Results 1  10
of
85
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 literatu ..."
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Cited by 146 (19 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 122 (30 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.
Approximate Bayesian computation: A nonparametric perspective
 Journal of the American Statistical Association
, 2010
"... Approximate Bayesian Computation is a family of likelihoodfree inference techniques that are wellsuited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics sobs from the data and simulating synthe ..."
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Cited by 40 (2 self)
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Approximate Bayesian Computation is a family of likelihoodfree inference techniques that are wellsuited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics sobs from the data and simulating synthetic summary statistics for different values of the parameter Θ. The posterior distribution is then approximated by an estimator of the conditional density g(Θsobs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a smaller number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. Last, we present model selection in Approximate Bayesian Computation and provide asymptotic properties of two estimators of the model probabilities. As for parameter estimation, the asymptotic results raise the importance of the curse of dimensionality in Approximate Bayesian Computation. Performing numerical simulations in a simple normal model confirms that the estimators may be less efficient as the number of summary statistics increases. Supplemental materials containing the details of the proofs are available online.
Bootstrap confidence bands for regression curves and their derivatives
 Ann. Statist
, 2003
"... Confidence bands for regression curves and their first p derivatives are obtained via local pth order polynomial estimation. The method allows for multiparameter local likelihood estimation as well as other unbiased estimating equations. As an alternative to the confidence bands obtained by asympt ..."
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Cited by 38 (2 self)
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Confidence bands for regression curves and their first p derivatives are obtained via local pth order polynomial estimation. The method allows for multiparameter local likelihood estimation as well as other unbiased estimating equations. As an alternative to the confidence bands obtained by asymptotic distribution theory, we also study smoothed bootstrap confidence bands. Simulations illustrate the finite sample properties of the methodology.
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 34 (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.
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 28 (7 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.
Local Likelihood Smoothing of Sample Extremes
, 1999
"... This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extremevalue distribution and related models. The uncertainty of fits is assessed using resampling methods. The methods are applied to data on extreme temperatures, on re ..."
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Cited by 28 (6 self)
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This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extremevalue distribution and related models. The uncertainty of fits is assessed using resampling methods. The methods are applied to data on extreme temperatures, on record times for the womens 3000m race, and on insurance claims.
Uniform Bahadur representation for local polynomial estimates of Mregression and its application to the additive model. Econometric Theory, accepted
, 2008
"... We use local polynomial fitting to estimate the nonparametric Mregression function for strongly mixing stationary processes {(Yi, X i)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fund ..."
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Cited by 25 (1 self)
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We use local polynomial fitting to estimate the nonparametric Mregression function for strongly mixing stationary processes {(Yi, X i)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging in such estimators into other functionals where some control over higher order terms are required. We apply our results to the estimation of an additive Mregression model.