Oracle 10G - Oracle Database 10G - SQL Fundamentals II -

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There is a vast amount of recent literature in this research area, and it is impossible for us to have an exhaustive list here. The importance of nonparametric modeling methods has been recognized in longitudinal data analysis and for practical applications, since nonparametric methods are flexible and robust against parametric assumptions. Such flexibility is useful for exploration and analysis of longitudinal data, when appropriate parametric models are unavailable. In this book, we do not intend to cover all nonparametric regression techniques.

2 Fundamental Development of the NPME Models Fundamental developments of the NPME modeling techniques will be presented in Chapters 4-7, and each chapter covers one popular nonparametric method. These are the core contents of this book and lay a good foundation for further extensions of the NPME models. Each of these chapters will also provide a review for the nonparametric population mean (NPM) model and naive smoothing methods before the mixed-effects modeling approach is introduced. In Chapter 4, we will mainly investigate local polynomial mixed-effects models after a review of the NPM model and the local polynomial kernel-based generalized estimating equations (LPK-GEE) methods.

Here y(s, t ) quantifies the bctween-subject variation while the ~ ‘ ( quantifies t) the within-subject variation. , v ( t ) GP(0, y), and t GP(0, y6). ~ - - - - SCOPE OF THE BOOK I1 Under the NPME modeling framework, we need to accomplish the following tasks: (1) to estimate the fixed-effect (population mean) function ~ ( t (2) ) ; to predict the random-effect functions v i ( t )and individual functions s i ( t ) = ~ ( t )vi(t), i = 1 , 2 , . . ,n; (3) to estimate the covariance function y(s, t ) ;and (4) to estimate the noise variance function a'(t).

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