ﻻ يوجد ملخص باللغة العربية
The paper continues the authors work on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper it is shown that if the mean response function satisfies a condition of `saturated identifiability, which was introduced by Pronzato cite{Pronzato}, then the adaptive least squares estimators are strongly consistent. The condition states that the regression parameter is identifiable under any saturated design, i.e., the values of the mean response function at any $p$ distinct design points determine the parameter point uniquely where, typically, $p$ is the dimension of the regression parameter vector. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. If the true parameter point is an interior point of the parameter space then under some smoothness assumptions and asymptotic homoscedasticity of random errors the asymptotic normality of adaptive least squares estimators is obtained.
We study the performance of the Least Squares Estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a $p$-th moment ($pgeq 1$). In such a heavy-tailed regression setting, we s
For a nonlinear regression model the information matrices of designs depend on the parameter of the model. The adaptive Wynn-algorithm for D-optimal design estimates the parameter at each step on the basis of the employed design points and observed r
The asymptotic optimality (a.o.) of various hyper-parameter estimators with different optimality criteria has been studied in the literature for regularized least squares regression problems. The estimators include e.g., the maximum (marginal) likeli
We study the asymptotic properties of the SCAD-penalized least squares estimator in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We are particularly interested in the use of this
We consider a nonparametric version of the integer-valued GARCH(1,1) model for time series of counts. The link function in the recursion for the variances is not specified by finite-dimensional parameters, but we impose nonparametric smoothness condi