Results 1  10
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49
SiZer for exploration of structures in curves
 Journal of the American Statistical Association
, 1997
"... In the use of smoothing methods in data analysis, an important question is often: which observed features are "really there?", as opposed to being spurious sampling artifacts. An approach is described, based on scale space ideas that were originally developed in computer vision literature. Assess ..."
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Cited by 82 (16 self)
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In the use of smoothing methods in data analysis, an important question is often: which observed features are "really there?", as opposed to being spurious sampling artifacts. An approach is described, based on scale space ideas that were originally developed in computer vision literature. Assessment of Significant ZERo crossings of derivatives, results in the SiZer map, a graphical device for display of significance of features, with respect to both location and scale. Here "scale" means "level of resolution", i.e.
Generalized Partially Linear SingleIndex Models
 Journal of the American Statistical Association
, 1998
"... The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, wher ..."
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Cited by 63 (24 self)
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The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, where 0 ( ) is an unknown function. We call these generalized partially linear singleindex models (GPLSIM). The models include the "singleindex" models, which have 0 = 0. Using local linear methods, estimates of the unknown parameters ( 0 ; 0 ) and the unknown function 0 ( ) are proposed, and their asymptotic distributions obtained. Examples illustrate the models and the proposed estimation methodology.
Testing monotonicity of regression
 Journal of Computational and Graphical Statistics
, 1998
"... This article provides a test of monotonicity of a regression function. The test is based on the size of a “critical ” bandwidth, the amount of smoothing necessary to force a nonparametric regression estimate to be monotone. It is analogous to Silverman’s test of multimodality in density estimation. ..."
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Cited by 24 (0 self)
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This article provides a test of monotonicity of a regression function. The test is based on the size of a “critical ” bandwidth, the amount of smoothing necessary to force a nonparametric regression estimate to be monotone. It is analogous to Silverman’s test of multimodality in density estimation. Bootstrapping is used to provide a null distribution for the test statistic. The methodology is particularly simple in regression models in which the variance is a specified function of the mean, but we also discuss in detail the homoscedastic case with unknown variance. Simulation evidence indicates the usefulness of the method. Two examples are given.
Local Nonlinear Least Squares: Using Parametric Information in Nonparametric Regression
 Journal of econometrics
, 2000
"... COWLES FOUNDATION DISCUSSION PAPER NO. 1075 ..."
Local Maximum Likelihood Estimation and Inference
 J. Royal Statist. Soc. B
, 1998
"... Local maximum likelihood estimation is a nonparametric counterpart of the widelyused parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issu ..."
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Cited by 16 (4 self)
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Local maximum likelihood estimation is a nonparametric counterpart of the widelyused parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This article provides a unified approach to selecting a bandwidth and constructing con dence intervals in local maximum likelihood estimation. The approach is then applied to leastsquares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powerful and encouraging.
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 ..."
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Cited by 14 (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.
Automatic Local Smoothing for Spectral Density Estimation
 Scandinavian Journal of Statistics
, 1998
"... This article uses local polynomial techniques to fit Whittle's likelihood for spectral density estimation. Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary effect is noted. We show that the Whittle likelihood based estima ..."
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Cited by 12 (2 self)
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This article uses local polynomial techniques to fit Whittle's likelihood for spectral density estimation. Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary effect is noted. We show that the Whittle likelihood based estimator has advantages over the leastsquares based logperiodogram. The bandwidth for the Whittle likelihoodbased method is chosen by a simple adjustment of a bandwidth selector proposed in Fan and Gijbels (1995). The effectiveness of the proposed procedure is demonstrated by a few simulated and real numerical examples. Our simulation results support the asymptotic theory that the likelihood based spectral density and logspectral density estimators are the most appealing among their peers. KEY WORDS: Bandwidth selection, local polynomial fit, periodogram, spectral density estimation, Whittle likelihood. 1 Introduction Spectral density estimation is useful for studying stationary time series,...
NONPARAMETRIC FUNCTIONAL DATA ANALYSIS THROUGH BAYESIAN DENSITY ESTIMATION
, 2007
"... In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivitytemperaturedepth (CTD) data in oceanography, doseresponse models in epidemiology and timecourse microarray ..."
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Cited by 12 (4 self)
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In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. Some examples are conductivitytemperaturedepth (CTD) data in oceanography, doseresponse models in epidemiology and timecourse microarray experiments in biology and medicine. In this paper we propose a hierarchical model that allows us to simultaneously estimate multiple curves nonparametrically by using dependent Dirichlet Process mixtures of Gaussians to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the outcome given the predictors. The resulting approach allows for flexible estimation and clustering, while borrowing information across curves. We also show that the function estimates we obtain are consistent on the space of integrable functions. As an illustration, we consider an application to the analysis of CTD data in the north Atlantic.
A Study of Variable Bandwidth Selection for Local Polynomial Regression
 Statistica Sinica
, 1996
"... A decisive question in nonparametric smoothing techniques is the choice of the bandwidth or smoothing parameter. The present paper addresses this question when using local polynomial approximations for estimating the regression function and its derivatives. A fullyautomatic bandwidth selection proc ..."
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Cited by 12 (2 self)
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A decisive question in nonparametric smoothing techniques is the choice of the bandwidth or smoothing parameter. The present paper addresses this question when using local polynomial approximations for estimating the regression function and its derivatives. A fullyautomatic bandwidth selection procedure has been proposed by Fan and Gijbels (1995), and the empirical performance of it was tested in detail via a variety of examples. Those experiences supported the methodology towards a great extend. In this paper we establish asymptotic results for the proposed variable bandwidth selector. We provide the rate of convergence of the bandwidth estimate, and obtain the asymptotic distribution of its error relative to the theoretical optimal variable bandwidth. Those asymptotic properties give extra support to the developed bandwidth selection procedure. It is also demonstrated how the proposed selection method can be applied in the density estimation setup. Some examples illustrate this ap...