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Efficient estimation in a semiparametric additive regression model with autoregressive errors

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  • Schick, Anton

Abstract

In this paper we characterize and construct efficient estimates of the regression parameter [beta] in the semiparametric additive regression model Yj = [beta]TUj+[gamma](Vj), J=1,2 ..., where [beta] is an unknown vector in Rm, [gamma] is an unknown Lipschitz-continuous function from [0, 1] to R, (U1, V1), (U2, V2), ... are independent Rm x [0, 1]-valued random vectors with common distribution G and are independent of X1, X2, ..., and X1, X2, ... is a stationary AR(1) process with parameter [alpha] belonging to the interval (- 1, 1) and innovation density f with mean 0 and finite variance.

Suggested Citation

  • Schick, Anton, 1996. "Efficient estimation in a semiparametric additive regression model with autoregressive errors," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 339-361, February.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:2:p:339-361
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    References listed on IDEAS

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    1. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    2. Schick, Anton, 1994. "Estimation of the autocorrelation coefficient in the presence of a regression trend," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 371-380, December.
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    Cited by:

    1. Sneddon, Gary & Sutradhar, Brajendra C., 2004. "On semiparametric familial-longitudinal models," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 369-379, September.
    2. Arash Nademi & Rahman Farnoosh, 2014. "Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 275-293, February.
    3. Germán Aneiros & Alejandro Quintela, 2001. "Asymptotic properties in partial linear models under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 333-355, December.
    4. Forrester Jeffrey S. & Hooper William J. & Peng Hanxiang & Schick Anton, 2003. "On the construction of efficient estimators in semiparametric models," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 109-138, February.

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