In this project we look at the case when two of fundamental assumptions in the method of Maximum Likelihood are violated. In particular, we study a special class of misspecified models, where the true model is a mixed effect model but the working model is a fixed effect model with parameters of dimension increasing with sample size. We provide a sufficient condition under which the MLE derived from the working model converges to a well-defined and asymptotically normally-distributed limit. In linear models, the sample variance is biased; but there exists a robust variance estimator of the MLE that converges to the true variance in probability. We also study the Criterion-based automatic model selection methods and find that they may select a linear model that contains spurious variables, but this can be avoided by using the robust variance estimator for the MLE in Bonferroni-adjusted model section or by choosing ?n that grows fast enough in Shao's GIC. In generalized linear models, general results are given and computational and simulation studies are carried out to corroborate asymptotic theoretical results as well as to calculate quantities that are not available in theoretical calculation. We find that when the link function in generalized linear mixed models is correctly specified, the estimated parameters have entries that are close to zero except for those corresponding to the fixed effects in the true model. The estimated variance of the MLE is always smaller than the true variance of the MLE, but the robust "sandwich" variance estimator can estimate the true variance very well, and extra significant variables will appear only when the link function is not correctly specified.

Missing the Random Effect

Science & Math

Chen, Ru

Mathematics

VDM Verlag Dr. Mueller e.K.

The book is for foreigners to learn spoken Chinese. By people activity situation, the learners can learn spoken Chinese easily, and grasp the daily communication of Chinese gradually.

Chinese Situational Dialogues (Chinese and English Edition)

Reference

Wang Tianhui

Foreign Language Study & Reference

Peking University Press

The Chinese language can be quite confusing to new learners because there is a large number of grammatical phenomena in the language where some words are always used together with others, forming a set structure or collocation which gives a specific meaning. Since these expressions are of a set structure, people usually call them ""set patterns"". This book is a compilation of common set patterns in the Chinese language designed to facilitate students' study. To help students learn these patterns faster, understand them more accurately and use them skillfully, this book has compiled 3,300 example sentences for the 330 patterns selected for the book. Each pattern is presented in its own section comprised of four parts: Explanation, Examples, Dialogues and Exercises. The Explanations are written to be as concise as possible and usages mentioned in the Explanations are the ones that are most commonly met, and are covered in the Examples and Dialogues, enabling learners to understand and master the expression more quickly. This also makes this book a valuable resource for teachers' reference and use. Examples are intentionally made easy or difficult, and some are idioms or set phrases, so as to arouse learners' interest and enhance their reading and speaking abilities. This can be a students' book and can be a tool for teachers.

Common Chinese Patterns 330

Zhu Xiao Yan

Sinolingua

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