论文信息 - Semi-nonparametric estimation with Bernstein polynomials

Semi-nonparametric estimation with Bernstein polynomials

Abstract This paper proposes a semi-nonparametric model based upon Bernstein polynomials. We prove that the univariate Bernstein semi-nonparametric estimator is consistent for the true function and its first and second derivatives, and thus it is globally flexible and globally regular.

Barry Smith | Neal Madras | Barry F. Smith | N. Madras | Pok Man Chak

[1] William A. Barnett,et al. The Müntz-Szatz demand system , 1983 .

[2] A. Gallant,et al. Unbiased determination of production technologies , 1982 .

[3] A. Ronald Gallant,et al. The Fourier Flexible Form , 1984 .

[4] S. Geman,et al. Nonparametric Maximum Likelihood Estimation by the Method of Sieves , 1982 .

[5] William A. Barnett,et al. The Muntz-Szatz demand system: An application of a globally well behaved series expansion , 1983 .

[6] Walter Diewert,et al. An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function , 1971, Journal of Political Economy.

[7] A. Gallant,et al. On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form , 1981 .

[8] P. Butzer. On Two-Dimensional Bernstein Polynomials , 1953, Canadian Journal of Mathematics.

[9] D. Terrell. Flexibility and regularity properties of the asymptotically ideal production model , 1995 .

[10] Edward H. Kingsley. Bernstein polynomials for functions of two variables of class , 1951 .