Convergence of least squares estimators in the adaptive Wynn algorithm for a class of nonlinear regression models

09/09/2019
by   Fritjof Freise, et al.
0

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 <cit.>, 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/05/2019

The adaptive Wynn-algorithm in generalized linear models with univariate response

For a nonlinear regression model the information matrices of designs dep...
research
07/05/2023

A p-step-ahead sequential adaptive algorithm for D-optimal nonlinear regression design

Under a nonlinear regression model with univariate response an algorithm...
research
05/14/2023

Nonlinear regression: finite sample guarantees

This paper offers a new approach for study the frequentist properties of...
research
04/11/2022

Consistent Estimators for Nonlinear Vessel Models

In this work, the issue of obtaining consistent parameter estimators for...
research
06/13/2023

Nonparametric inference on non-negative dissimilarity measures at the boundary of the parameter space

It is often of interest to assess whether a function-valued statistical ...
research
06/20/2019

On Statistical Properties of A Veracity Scoring Method for Spatial Data

Measuring veracity or reliability of noisy data is of utmost importance,...
research
11/02/2018

The Goldenshluger-Lepski Method for Constrained Least-Squares Estimators over RKHSs

We study an adaptive estimation procedure called the Goldenshluger-Lepsk...

Please sign up or login with your details

Forgot password? Click here to reset