Extensions of estimation methods using the EM algorithm

Abstract The EM algorithm described by Dempster, Laid, and Rubin (1977) is reviewed with the purpose of clarifying several misconceptions in the statistical and econometric literature. The clarifications lead to several applications of the algorithm to models that have appeared to be less tractable. The relationship between the EM algorithm and the method of scoring is also explained, providing estimators of the score and the information from the EM algorithm. The EM algorithm is extended to missing-data problems and an estimation method based on simulations.

[1]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[2]  R. Olsen,et al.  Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model , 1978 .

[3]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[4]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[5]  D. McFadden.  A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration , 1989 .

[6]  Ray C. Fair,et al.  A Theory of Extramarital Affairs , 1978, Journal of Political Economy.

[7]  I. Meilijson.  A fast improvement to the EM algorithm on its own terms , 1989 .

[8]  M. Sampford.  Some Inequalities on Mill's Ratio and Related Functions , 1953 .

[9]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[10]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[11]  B. Efron,et al.  Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[12]  T. Rothenberg.  Identification in Parametric Models , 1971 .

[13]  T. Bresnahan.  Departures from marginal-cost pricing in the American automobile industry: Estimates for 1977–1978 , 1981 .

[14]  R. A. Boyles.  On the Convergence of the EM Algorithm , 1983 .

[15]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[16]  Bronwyn H Hall,et al.  Estimation and Inference in Nonlinear Structural Models , 1974 .

[17]  N. Kiefer.  Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model , 1978 .

[18]  Ray C. Fair,et al.  A Note on the Computation of the Tobit Estimator , 1977 .

[19]  R. McKelvey,et al.  A statistical model for the analysis of ordinal level dependent variables , 1975 .

[20]  R. Engle,et al.  Alternative Algorithms for the Estimation of Dynamic Factor , 1983 .

[21]  N. Kiefer.  A Note on Switching Regressions and Logistic Discrimination , 1980 .

[22]  Nicholas P. Jewell,et al.  Mixtures of Exponential Distributions , 1982 .

[23]  Dorothy T. Thayer,et al.  EM algorithms for ML factor analysis , 1982 .

[24]  F. Nelson,et al.  ESTIMATION OF THE TWO-LIMIT PROBIT REGRESSION MODEL , 1975 .

[25]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[26]  P. Schmidt,et al.  Limited-Dependent and Qualitative Variables in Econometrics. , 1984 .