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

07/05/2019
by   Fritjof Freise, et al.
0

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 responses so far, and selects the next design point as in the classical Wynn-algorithm for D-optimal design. The name `Wynn-algorithm' is in honor of Henry P. Wynn who established the latter `classical' algorithm in his 1970 paper. The asymptotics of the sequences of designs and maximum likelihood estimates generated by the adaptive algorithm is studied for an important class of nonlinear regression models: generalized linear models whose (univariate) response variables follow a distribution from a one-parameter exponential family. Under the assumptions of compactness of the experimental region and of the parameter space together with some natural continuity assumptions it is shown that the adaptive ML-estimators are strongly consistent and the design sequence is asymptotically locally D-optimal at the true parameter point. If the true parameter point is an interior point of the parameter space then under some smoothness assumptions the asymptotic normality of the adaptive ML-estimators is obtained.

READ FULL TEXT

page 1

page 2

page 3

page 4

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
09/09/2019

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

The paper continues the authors' work on the adaptive Wynn algorithm in ...
research
11/19/2020

In- and Equivariance for Optimal Designs in Generalized Linear Models: The Gamma Model

We give an overview over the usefulness of the concept of equivariance a...
research
11/16/2009

Kullback-Leibler aggregation and misspecified generalized linear models

In a regression setup with deterministic design, we study the pure aggre...
research
10/12/2017

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalised linear models

Reduced-rank regression is a dimensionality reduction method with many a...
research
02/26/2019

Parameter Redundancy and the Existence of Maximum Likelihood Estimates in Log-linear Models

In fitting log-linear models to contingency table data, the presence of ...
research
03/03/2021

Product Partition Dynamic Generalized Linear Models

Detection and modeling of change-points in time-series can be considerab...

Please sign up or login with your details

Forgot password? Click here to reset