Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 319-328.

PARAMETER ESTIMATION PROBLEM IN THE BOX-COX SIMPLE LINEAR MODEL

Darija Marković

Department of Mathematics, University of Osijek, 31 000 Osijek, Croatia
e-mail: darija@mathos.hr


Abstract.   Given the data (xi, yi), i = 1, ..., n, such that yi > 0 for all i = 1, ..., n, we consider the parameter estimation problem in a simple linear model with the Box-Cox transformation of the dependent variable. Maximum likelihood estimation of its parameter reduces to one nonlinear least squares problem. As a main result, we obtained three theorems in which we give necessary and sufficient conditions which guarantee the existence of the least squares estimate. In the most interesting case when at least three xi's are different, it is shown that the least squares estimate exists.

2020 Mathematics Subject Classification.   65C20, 62J02.

Key words and phrases.   Box-Cox regression model, maximum likelihood estimate, nonlinear least squares, least squares estimate, existence problem.


Full text (PDF) (free access)

DOI: https://doi.org/10.21857/mnlqgc3kjy


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