D-Optimal Designs for the Mitscherlich Non-Linear Regression Function

IF 0.8 Q3 STATISTICS & PROBABILITY

Mathematical Methods of Statistics Pub Date : 2022-07-18 DOI:10.3103/s1066530722010033

Maliheh Heidari, Md Abu Manju, Pieta C. IJzerman-Boon, Edwin R. van den Heuvel

引用次数: 1

Abstract

Mitscherlich’s function is a well-known three-parameter non-linear regression function that quantifies the relation between a stimulus or a time variable and a response. It has many applications, in particular in the field of measurement reliability. Optimal designs for estimation of this function have been constructed only for normally distributed responses with homoscedastic variances. In this paper we generalize this literature to D-optimal designs for discrete and continuous responses having their distribution function in the exponential family. We also demonstrate that our D-optimal designs can be identical to and different from optimal designs for variance weighted linear regression.

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非线性回归函数的d -最优设计

摘要mitscherlich函数是一个著名的三参数非线性回归函数，用于量化刺激或时间变量与响应之间的关系。它有许多应用，特别是在测量可靠性领域。估计该函数的最优设计仅适用于具有均方差的正态分布响应。在本文中，我们将这些文献推广到离散和连续响应具有指数族分布函数的d -最优设计。我们还证明了我们的d -最优设计可以与方差加权线性回归的最优设计相同或不同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods of Statistics STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.