The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models
Geurt Jongbloed, Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. E‐mail: G.Jongbloed@tudelft.nl
Abstract
Abstract. In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute non‐parametric M‐estimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the ‘Aspect problem’ in quantum physics.
Citing Literature
Number of times cited according to CrossRef: 27
- Fadoua Balabdaoui, Yulia Kulagina, Completely monotone distributions: Mixing, approximation and estimation of number of species, Computational Statistics & Data Analysis, 10.1016/j.csda.2020.107014, 150, (107014), (2020).
- Sergey V. Malov, Uniform convergence rate of the nonparametric maximum likelihood estimator for current status data with competing risks, Statistics, 10.1080/02331888.2020.1811281, (1-21), (2020).
- Jun Park, Giorgos Bakoyannis, Constantin T. Yiannoutsos, Semiparametric Competing Risks Regression Under Interval Censoring Using the R Package intccr, Computer Methods and Programs in Biomedicine, 10.1016/j.cmpb.2019.03.002, (2019).
- Fadoua Balabdaoui, Gabriella de Fournas-Labrosse, Least squares estimation of a completely monotone pmf: From Analysis to Statistics, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2019.04.006, (2019).
- Sergey V. Malov, Nonparametric estimation for a current status right‐censored data model, Statistica Neerlandica, 10.1111/stan.12180, 73, 4, (475-495), (2019).
- Yong Wang, Computation of the nonparametric maximum likelihood estimate of a univariate log‐concave density, Wiley Interdisciplinary Reviews: Computational Statistics, 10.1002/wics.1452, 11, 1, (2018).
- Yu Liu, Yong Wang, A fast algorithm for univariate log‐concave density estimation, Australian & New Zealand Journal of Statistics, 10.1111/anzs.12232, 60, 2, (258-275), (2018).
- Farzad Alavi Fard, Armin Pourkhanali, Malick Sy, A non-parametric inference for implied volatility governed by a Lévy-driven Ornstein–Uhlenbeck process, Algorithmic Finance, 10.3233/AF-180200, 7, 1-2, (15-30), (2018).
- Jiaying Gu, Roger Koenker, Stanislav Volgushev, TESTING FOR HOMOGENEITY IN MIXTURE MODELS, Econometric Theory, 10.1017/S0266466617000299, 34, 4, (850-895), (2017).
- Yong Wang, Shabnam Fani, Nonparametric maximum likelihood computation of a U-shaped hazard function, Statistics and Computing, 10.1007/s11222-017-9724-z, 28, 1, (187-200), (2017).
- Chew-Seng Chee, A mixture model-based nonparametric approach to estimating a count distribution, Computational Statistics & Data Analysis, 10.1016/j.csda.2016.11.012, 109, (34-44), (2017).
- Clifford Anderson-Bergman, An Efficient Implementation of the EMICM Algorithm for the Interval Censored NPMLE, Journal of Computational and Graphical Statistics, 10.1080/10618600.2016.1208616, 26, 2, (463-467), (2016).
- Cécile Durot, Sylvie Huet, François Koladjo, Stéphane Robin, Nonparametric species richness estimation under convexity constraint, Environmetrics, 10.1002/env.2352, 26, 7, (502-513), (2015).
- Fidelis T. Musakwa, Pricing a Motor Extended Warranty with Limited Usage Cover, ASTIN Bulletin, 10.1017/asb.2014.27, 45, 01, (101-125), (2014).
- Roger Koenker, Ivan Mizera, Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules, Journal of the American Statistical Association, 10.1080/01621459.2013.869224, 109, 506, (674-685), (2014).
- Mahdis Azadbakhsh, Hanna Jankowski, Xin Gao, Computing confidence intervals for log-concave densities, Computational Statistics & Data Analysis, 10.1016/j.csda.2014.01.020, 75, (248-264), (2014).
- Elizabeth Juarez‐Colunga, C. B. Dean, Analysis of over‐and Underdispersed Data, Methods and Applications of Statistics in Clinical Trials, 10.1002/9781118596333, (1-9), (2014).
- Cécile Durot, Sylvie Huet, François Koladjo, Stéphane Robin, Least-squares estimation of a convex discrete distribution, Computational Statistics & Data Analysis, 10.1016/j.csda.2013.04.019, 67, (282-298), (2013).
- Piet Groeneboom, Nonparametric (smoothed) likelihood and integral equations, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2013.07.001, 143, 12, (2039-2065), (2013).
- Yong Wang, Stephen M. Taylor, Efficient computation of nonparametric survival functions via a hierarchical mixture formulation, Statistics and Computing, 10.1007/s11222-012-9341-9, 23, 6, (713-725), (2012).
- Piet Groeneboom, Geurt Jongbloed, Stefanie Michael, Consistency of maximum likelihood estimators in a large class of deconvolution models, Canadian Journal of Statistics, 10.1002/cjs.11152, 41, 1, (98-110), (2012).
- Michael Fay, Sally Hunsberger, Practical Issues on Using Weighted Logrank Tests with Interval-Censored Events in Clinical Trials, Interval-Censored Time-to-Event Data, 10.1201/b12290-17, (2012).
- Jiaping Wang, Qiqing Yu, George Y. C. Wong, The random partition masking model for interval-censored and masked competing risks data, Journal of Statistical Computation and Simulation, 10.1080/00949655.2011.566567, 82, 7, (981-1002), (2012).
- M. H. Maathuis, M. G. Hudgens, Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times, Biometrika, 10.1093/biomet/asq083, 98, 2, (325-340), (2011).
- Kaspar Rufibach, An active set algorithm to estimate parameters in generalized linear models with ordered predictors, Computational Statistics & Data Analysis, 10.1016/j.csda.2010.01.014, 54, 6, (1442-1456), (2010).
- Fadoua Balabdaoui, Jon A. Wellner, Estimation of a k‐monotone density: characterizations, consistency and minimax lower bounds, Statistica Neerlandica, 10.1111/j.1467-9574.2009.00438.x, 64, 1, (45-70), (2009).
- Hanna K. Jankowski, Jon A. Wellner, Computation of nonparametric convex hazard estimators via profile methods, Journal of Nonparametric Statistics, 10.1080/10485250902745359, 21, 4, (505-518), (2009).
