Abstract
Abstract: Mitscherlich’s function is a well-known three-parameter non-linearregression function that quantifies the relation between astimulus or a time variable and a response. It has manyapplications, in particular in the field of measurementreliability. Optimal designs for estimation of this function havebeen constructed only for normally distributed responses withhomoscedastic variances. In this paper we generalize thisliterature to D-optimal designs for discrete and continuousresponses having their distribution function in the exponentialfamily. We also demonstrate that our D-optimal designs can beidentical to and different from optimal designs for varianceweighted linear regression.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | Mathematical Methods of Statistics |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 2022 |
Bibliographical note
Funding Information:This work is part of the research program Rapid Micro Statistics with project no. 15990, which is (partly) financed by the Netherlands Organization for Scientific Research (NWO). The authors gratefully acknowledge the support of the user committee and the funding organization.
Funding
This work is part of the research program Rapid Micro Statistics with project no. 15990, which is (partly) financed by the Netherlands Organization for Scientific Research (NWO). The authors gratefully acknowledge the support of the user committee and the funding organization.
Keywords
- exponential family
- generalized non-linear models
- weighted least squares