Traditional ML Research Articles

Maximum a Posteriori Estimation of Linear Shape Variation With Application to Vertebra and Cartilage Modeling

The estimation of covariance matrices is a crucial step in several statistical tasks. Especially when using few samples of a high dimensional representation of shapes, the standard maximum likelihood estimation (ML) of the covariance matrix can be far from the truth, is often rank deficient, and may lead to unreliable results. In this paper, we discuss regularization by prior knowledge using maximum a posteriori (MAP) estimates. We compare ML to MAP using a number of priors and to Tikhonov regularization. We evaluate the covariance estimates on both synthetic and real data, and we analyze the estimates' influence on a missing-data reconstruction task, where high resolution vertebra and cartilage models are reconstructed from incomplete and lower dimensional representations. Our results demonstrate that our methods outperform the traditional ML method and Tikhonov regularization.

Identification, estimation and testing of conditionally heteroskedastic factor models

We investigate the effects of dynamic heteroskedasticity on statistical factor analysis. We show that identification problems are alleviated when variation in factor variances is accounted for. Our results apply to dynamic APT models and other structural models. We also find that traditional ML estimation of unconditional variance parameters remains consistent if the factor loadings are identified from the unconditional distribution, but their standard errors must be robustified. We develop a simple preliminary LM test for ARCH effects in the common factors, and discuss two-step consistent estimation of the conditional variance parameters. Finally, we conduct a detailed simulation exercise.