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Semiparametric regression is concerned with the flexible incorporation of nonlinear functional relationships in regression analyses. Any application area that uses regression analysis can benefit from semiparametric regression. Assuming only a basic familiarity with ordinary parametric regression, this user-friendly book explains the techniques and benefits… (More)

We consider the problem of testing null hypotheses that include restrictions on the variance component in a linear mixed model with one variance component. We derive the finite sample and asymptotic distribution of the likelihood ratio test (LRT) and the restricted likelihood ratio test (RLRT). The spectral representations of the LRT and RLRT statistics are… (More)

- David Ruppert
- 1997

A data-based local bandwidth selector is proposed for nonparametric regression by local tting of polynomials. The estimator, called the empirical-bias bandwidth selector (EBBS), is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function. EBBS minimizes an estimate of mean square… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in… (More)

We study spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. Our estimates are pth degree piecewise polynomials with p− 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty on the jumps of the pth derivative at the knots. To be… (More)

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact… (More)

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely dif cult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a exible regression… (More)

- Yingxing Li, David Ruppert
- 2007

The asymptotic behaviour of penalized spline estimators is studied in the univariate case. We use B -splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya-Watson kernel estimators with… (More)

- Ciprian M. Crainiceanu, David Ruppert, Raymond J. Carroll, Adarsh Joshi, Billy Goodner
- 2007

Penalized splines have become an increasingly popular tool for nonparametric smoothing because of their use of low-rank spline bases, which makes computations tractable while maintaining accuracy as good as smoothing splines. This article extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially… (More)

While the additive model is a popular nonparametric regression method, many of its theoretical properties are not well understood, especially when the back tting algorithm is used for computation of the the estimators. This article explores those properties when the additive model is tted by local polynomial regression. Su cient conditions guaranteeing the… (More)