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Hybrid Paired Comparison Analysis, with Applications to the Ranking of College Football Teams
, 2005
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Sampling bias and logistic models
"... Proofs subject to correction. Not to be reproduced without permission. Contributions to the discussion must not exceed 400 words. Contributions longer than 400 words will be cut by the editor. ..."
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Proofs subject to correction. Not to be reproduced without permission. Contributions to the discussion must not exceed 400 words. Contributions longer than 400 words will be cut by the editor.
1 Potential functions and conservative estimating functions
"... 1. INTRODUCTION An unbiased estimating function g(`; y) is defined to be a function of the data y and parameter ` having zero mean for all `. In other words, E`fg(`; Y)g = 0 for all `. One purpose of an estimating function is to produce an estimate ^ ` of the parameter from data y, the ..."
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1. INTRODUCTION An unbiased estimating function g(`; y) is defined to be a function of the data y and parameter ` having zero mean for all `. In other words, E`fg(`; Y)g = 0 for all `. One purpose of an estimating function is to produce an estimate ^ ` of the parameter from data y, the
Notes And
"... ictor variable such as time or temperature. In its basic form, the classical linear model is unable to account for such effects. It is possible, however, to generalize the linear model, and allow it to overcome these limitations. The generalizations accept forms of nonnormal data, and also link the ..."
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ictor variable such as time or temperature. In its basic form, the classical linear model is unable to account for such effects. It is possible, however, to generalize the linear model, and allow it to overcome these limitations. The generalizations accept forms of nonnormal data, and also link the mean response to the linear predictor in a possibly nonlinear fashion. We call this the family of generalized linear models (GLiMs). The basic precept of a GLiM is to extend the linear model in two ways: (a) generalize to nonnormal parent distributions such as binomial, Poisson, or gamma; and/or (b) generalize to nonlinear functions that link the unknown means of the parent distribution with the predictor variables. In the former case, certain generalizations to nonnormal parent distributions can be grouped into a class of densities known as the exponential family. The density functions satisfy two basic requirements: (1) the random variable, Y, has a support
Generalized Linear Autoregressions
, 1995
"... This paper develops a class of autoregressive and moving average models which extend the generalized linear model. Likelihood and quasilikelihood estimation procedures are developed which allow the models to be easily estimated and tested. Several examples are given which illustrate the usefulness ..."
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This paper develops a class of autoregressive and moving average models which extend the generalized linear model. Likelihood and quasilikelihood estimation procedures are developed which allow the models to be easily estimated and tested. Several examples are given which illustrate the usefulness and simplicity of the approach advocated in this paper. Some key words: Autoregression, Diagnostic checking, Generalized linear model, Martingale difference, Overdispersion, Poisson. 1 INTRODUCTION This paper develops autoregressive and moving average extensions of the generalized linear model. These allow serial dependence by specifying a onestepahead prediction distribution, so yielding the likelihood, which frees the predicted mean of the model to depend on lagged values of the observations. The class of generalized linear models put forward here have f(y t j Y t\Gamma1 ) =<F1
Estimation of the Fire Interval Distribution for . . .
"... This paper describes a new method for estimating the fire interval distribution of a region using historical wildfire boundary data. The new procedure does not assume a specific parametric model and can adapt to various types of fire interval relationships. The estimator first averages the proporti ..."
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This paper describes a new method for estimating the fire interval distribution of a region using historical wildfire boundary data. The new procedure does not assume a specific parametric model and can adapt to various types of fire interval relationships. The estimator first averages the proportions of certain age classes which burn across time and weights these proportions by the amount of available fuel. Then, rather than fit known theoretical models, we use local linear smoothing methods to ascertain the overall relationship between fuel age and burning. In Los Angeles County, California, detailed information on wildfires has been made available through the use of geographic information systems (GIS) technology. The proposed procedure is applied to GIS data covering the years 1878–1996 and reveals an apparent nonlinear thresholdtype relationship with burn area. The result is compared with two wellknown parametric models and the relationship appears to conform to the well known Olson model for a fire interval distribution.
May 1990ON LIKELIHOOD RATIO TESTS OF ONESIDED HYPOTHESES IN GENERALIZED LINEAR MODELS WITH CANONICAL LINKS
"... For generalized linear models with multivariate response and natural link functions, likelihood ratio test of onesided hypothesis on the regression parameter is considered under rather general conditions. The nullasymptotic distribution of the test statistic turns out to be chibar squared. The ex ..."
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For generalized linear models with multivariate response and natural link functions, likelihood ratio test of onesided hypothesis on the regression parameter is considered under rather general conditions. The nullasymptotic distribution of the test statistic turns out to be chibar squared. The extension of the above results to include quasilikellihood ratio test to incorporate overdispersion when the response is univariate is also discussed. A simple example illustrates the application of the main result. Keywords and phrases: asymptotic distribution; chibar squared distribution; logistic regression; quasilikelihood;
THE ANALYSIS OF BINARY DATA WITH LARGE, UNBALANCED, AND INCOMPLETE CLUSTERS USING RATIO MEAN AND WEIGHTED REGRESSION METHODS
, 1993
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Data Analysis
, 2002
"... In this paper we introduce robust techniques for inference and model selection in the analysis of longitudinal data. Robust versions of quasilikelihood functions are obtained by building upon a set of robust estimating equations where robustness is achieved by weighting the classical estimating equ ..."
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In this paper we introduce robust techniques for inference and model selection in the analysis of longitudinal data. Robust versions of quasilikelihood functions are obtained by building upon a set of robust estimating equations where robustness is achieved by weighting the classical estimating equations. The robust quasilikelihood functions are then used to construct a class of test statistics for model selection. We derive the asymptotic distribution of this class of test statistics, and show its robustness properties in terms of stability of the asymptotic level and power under contamination. We also address the problem of the robust estimation of the nuisance parameters. The application to a real dataset confirms the benefit of our robust analysis. KEY WORDS: estimating equations; model selection; nuisance parameters estimation; quasilikelihoods functions; robust estimation; robust inference.