Results 1  10
of
27
Smoothing by Local Regression: Principles and Methods
"... this paper we describe two adaptive procedures, one based on C p and the other based on crossvalidation. Still, when we have a final adaptive fit in hand, it is critical to subject it to graphical diagnostics to study its performance. The important implication of these statements is that the above c ..."
Abstract

Cited by 88 (1 self)
 Add to MetaCart
this paper we describe two adaptive procedures, one based on C p and the other based on crossvalidation. Still, when we have a final adaptive fit in hand, it is critical to subject it to graphical diagnostics to study its performance. The important implication of these statements is that the above choices must be tailored to each data set in practice; that is, the choices represent a modeling of the data. It is widely accepted that in global parametric regression there are a variety of choices that must be made  for example, the parametric family to be fitted and the form of the distribution of the response  and that we must rely on our knowledge of the mechanism generating the data, on model selection diagnostics, and on graphical diagnostic methods to make the choices. The same is true for smoothing. Cleveland (1993) presents many examples of this modeling process. For example, in one application, oxides of nitrogen from an automobile engine are fitted to the equivalence ratio, E, of the fuel and the compression ratio, C, of the engine. Coplots show that it is reasonable to use quadratics as the local parametric family but with the added assumption that given E the fitted f
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 ..."
Abstract

Cited by 82 (16 self)
 Add to MetaCart
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.
Local polynomial kernel regression for generalized linear models and quasilikelihood functions
 Journal of the American Statistical Association,90
, 1995
"... were introduced as a means of extending the techniques of ordinary parametric regression to several commonlyused regression models arising from nonnormal likelihoods. Typically these models have a variance that depends on the mean function. However, in many cases the likelihood is unknown, but the ..."
Abstract

Cited by 57 (7 self)
 Add to MetaCart
were introduced as a means of extending the techniques of ordinary parametric regression to several commonlyused regression models arising from nonnormal likelihoods. Typically these models have a variance that depends on the mean function. However, in many cases the likelihood is unknown, but the relationship between mean and variance can be specified. This has led to the consideration of quasilikelihood methods, where the conditionalloglikelihood is replaced by a quasilikelihood function. In this article we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to these more general contexts. In the ordinary regression case local polynomial fitting has been seen to possess several appealing features in terms of intuitive and mathematical simplicity. One noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators. These properties are shown to carryover to the generalized linear model and quasilikelihood model. The end result is a class of kernel type estimators for smoothing in quasilikelihood models. These estimators can be viewed as a straightforward generalization of the usual parametric estimators. In addition, their simple asymptotic distributions allow for simple interpretation
Piecewisepolynomial regression trees
 Statistica Sinica
, 1994
"... A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data ..."
Abstract

Cited by 30 (7 self)
 Add to MetaCart
A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data space. Partitioning is carried out recursively as in a treestructured method. If the estimate is required to be smooth, the polynomial pieces may be glued together by means of weighted averaging. The smoothed estimate is thus obtained in three steps. In the first step, the regressor space is recursively partitioned until the data in each piece are adequately fitted by a polynomial of a fixed order. Partitioning is guided by analysis of the distributions of residuals and crossvalidation estimates of prediction mean square error. In the second step, the data within a neighborhood of each partition are fitted by a polynomial. The final estimate of the regression function is obtained by averaging the polynomial pieces, using smooth weight functions each of which diminishes rapidly to zero outside its associated partition. Estimates of derivatives of the regression function may be
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 ..."
Abstract

Cited by 16 (4 self)
 Add to MetaCart
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.
Statistics and Music: Fitting a Local Harmonic Model to Musical Sound Signals
, 1998
"... Statistical modeling and analysis have been applied to different music related fields. One of them is sound synthesis and analysis. Sound can be represented as a realvalued function of time. This function can be sampled at a small enough rate so that the resulting discrete version is almost as goo ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
Statistical modeling and analysis have been applied to different music related fields. One of them is sound synthesis and analysis. Sound can be represented as a realvalued function of time. This function can be sampled at a small enough rate so that the resulting discrete version is almost as good as the continuous one. This permits one to study musical sounds as a discrete time series, an entity for whichmany statistical techniques are available. Physical modeling suggests that manymusical instruments' sounds are characterized bya harmonic and an additive noise signal. The noise is not something to get rid of rather it's an important part of the signal. In this research the interest is in separating these two elements of the sound. To do so a local harmonic model that tracks ch...
From local polynomial approximation to pointwise shapeadaptive transforms: an evolutionary nonparametric regression perspective
 PROC. 2006 INT. TICSP WORKSHOP SPECTRAL METH. MULTIRATE SIGNAL PROCESS., SMMSP 2006
, 2006
"... In this paper we review and discuss some of the theoretical and practical aspects, the problems, and the considerations that pushed our research from the onedimensional LPAICI (local polynomial approximation interesection of conÞdence intervals) algorithm [27] to the development of powerful trans ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
In this paper we review and discuss some of the theoretical and practical aspects, the problems, and the considerations that pushed our research from the onedimensional LPAICI (local polynomial approximation interesection of conÞdence intervals) algorithm [27] to the development of powerful transformbased methods for anisotropic image
Geographically Weighted Regression as a Statistical Model
, 2000
"... Recent work on Geographically Weighted Regression (GWR) (Brunsdon, Fotheringham, and Charlton 1996) has provided a means of investigating spatial nonstationarity in linear regression models. However, the emphasis of much of this work has been exploratory. Despite this, GWR borrows from a well f ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Recent work on Geographically Weighted Regression (GWR) (Brunsdon, Fotheringham, and Charlton 1996) has provided a means of investigating spatial nonstationarity in linear regression models. However, the emphasis of much of this work has been exploratory. Despite this, GWR borrows from a well founded statistical methodology (Tibshirani and Hastie 1987; Staniswalis 1987a; Hastie and Tibshirani 1993) and may be used in a more formal modelling context. In particular, one may compare GWR models against other models using modern statistical inferential theories. Here, we demonstatrate how Akaike's Information Criterion (AIC) (Akaike 1973) may be used to decide whether GWR or ordinary regression provide the best model for a given geographical data set. We also demonstrate how the AIC may be used to choose the degree of smoothing used in GWR, and how basic GWR models may be compared to `mixed' models in which some regression coe#cients are fixed and others are nonstationary.