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On invariant density estimation for ergodic diffusion processes.

Yuri A. Kutoyants (2004)

SORT

We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.

On optimality of the orthogonal block design

Ewa Synówka-Bejenka, Stefan Zontek (2012)

Discussiones Mathematicae Probability and Statistics

In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.

On orthogonal series estimation of bounded regression functions

Waldemar Popiński (2001)

Applicationes Mathematicae

The problem of nonparametric estimation of a bounded regression function f L ² ( [ a , b ] d ) , [a,b] ⊂ ℝ, d ≥ 1, using an orthonormal system of functions e k , k=1,2,..., is considered in the case when the observations follow the model Y i = f ( X i ) + η i , i=1,...,n, where X i and η i are i.i.d. copies of independent random variables X and η, respectively, the distribution of X has density ϱ, and η has mean zero and finite variance. The estimators are constructed by proper truncation of the function f ̂ ( x ) = k = 1 N ( n ) c ̂ k e k ( x ) , where the coefficients c ̂ , . . . , c ̂ N ( n ) are determined...

On pointwise adaptive curve estimation based on inhomogeneous data

Stéphane Gaïffas (2007)

ESAIM: Probability and Statistics

We want to recover a signal based on noisy inhomogeneous data (the amount of data can vary strongly on the estimation domain). We model the data using nonparametric regression with random design, and we focus on the estimation of the regression at a fixed point x0 with little, or much data. We propose a method which adapts both to the local amount of data (the design density is unknown) and to the local smoothness of the regression function. The procedure consists of a local polynomial...

On robust GMM estimation with applications in economics and finance

Ansgar Steland (2000)

Discussiones Mathematicae Probability and Statistics

Generalized Methods of Moments (GMM) estimators are a popular tool in econometrics since introduced by Hansen (1982), because this approach provides feasible solutions for many problems present in economic data where least squares or maximum likelihood methods fail when naively applied. These problems may arise in errors-in-variable regression, estimation of labor demand curves, and asset pricing in finance, which are discussed here. In this paper we study a GMM estimator for the rank modelingapproach...

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