A computational strategy for doubly smoothed MLE exemplified in the normal mixture model

Computational Statistics and Data Analysis

Volumn 54, Issue 8, 2010, Pages 1930-1941

  Seo, Byungtae ^a   Lindsay, Bruce G ^b  

^a TEXAS TECH UNIVERSITY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Bandwidth selection; DS MLE; Kernel smoothing; Monte Carlo; Normal mixture; Spectral degrees of freedom

Indexed keywords

BANDWIDTH SELECTIONS; KERNEL SMOOTHING; MONTE CARLO; NORMAL MIXTURES; SPECTRAL DEGREE;

BANDWIDTH; DIELECTRIC RELAXATION; MAXIMUM LIKELIHOOD ESTIMATION; MECHANICS; MIXTURES; PARAMETER ESTIMATION;

MONTE CARLO METHODS;

EID: 77950928385     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.02.026     Document Type: Article

References (29)

1. Bohning D. A vertex-exchange-method in D-optimal design theory. Metrika 33 (1986) 337-347
2. Bowman A.W. An alternative method of cross-validation for the smoothing of density estimates. Biometrika 71 (1984) 353-360
3. Chen J., and Tan X. Inference for multivariate normal mixtures. Journal of Multivariate Analysis 100 (2009) 1367-1383
4. Chen J., Tan X., and Zhang R. Consistency of penalized mle for normal mixtures in mean and variance. Statistica Sinica 18 (2008) 443-465
5. Ciuperca G.A., Ridolfi A., and Idier J. Penalized maximum likelihood estimator for normal mixtures. Scandinavian Journal of Statistics 30 (2003) 45-59
6. Crawford S.K., Degroot M.H., Kadane J.B., and Small M.J. Modeling lake chemistry distributions: approximate Bayesian methods for estimating a finite mixture model. Technometrics 34 (1992) 441-453
7. Day N.E. Estimating the components of a mixture of normal distributions. Biometrika 56 (1969) 463-474
8. Faraway J.J., and Jhun M. Bootstrap choice of bandwidth for density estimation. Journal of the American Statistical Association 85 (1990) 1119-1122
9. Hall P. Large sample optimality of least squares cross-validation in density estimation. Annals of Statistics 11 (1983) 1156-1174
10. Hall P. Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems. Journal of Multivariate Analysis 32 (1990) 177-203
11. Hathaway R.J. A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Annals of Statistics 13 (1985) 795-800
12. Hathaway R.J. A constrained EM-algorithm for univariate normal mixtures. Journal of Statistical Computation and Simulation 23 (1986) 211-230
13. Ingrassia S., and Rocci R. Constrained monotone EM algorithms for finite mixture of multivariate Gaussians. Computational Statistics & Data analysis 51 (2007) 5339-5351
14. Jones M.C., Marron J.S., and Sheather S.J. A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association 91 (1996) 401-407
15. Jones M.C., Marron J.S., and Sheather S.J. Progress in data-based bandwidth selection for kernel density estimation. Computational Statistics and Data Analysis 11 (1996) 337-381
16. Kiefer J., and Wolfowitz J. Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Annals of Mathematical Statistics 27 (1956) 886-906
17. Laird N.M. Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association 73 (1978) 805-811
18. Lesperance M.L., and Kalbfleisch J.D. An algorithm for computing the nonparametric MLE of a mixing distribution. Journal of the American Statistical Association 87 (1992) 120-126
19. Lindsay B.G., Markatou M., Ray S., Yang K., and Chen S. Quadratic distances on probabilities: a unified foundation. Annals of Statistics 36 (2008) 983-1006
20. Marin J.M., Mengersen K.L., and Rovert C.P. Bayesian modelling and inference on mixtures of distributions. In: Dey D., and Rao C.R. (Eds). Handbook of Statistics vol. 25 (2005)
21. Mcfadden D. A method of simulated moments for estimation of discrete response modes without numerical ingegration. Econometrica 57 (1989) 995-1026
22. Mielniczuk J., Sarda P., and Vieu P. Local data-driven bandwidth choice for density estimation. Journal of Statistical Planning and Inference 23 (1989) 53-69
23. Richardson G., and Green P.J. On bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society. Series B 59 (1997) 731-792
24. Ridolfi A., and Idier J. Penalized maximum likelihood estimation for univariate normal mixture distributions. Proc. 20th Int. Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt) (2000), American Institute of Physics, Gif-sur-Yvette, France
25. Rudemo M. Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics 9 (1982) 65-78
26. Scheather S.J. A data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics and Data Analysis 1 (1983) 229-238
27. Seo, B., Lindsay, B.G., A universally consistent modification of maximum likelihood (in preparation ).
28. Tanaka K., and Takemura A. Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when the scale parameters are exponentially small. Bernoulli 12 (2006) 1003-1017
29. Wang L. Estimation of nonlinear models with Berkson measurement errors. Annals of Statistics 32 (2004) 2559-2579