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A new approach to maximum likelihood estimation of sum‐constrained linear models in case of undersized samples
Author(s) -
De Boer P. M. C.,
Harkema R.
Publication year - 1997
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00038
Subject(s) - maximum likelihood , mathematics , covariance , covariance matrix , constant (computer programming) , maximum likelihood sequence estimation , restricted maximum likelihood , statistics , econometrics , computer science , programming language
Maximum likelihood procedures for estimating sum‐constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories ( n ) is large as compared with the number of observations ( T ). In applied research, this problem is usually resolved by postulating the contemporaneous covariance matrix of the dependent variables to be known apart from a constant of proportionality. In this paper we develop a maximum likelihood procedure for sum‐constrained models with large numbers of categories, which does not require too many observations, but nevertheless allows for n covariance parameters to be estimated freely.