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Doubly penalized likelihood estimator in heteroscedastic regression

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  • Yuan, Ming
  • Wahba, Grace

Abstract

A penalized likelihood estimation procedure is developed for heteroscedastic regression. A distinguishing feature of the new methodology is that it estimates both the mean and variance functions simultaneously without parametric assumption for either. An efficient implementation of the estimating procedure is also provided. The procedure is illustrated by a Monte Carlo example. A potential generalization, and application to the covariance modeling problem in numerical weather prediction is noted.

Suggested Citation

  • Yuan, Ming & Wahba, Grace, 2004. "Doubly penalized likelihood estimator in heteroscedastic regression," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 11-20, August.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:11-20
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    References listed on IDEAS

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    1. Ruppert, D. & Wand, M.P. & Holst, U. & Hossjer, O., "undated". "Local Polynomial Variance Function Estimation," Statistics Working Paper _007, Australian Graduate School of Management.
    2. Gallant, A. Ronald & Tauchen, George, 1997. "Estimation Of Continuous-Time Models For Stock Returns And Interest Rates," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 135-168, January.
    3. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    4. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
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    1. I. Gijbels & I. Prosdocimi, 2011. "Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2391-2411, December.

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