Abstract
Suppose independent observations Xi, i = 1, ..., n are observed from a mixture model f (x ; Q) ≡ ∫ f (x ; λ) d Q (λ), where λ is a scalar and Q (λ) is a nondegenerate distribution with an unspecified form. We consider to estimate Q (λ) by nonparametric maximum likelihood (NPML) method under two scenarios: (1) the likelihood is penalized by a functional g (Q); and (2) Q is under a constraint g (Q) = g0. We propose a simple and reliable algorithm termed VDM/ECM for Q-estimation when the likelihood is penalized by a linear functional. We show this algorithm can be applied to a more general situation where the penalty is not linear, but a function of linear functionals by a linearization procedure. The constrained NPMLE can be found by penalizing the quadratic distance | g (Q) - g0 |2 under a large penalty factor γ > 0 using this algorithm. The algorithm is illustrated with two real data sets.
Original language | English (US) |
---|---|
Pages (from-to) | 2946-2957 |
Number of pages | 12 |
Journal | Computational Statistics and Data Analysis |
Volume | 51 |
Issue number | 6 |
DOIs | |
State | Published - Mar 1 2007 |
Keywords
- Computing algorithm
- Constrained NPMLE
- Mixture models
- Nonparametric maximum likelihood
- Penalized NPMLE
- VDM/ECM
ASJC Scopus subject areas
- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics