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A Bayesian Approach to Robust Binary Nonparametric Regression
, 1997
"... This paper presents a Bayesian approach to binary nonparametric regression which assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The paper makes the following contributions. First, a comprehensive approach is presented ..."
Abstract

Cited by 15 (1 self)
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This paper presents a Bayesian approach to binary nonparametric regression which assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The paper makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out, and the estimates made robust to outliers. Second, the approach can handle a wide rage of link functions. Third, efficient state space based algorithms are used to carry out the computations. Fourth, an extensive set of simulations is carried out which show that the Bayesian estimator works well and compares favorably to two estimators which are widely used in practice.
Approaches for Semiparametric Bayesian Regression
 Computational Approach for Full Nonparametric Bayesian Inference under Dirichlet Process Mixture Models,&quot; Journal of Computational and Graphical Statistics
, 1997
"... Developing regression relationships is a primary inferential activity. We consider such relationships in the context of hierarchical models incorporating linear structure at each stage. Modern statistical work encourages less presumptive, i.e., nonparametric specifications for at least a portion of ..."
Abstract

Cited by 5 (2 self)
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Developing regression relationships is a primary inferential activity. We consider such relationships in the context of hierarchical models incorporating linear structure at each stage. Modern statistical work encourages less presumptive, i.e., nonparametric specifications for at least a portion of the modeling. That is, we seek to enrich the class of standard parametric hierarchical models by wandering nonparametrically near (in some sense) the standard class but retaining the linear structure. This enterprise falls within what is referred to as semiparametric modeling. We focus here on nonparametric modeling of monotone functions associated with the model. Such monotone functions arise, for example, as the stochastic mechanism itself using the cumulative distribution function, as the link function in a generalized linear model, as the cumulative hazard function in survival analysis models, and as the calibration function in errorsinvariables models. Nonparametric approaches for mod...