@article {9349,
	title = {Switching nonparametric regression models for multi-curve data},
	journal = {Canadian Journal of Statistics},
	volume = {45},
	year = {2017},
	pages = {442{\textendash}460},
	keywords = {EM algorithm, Functional data analysis, latent variables, machine learning, MSC 2010: Primary 62G08, nonparametric regression, power usage, secondary 62G05, switching nonparametric regression model},
	issn = {1708-945X},
	doi = {10.1002/cjs.11331},
	url = {http://dx.doi.org/10.1002/cjs.11331},
	author = {de Souza, Camila P. E. and Heckman, Nancy E. and Xu, Fan}
}
@article { ISI:000337869500017,
	title = {Parsimonious parameterization of correlation matrices using truncated vines and factor analysis},
	journal = {Computational Statistics \& Data Analysis},
	volume = {77},
	year = {2014},
	month = {SEP},
	pages = {233-251},
	publisher = {Elsevier Science BV},
	type = {Article},
	abstract = {Both in classical multivariate analysis and in modern copula modeling, correlation matrices are a central concept of dependence modeling using multivariate normal distributions and copulas. Since the number of correlation parameters quadratically increases with the number of variables, parsimonious parameterizations of large correlation matrices in terms of O(d) parameters are important. While factor analysis is commonly used for this purpose, the use of vines is an attractive alternative: vines are graphical models based on a sequence of trees, and are based on the decomposition of a correlation matrix in terms of algebraically independent correlations and partial correlations. By limiting the number of trees, with the so-called truncation, parsimonious parameterizations of correlation matrices may be found. Moreover, truncated vines and factor models may be joined to define a combined model, with individual benefits from each of the two approaches. The different parameterizations and how they are estimated for data are discussed. In particular, spanning tree algorithms for truncated vines and a modified EM algorithm for the combined factor-vine model are proposed and evaluated in a simulation study. Three applications to psychometric and finance data sets illustrate the different parsimonious models. (C) 2014 Elsevier B.V. All rights reserved.},
	keywords = {EM algorithm, Markov trees, Multivariate normal, Partial correlations, Regular vines},
	issn = {0167-9473},
	doi = {10.1016/j.csda.2014.03.002},
	author = {Brechmann, Eike C. and Joe, Harry}
}
@article { ISI:000343808700001,
	title = {Switching nonparametric regression models},
	journal = {JOURNAL OF NONPARAMETRIC STATISTICS},
	volume = {26},
	number = {4},
	year = {2014},
	month = {OCT 2},
	pages = {617-637},
	publisher = {TAYLOR \& FRANCIS LTD},
	type = {Article},
	address = {4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND},
	abstract = {We propose a methodology to analyse data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z. The states form a stochastic process and their possible values are j=1, horizontal ellipsis , J. If z equals j the expected response of y is one of J unknown smooth functions evaluated at x. We call this model a switching nonparametric regression model. We develop an Expectation-Maximisation algorithm to estimate the parameters of the latent state process and the functions corresponding to the J states. We also obtain standard errors for the parameter estimates of the state process. We conduct simulation studies to analyse the frequentist properties of our estimates. We also apply the proposed methodology to the well-known motorcycle dataset treating the data as coming from more than one simulated accident run with unobserved run labels.},
	keywords = {EM algorithm, latent variables, machine learning, mixture of Gaussian processes, motorcycle data, nonparametric regression},
	issn = {1048-5252},
	doi = {10.1080/10485252.2014.941364},
	author = {de Souza, Camila P. E. and Heckman, Nancy E.}
}
@article { ISI:000309793400033,
	title = {Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data},
	journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
	volume = {107},
	number = {499},
	year = {2012},
	month = {SEP},
	pages = {1178-1186},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {732 N WASHINGTON ST, ALEXANDRIA, VA 22314-1943 USA},
	abstract = {Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S-estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random. We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online.},
