Maximum likelihood estimation of the mixture of log-concave densities

Computational Statistics and Data Analysis - Tập 101 - Trang 137-147 - 2016
Hao Hu1, Yichao Wu1, Weixin Yao2
1Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA
2Department of Statistics, University of California, Riverside, CA 92521, USA

Tài liệu tham khảo

Balabdaoui, Fadoua, Doss, Charles R., 2014. Inference for a mixture of symmetric distributions under log-concavity. ArXiv preprint arXiv:1411.4708. Balabdaoui, 2009, Limit distribution theory for maximum likelihood estimation of a log-concave density, Ann. Statist., 37, 1299, 10.1214/08-AOS609 Benaglia, 2009, mixtools: An R package for analyzing finite mixture models, J. Stat. Softw., 32, 1, 10.18637/jss.v032.i06 Bordes, 2006, Semiparametric estimation of a two-component mixture model where one component is known, Scand. J. Statist., 33, 733, 10.1111/j.1467-9469.2006.00515.x Bordes, 2006, Semiparametric estimation of a two-component mixture model, Ann. Statist., 34, 1204, 10.1214/009053606000000353 Bordes, 2010, Semiparametric two-component mixture model with a known component: an asymptotically normal estimator, Math. Methods Statist., 19, 22, 10.3103/S1066530710010023 Butucea, 2014, Semiparametric mixtures of symmetric distributions, Scand. J. Statist., 41, 227, 10.1111/sjos.12015 Campbell, 1974, A multivariate study of variation in two species of rock crab of the genus Leptograpsus, Aust. J. Zool., 22, 417, 10.1071/ZO9740417 Chang, 2007, Clustering with mixtures of log-concave distributions, Comput. Statist. Data Anal., 51, 6242, 10.1016/j.csda.2007.01.008 Chee, 2013, Estimation of finite mixtures with symmetric components, Stat. Comput., 23, 233, 10.1007/s11222-011-9305-5 Chen, 2013, Smoothed log-concave maximum likelihood estimation with applications, Statist. Sinica, 23, 1373 Chen, 2008, Inference for normal mixtures in mean and variance, Statist. Sinica, 18, 443 Cule, 2009, LogConcDEAD: An R package for maximum likelihood estimation of a multivariate log-concave density, J. Stat. Softw., 29, 1, 10.18637/jss.v029.i02 Cule, 2010, Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density, Electron. J. Stat., 4, 254, 10.1214/09-EJS505 Cule, 2010, Maximum likelihood estimation of a multi-dimensional log-concave density, J. R. Stat. Soc. Ser. B Stat. Methodol., 72, 545, 10.1111/j.1467-9868.2010.00753.x Dempster, 1977, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B Stat. Methodol., 1 Doss, Charles, Wellner, Jon A., 2013. Global rates of convergence of the MLEs of log-concave and s-concave densities. ArXiv preprint arXiv:1306.1438. Dümbgen, 2009, Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency, Bernoulli, 15, 40, 10.3150/08-BEJ141 Dümbgen, 2011, Approximation by log-concave distributions, with applications to regression, Ann. Statist., 39, 702, 10.1214/10-AOS853 Hathaway, 1985, A constrained formulation of maximum-likelihood estimation for normal mixture distributions, Ann. Statist., 795 Hohmann, 2013, Semiparametric location mixtures with distinct components, Statistics, 47, 348, 10.1080/02331888.2011.652118 Hubert, 1985, Comparing partitions, J. Classification, 2, 193, 10.1007/BF01908075 Hunter, 2007, Inference for mixtures of symmetric distributions, Ann. Statist., 224 Kim, Arlene K.H., Samworth, Richard J., 2014. Global rates of convergence in log-concave density estimation. ArXiv preprint arXiv:1404.2298. Ma, 2015, Flexible estimation of a semiparametric two-component mixture model with one parametric component, Electron. J. Stat., 9, 444, 10.1214/15-EJS1008 McLachlan, 2007 McLachlan, 2000 Mcnicholas, 2008, Parsimonious Gaussian mixture models, Stat. Comput., 18, 285, 10.1007/s11222-008-9056-0 Pal, 2007, Estimating a polya frequency function2, Lecture Notes Monogr. Ser., 239, 10.1214/074921707000000184 Rufibach, 2007, Computing maximum likelihood estimators of a log-concave density function, J. Stat. Comput. Simul., 77, 561, 10.1080/10629360600569097 Stephens, 2000, Dealing with label switching in mixture models, J. R. Stat. Soc. Ser. B Stat. Methodol., 62, 795, 10.1111/1467-9868.00265 Walther, 2002, Detecting the presence of mixing with multiscale maximum likelihood, J. Amer. Statist. Assoc., 97, 508, 10.1198/016214502760047032 Xiang, 2014, Minimum profile Hellinger distance estimation for a semiparametric mixture model, Canad. J. Statist., 42, 246, 10.1002/cjs.11211 Yao, 2010, A profile likelihood method for normal mixture with unequal variance, J. Statist. Plann. Inference, 140, 2089, 10.1016/j.jspi.2010.02.004 Yao, 2015, Label switching and its solutions for frequentist mixture models, J. Stat. Comput. Simul., 85, 1000, 10.1080/00949655.2013.859259 Yao, 2009, Bayesian mixture labeling by highest posterior density, J. Amer. Statist. Assoc., 10.1198/jasa.2009.0237