Asymptotic Equivalence Theory for Nonparametric Regression With Random Design

Asymptotic Equivalence Theory for Nonparametric Regression with Random Design by Lawrence

This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings between the nonparametric regression and the whitenoise experiments, which provide synthetic obser...

Asymptotic equivalence for nonparametric regression with multivariate and random design

We show that nonparametric regression is asymptotically equivalent in Le Cam’s sense with a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework based on approximation spaces, which permits to achieve asymptotic equivalence even in the cases of multivariate and random design.

Asymptotic Equivalence Theory For Nonparametric Regression With Random Noise

Asymptotic Equivalence of Nonparametric Autoregression and Nonparametric Regression

where (εi)i=1,...,n are i.i.d. random variables. The unknown autoregression function f is then the target of statistical inference and the development of efficient estimators is a natural task for theoretically oriented statisticians. On the one hand, it has been recognized for a long time that commonly used estimators in model (1) have the same asymptotic behavior as corresponding estimators i...

Wavelets for Nonparametric Stochastic Regression with Pairwise Negative Quadrant Dependent Random Variables

We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of pairwise negative quadrant dependent random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts st...