	keywords = {Consistent, Elliptical distribution, EM algorithm, Fixed point equation},
	issn = {0162-1459},
	doi = {10.1080/01621459.2012.699792},
	author = {Danilov, Mike and Yohai, Victor J. and Zamar, Ruben H.}
}
@article { ISI:000284674900012,
	title = {Model-based linear clustering},
	journal = {CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE},
	volume = {38},
	number = {4},
	year = {2010},
	month = {DEC},
	pages = {716-737},
	publisher = {WILEY-BLACKWELL},
	type = {Article},
	address = {COMMERCE PLACE, 350 MAIN ST, MALDEN 02148, MA USA},
	abstract = {The authors propose a profile likelihood approach to linear clustering which explores potential linear clusters in a data set For each linear cluster an errors in variables model is assumed The optimization of the derived profile likelihood can be achieved by an EM algorithm Its asymptotic properties and its relationships with several existing clustering methods are discussed Methods to determine the number of components in a data set are adapted to this linear clustering setting Several simulated and real data sets are analyzed for comparison and illustration purposes The Canadian Journal of Statistics 38 716-737 2010 (C) 2010 Statistical Society of Canada},
	keywords = {EM algorithm, errors in-variables model, linear cluster, mixture model, orthogonal regression, profile likelihood},
	issn = {0319-5724},
	doi = {10.1002/cjs.10082},
	author = {Yan, Guohua and Welch, William J. and Zamar, Ruben H.}
}
@article {wu_approximate_2008,
	title = {An approximate method for nonlinear mixed-effects models with nonignorably missing covariates},
	journal = {Statistics \& Probability Letters},
	volume = {78},
	number = {4},
	year = {2008},
	pages = {384{\textendash}389},
	abstract = {Nonlinear mixed-effect (NLME) models are very useful in many longitudinal studies. In practice, covariates in NLME models may contain missing data, and the missing data may be nonignorable. Likelihood inference for NLME models with missing covariates can be computationally very intensive. We propose a computationally much more efficient approximate method for NLME models with nonignorably missing covariates. We illustrate the method using a real data example.},
	keywords = {EM algorithm, Linearization, Longitudinal data, Taylor expansion},
	issn = {0167-7152},
	doi = {10.1016/j.spl.2007.07.011},
	url = {http://www.sciencedirect.com/science/article/pii/S0167715207002519},
	author = {WU, LANG}
}
@article {wu_joint_2008,
	title = {Joint inference for nonlinear mixed-effects models and time to event at the presence of missing data},
	journal = {Biostatistics},
	volume = {9},
	number = {2},
	year = {2008},
	pages = {308{\textendash}320},
	abstract = {In many longitudinal studies, the individual characteristics associated with the repeated measures may be possible covariates of the time to an event of interest, and thus, it is desirable to model the time-to-event process and the longitudinal process jointly. Statistical analyses may be further complicated in such studies with missing data such as informative dropouts. This article considers a nonlinear mixed-effects model for the longitudinal process and the Cox proportional hazards model for the time-to-event process. We provide a method for simultaneous likelihood inference on the 2 models and allow for nonignorable data missing. The approach is illustrated with a recent AIDS study by jointly modeling HIV viral dynamics and time to viral rebound.},
	keywords = {EM algorithm, Longitudinal data, proportional hazards model, shared parameter model},
	issn = {1465-4644, 1468-4357},
	doi = {10.1093/biostatistics/kxm029},
	url = {http://biostatistics.oxfordjournals.org/content/9/2/308},
	author = {WU, LANG and Hu, X. Joan and Wu, Hulin}
}
@article {wu_computationally_2007,
	title = {A computationally efficient method for nonlinear mixed-effects models with nonignorable missing data in time-varying covariates},
	journal = {Computational Statistics \& Data Analysis},
	volume = {51},
	number = {5},
	year = {2007},
	pages = {2410{\textendash}2419},
	abstract = {Nonlinear mixed-effects (NLME) models are widely used for longitudinal data analyses. Time-dependent covariates are often introduced to partially explain inter-individual variation. These covariates often have missing data, and the missingness may be nonignorable. Likelihood inference for NLME models with nonignorable missing data in time-varying covariates can be computationally very intensive and may even offer computational difficulties such as nonconvergence. We propose a computationally very efficient method for approximate likelihood inference. The method is illustrated using a real data example.},
