L-functions From Langlands-Shahidi Method for GSpin Groups and the Generic Arthur L-packet Conjecture

Committee: F. Shahidi(Ch), E. Goins, D. Goldberg, T. Liu

Scattering and Inverse Scattering on Asymptotically Hyperbolic Manifolds

Committee: A. Sa Barreto(Ch), R. Bañuelos, M. De Hoop, P. Stefanov

Inference Function for Mixed Effects Models

In longitudinal studies, mixed-effects models are important for addressing subject-specific effects. However, most existing approaches assume a normal distribution for the random effects, and this could affect the bias and efficiency of the fixed effects estimator. Even in cases where the estimation of the fixed effects is robust with a misspecified distribution of the random effects, the estimation of the random effects could be invalid. We propose a new approach to estimate fixed and random effects using conditional quadratic inference functions. The new approach does not require the specification of likelihood functions or a normality assumption for random effects. It can also accommodate serial correlation between observations within the same cluster, in addition to mixed-effects modeling. Other advantages include not requiring the estimation of the unknown variance components associated with the random effects, or the nuisance parameters associated with the working correlations. We establish asymptotic results for the fixed effect parameter estimators which do not rely on the consistency of the random-effect estimators. Some applications of the proposed approach will also be presented.

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Refreshments will be served in the Math Library Lounge at 3:00 P.M.