Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture
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In this article, the authors considered the convergence of variance type models for a regression function or for the logarithm of a probability function, conditional probability functions, density function, hazard function, or spectral density function.Abstract:
Analysis of variance type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function or spectral density function. Polynomial splines are used to model the main effects, and their tensor products are used to model any interaction components that are included. In the special context of survival analysis, the baseline hazard function is modeled and nonproportionality is allowed. In general, the theory involves the $L_2$ rate of convergence for the fitted model and its components. The methodology involves least squares and maximum likelihood estimation, stepwise addition of basis functions using Rao statistics, stepwise deletion using Wald statistics and model selection using the Bayesian information criterion, cross-validation or an independent test set. Publicly available software, written in C and interfaced to S/S-PLUS, is used to apply this methodology to real data.read more
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References
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Nonparametric Estimation from Incomplete Observations
Edward L. Kaplan,Paul Meier +1 more
TL;DR: In this article, the product-limit (PL) estimator was proposed to estimate the proportion of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t).
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Estimating the Dimension of a Model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Estimating the dimension of a model
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).