Topic
Generalized linear array model
About: Generalized linear array model is a research topic. Over the lifetime, 1056 publications have been published within this topic receiving 85672 citations.
Papers published on a yearly basis
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Papers
TL;DR: This paper investigates the large sample properties of generalized method of moments (GMM) estimators, a class of estimators that encompasses various standard econometric estimators, and demonstrates their strong consistency and asymptotic normality under certain conditions.
Abstract: IN THIS PAPER we study the large sample properties of a class of generalized method of moments (GMM) estimators which subsumes many standard econometric estimators. To motivate this class, consider an econometric model whose parameter vector we wish to estimate. The model implies a family of orthogonality conditions that embed any economic theoretical restrictions that we wish to impose or test. For example, assumptions that certain equations define projections or that particular variables are predetermined give rise to orthogonality conditions in which expected cross products of unobservable disturbances and functions of observable variables are equated to zero. Heuristically, identification requires at least as many orthogonality conditions as there are coordinates in the parameter vector to be estimated. The unobservable disturbances in the orthogonality conditions can be replaced by an equivalent expression involving the true parameter vector and the observed variables. Using the method of moments, sample estimates of the expected cross products can be computed for any element in an admissible parameter space. A GMM estimator of the true parameter vector is obtained by finding the element of the parameter space that sets linear combinations of the sample cross products as close to zero as possible. In studying strong consistency of GMM estimators, we show how to construct a class of criterion functions with minimizers that converge almost surely to the true parameter vector. The resulting estimators have the interpretation of making the sample versions of the population orthogonality conditions as close as possible to zero according to some metric or measure of distance. We use the metric to index the alternative estimators. This class of estimators includes the nonlinear instrumental variables estimators considered by, among others, Amemiya [1, 2], Jorgenson and Laffont [24], and Gallant [11].2 There the
15,361 citations
Book•
30 May 2017
TL;DR: In this article, a simple linear model is proposed to describe the geometry of linear models, and a general linear model specification in R is presented. But the theory of linear model theory is not discussed.
Abstract: LINEAR MODELS A simple linear model Linear models in general The theory of linear models The geometry of linear modelling Practical linear models Practical modelling with factors General linear model specification in R Further linear modelling theory Exercises GENERALIZED LINEAR MODELS The theory of GLMs Geometry of GLMs GLMs with R Likelihood Exercises INTRODUCING GAMS Introduction Univariate smooth functions Additive models Generalized additive models Summary Exercises SOME GAM THEORY Smoothing bases Setting up GAMs as penalized GLMs Justifying P-IRLS Degrees of freedom and residual variance estimation Smoothing Parameter Estimation Criteria Numerical GCV/UBRE: performance iteration Numerical GCV/UBRE optimization by outer iteration Distributional results Confidence interval performance Further GAM theory Other approaches to GAMs Exercises GAMs IN PRACTICE: mgcv Cherry trees again Brain imaging example Air pollution in Chicago example Mackerel egg survey example Portuguese larks example Other packages Exercises MIXED MODELS and GAMMs Mixed models for balanced data Linear mixed models in general Linear mixed models in R Generalized linear mixed models GLMMs with R Generalized additive mixed models GAMMs with R Exercises APPENDICES A Some matrix algebra B Solutions to exercises Bibliography Index
8,519 citations
Book•
1 Jan 1974
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
Abstract: * Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of Generalized Inverses * Spectral Generalized Inverses * Generalized Inverses of Partitioned Matrices * A Spectral Theory for Rectangular Matrices * Computational Aspects of Generalized Inverses * Miscellaneous Applications * Generalized Inverses of Linear Operators between Hilbert Spaces * Appendix A: The Moore of the Moore-Penrose Inverse * Bibliography * Subject Index * Author Index
5,096 citations
TL;DR: This new text is a substantially enlarged and revised version of Professor Chen's earlier book on linear systems, which is a balanced and comprehensive treatment of all the useful concepts from both state space and frequency domain approaches for the analysis and design of linear control systems.
3,427 citations
TL;DR: The class of generalized additive models is introduced, which replaces the linear form E fjXj by a sum of smooth functions E sj(Xj), and has the advantage of being completely auto- matic, i.e., no "detective work" is needed on the part of the statistician.
Abstract: Likelihood-based regression models such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariates $X_1, X_2, \cdots, X_p$. We introduce the class of generalized additive models which replaces the linear form $\sum \beta_jX_j$ by a sum of smooth functions $\sum s_j(X_j)$. The $s_j(\cdot)$'s are unspecified functions that are estimated using a scatterplot smoother, in an iterative procedure we call the local scoring algorithm. The technique is applicable to any likelihood-based regression model: the class of generalized linear models contains many of these. In this class the linear predictor $\eta = \Sigma \beta_jX_j$ is replaced by the additive predictor $\Sigma s_j(X_j)$; hence, the name generalized additive models. We illustrate the technique with binary response and survival data. In both cases, the method proves to be useful in uncovering nonlinear covariate effects. It has the advantage of being completely automatic, i.e., no "detective work" is needed on the part of the statistician. As a theoretical underpinning, the technique is viewed as an empirical method of maximizing the expected log likelihood, or equivalently, of minimizing the Kullback-Leibler distance to the true model.
3,291 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2023 | 3 |
| 2022 | 1 |
| 2021 | 1 |
| 2018 | 8 |
| 2017 | 41 |