Abstract
A nuisance parameter is introduced to the semimartingale regression model proposed by Aalen (1980), and we construct two estimators for this nuisance parameter based on the results of parametric estimation which were given by Mckeague (1986) using the method of sieves. The consistency of the estimators is also provided.
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References
Aalen, O. O., A model for nonparametric regression analysis of counting processes. Lecture Notes in Statistics 2, pp. 1–25, Springer, New York, 1980.
Geman, S. and Hwang, C. R., Nonparametric maximum likelihood estimation by the method of sieves,The Annals of Statistics,10 2 (1982), 401–414.
Mckeague, I. W., Estimation for a semimartingale regression model using the method of sieves,The Annals of Statistics,14 2 (1986), 579–589.
Nguyen, H. T. and Pham, T. D., Identification of nonstatinary diffusion model by the method of sieves,SIAM J. Control and Optimization,20 (1982).
Taylor, R. L., Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces, Lecture Notes in Math. 672, Springer-Verlag, 1978.
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Pan, Y., Luo, S. Estimation of the nuisance parameter for a seminartingale regression model. Acta Mathematicae Applicatae Sinica 7, 1–5 (1991). https://doi.org/10.1007/BF02080198
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DOI: https://doi.org/10.1007/BF02080198