Nonparametric curve estimation with bernstein estimates
Copyright policy )Nonparametric curve estimation with bernstein estimates
For the estimation of the regression function in a random design model a Bernstein type estimator is proposed. The author studies various local and global asymptotic properties of this estimator: Consistency and asymptotic normality at a fixed point are proved and an asymptotic expression for the expectation of the estimator is derived. Further, an asymptotic expansion for the expectation of a quadratic deviation of the estimator is given; this criterion can be regarded as a modification of the mean integrated squared error. Finally, sufficient conditions for strong consistency, measured in \(L_1\)- and sup- norm are presented.
- DigiZeitschriften Germany
- Osnabrück University Germany
asymptotic expansion, Bernstein polynomials, Article, random design model, Density estimation, 510.mathematics, nonparametric regression, Asymptotic properties of nonparametric inference, smoothed regressograms
asymptotic expansion, Bernstein polynomials, Article, random design model, Density estimation, 510.mathematics, nonparametric regression, Asymptotic properties of nonparametric inference, smoothed regressograms
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).44 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!