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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