 · Zbl 06185947
[22] Zhang, Z. Z.; Wang, D. R., Simultaneous variable selection for heteroscedastic regression models, Sci. China Math., 54, 3, 515-530, (2011) · Zbl 1216.62104
[23] Zhao, P. X.; Xue, L. G., Variable selection for semiparametric varying coefficient partially linear errors-in-variables models, J. Multivariate Anal., 101, 1872-1883, (2010) · Zbl 1190.62090
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.