Maximum likelihood estimation with missing outcomes: From simplicity to complexity

Maximum Likelihood Estimation in Graphical Models with Missing Values

Semiparametric Maximum Likelihood Estimation in Parametric Regression with Missing Covariates

The Algebraic Complexity of Maximum Likelihood Estimation for Bivariate Missing Data

We study the problem of maximum likelihood estimation for general patterns of bivariate missing data for normal and multinomial random variables, under the assumption that the data is missing at random (MAR). For normal data, the score equations have nine complex solutions, at least one of which is real and statistically significant. Our computations suggest that the number of real solutions is...

Fossilisation: From Simplicity to Complexity

The second language acquisition (SLA) literatureover the past 30 yearshas seen miscellaneous interpretations and applications of the term ‘fossilisation’. This, on the one hand, is a sign of improvement in the general understanding of the theoretical construct. On the other hand, however, the lack of uniformity in interpretation and application creates confusion, which can be counterproductive ...

ELEN6887 Lecture 14: Maximum Likelihood Estimation and Complexity Regularization

Yi i.i.d. ∼ pθ∗ , i = {1, . . . , n} where θ∗ ∈ Θ. We can view pθ∗ as a member of a parametric class of distributions, P = {pθ}θ∈Θ. Our goal is to use the observations {Yi} to select an appropriate distribution (e.g., model) from P. We would like the selected distribution to be close to pθ in some sense. We use the negative log-likelihood loss function, defined as l(θ, Yi) = − log pθ(Yi). The e...