	keywords = {EM algorithm, Linearization, Longitudinal data, Random effects model},
	issn = {0167-9473},
	doi = {10.1016/j.csda.2006.07.036},
	url = {http://www.sciencedirect.com/science/article/pii/S0167947306002556},
	author = {WU, LANG}
}
@article {wu_nonlinear_2004,
	title = {Nonlinear mixed-effect models with nonignorably missing covariates},
	journal = {Canadian Journal of Statistics},
	volume = {32},
	number = {1},
	year = {2004},
	month = {mar},
	pages = {27{\textendash}37},
	abstract = {Nonlinear mixed-effect models are often used in the analysis of longitudinal data. However, it sometimes happens that missing values for some of the model covariates are not purely random. Motivated by an application to HTV viral dynamics, where this situation occurs, the author considers likelihood inference for this type of problem. His approach involves a Monte Carlo EM algorithm, along with a Gibbs sampler and rejection/importance sampling methods. A concrete application is provided.},
	keywords = {EM algorithm, Gibbs sampling, Longitudinal data, missing data, Rejection sampling},
	issn = {1708-945X},
	doi = {10.2307/3315997},
	url = {http://onlinelibrary.wiley.com/doi/10.2307/3315997/abstract},
	author = {WU, LANG}
}
@article {wu_simultaneous_2004,
	title = {Simultaneous inference for longitudinal data with detection limits and covariates measured with errors, with application to AIDS studies},
	journal = {Statistics in Medicine},
	volume = {23},
	number = {11},
	year = {2004},
	month = {jun},
	pages = {1715{\textendash}1731},
	abstract = {In AIDS studies such as HIV viral dynamics, statistical inference is often complicated because the viral load measurements may be subject to left censoring due to a detection limit and time-varying covariates such as CD4 counts may be measured with substantial errors. Mixed-effects models are often used to model the response and the covariate processes in these studies. We propose a unified approach which addresses the censoring and measurement errors simultaneously. We estimate the model parameters by a Monte-Carlo EM algorithm via the Gibbs sampler. A simulation study is conducted to compare the proposed method with the usual two-step method and a naive method. We find that the proposed method produces approximately unbiased estimates with more reliable standard errors. A real data set from an AIDS study is analysed using the proposed method. Copyright {\textcopyright} 2004 John Wiley \& Sons, Ltd.},
	keywords = {EM algorithm, Gibbs sampler, HIV, mixed-effects model},
	issn = {1097-0258},
	doi = {10.1002/sim.1748},
	url = {http://onlinelibrary.wiley.com/doi/10.1002/sim.1748/abstract},
	author = {WU, LANG}
}
@article {wu_model-restricted_2000,
	title = {Some model-restricted shrinkage estimators for contingency tables with missing data},
	journal = {Metrika},
	volume = {50},
	number = {3},
	year = {2000},
	month = {apr},
	pages = {221{\textendash}245},
	abstract = {. For contingency tables with extensive missing data, the unrestricted MLE under the saturated model, computed by the EM algorithm, is generally unsatisfactory. In this case, it may be better to fit a simpler model by imposing some restrictions on the parameter space. Perlman and Wu (1999) propose lattice conditional independence (LCI) models for contingency tables with arbitrary missing data patterns. When this LCI model fits well, the restricted MLE under the LCI model is more accurate than the unrestricted MLE under the saturated model, but not in general. Here we propose certain empirical Bayes (EB) estimators that adaptively combine the best features of the restricted and unrestricted MLEs. These EB estimators appear to be especially useful when the observed data is sparse, even in cases where the suitability of the LCI model is uncertain. We also study a restricted EM algorithm (called the ER algorithm) with similar desirable features.},
	keywords = {EM algorithm, empirical Bayes estimator, Key words: Sparse data, lattice conditional independence model, restricted maximum likelihood estimator},
	issn = {0026-1335, 1435-926X},
	doi = {10.1007/s001840050047},
	url = {http://link.springer.com/article/10.1007/s001840050047},
	author = {WU, LANG and Reeves, Jaxk and Perlman, Michael D.}
}
