Results 1  10
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11
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 ..."
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Cited by 86 (7 self)
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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
Bandwidth Selection in Kernel Density Estimation: A Review
 CORE and Institut de Statistique
"... Allthough nonparametric kernel density estimation is nowadays a standard technique in explorative dataanalysis, there is still a big dispute on how to assess the quality of the estimate and which choice of bandwidth is optimal. The main argument is on whether one should use the Integrated Squared ..."
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Cited by 82 (1 self)
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Allthough nonparametric kernel density estimation is nowadays a standard technique in explorative dataanalysis, there is still a big dispute on how to assess the quality of the estimate and which choice of bandwidth is optimal. The main argument is on whether one should use the Integrated Squared Error or the Mean Integrated Squared Error to define the optimal bandwidth. In the last years a lot of research was done to develop bandwidth selection methods which try to estimate the optimal bandwidth obtained by either of this error criterion. This paper summarizes the most important arguments for each criterion and gives an overview over the existing bandwidth selection methods. We also summarize the small sample behaviour of these methods as assessed in several MonteCarlo studies. These MonteCarlo studies are all restricted to very small sample sizes due to the fact that the numerical effort of estimating the optimal bandwidth by any of these bandwidth selection methods is proporti...
DataBased Choice of Histogram Bin Width
 The American Statistician
, 1996
"... The most important parameter of a histogram is the bin width, since it controls the tradeoff between presenting a picture with too much detail ("undersmoothing ") or too little detail ("oversmoothing") with respect to the true distribution. Despite this importance there has been ..."
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Cited by 35 (0 self)
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The most important parameter of a histogram is the bin width, since it controls the tradeoff between presenting a picture with too much detail ("undersmoothing ") or too little detail ("oversmoothing") with respect to the true distribution. Despite this importance there has been surprisingly little research into estimation of the "optimal" bin width. Default bin widths in most common statistical packages are, at least for large samples, quite far from the optimal bin width. Rules proposed by, for example, Scott (1992) lead to better large sample performance of the histogram, but are not consistent themselves. In this paper we extend the bin width rules of Scott to those that achieve rootn rates of convergence to the L 2 optimal bin width; thereby providing firm scientific justification for their use. Moreover, the proposed rules are simple, easy and fast to compute and perform well in simulations. KEY WORDS: Binning; Data analysis; Density estimation; Kernel functional estimator; S...
Universal smoothing factor selection in density estimation: theory and practice (with discussion
 Test
, 1997
"... In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L1 error of the corresponding kernel estimate is not larger than 3+e times the error of the estimate with the optimal smoothing fac ..."
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Cited by 32 (11 self)
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In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L1 error of the corresponding kernel estimate is not larger than 3+e times the error of the estimate with the optimal smoothing factor plus a constant times Ov~~n/n, where n is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for each n. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method.
ZeroBias Locally Adaptive Density Estimators
 Journal of the Royal Statistical Society, B (Submitted
, 2000
"... this paper, is referred to as a local density or balloon estimator. The local density estimator varies the bandwidth with the estimation point, i.e. ..."
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Cited by 7 (0 self)
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this paper, is referred to as a local density or balloon estimator. The local density estimator varies the bandwidth with the estimation point, i.e.
Bias Correction and Higher Order Kernel Functions
"... Abstract. Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(h~). In this note, a method of corr~cting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, t ..."
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Cited by 4 (0 self)
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Abstract. Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(h~). In this note, a method of corr~cting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, this method produces a higher order kernel based on a second order kernel. For a kernel function K, the functions and 1 K(lcl) ()/ f~oo K(lcl)(z)/zdz z z are kernels of order k, under some mild conditions.
Fourier
"... series based direct plugin bandwidth selectors for kernel density estimation∗ ..."
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series based direct plugin bandwidth selectors for kernel density estimation∗
STATISTICAL COMPUTING AND GRAPHICS DataBased Choice of Histogram Bin Width
"... The most important parameter of a histogram is the bin width because it controls the tradeoff between presenting a picture with too much detail ("undersmoothing") or too little detail ("oversmoothing") with respect to the true distribution. Despite this importance there has been ..."
Abstract
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The most important parameter of a histogram is the bin width because it controls the tradeoff between presenting a picture with too much detail ("undersmoothing") or too little detail ("oversmoothing") with respect to the true distribution. Despite this importance there has been surprisingly little research into estimation of the "optimal " bin width. Default bin widths in most common statistical packages are, at least for large samples, quite far from the optimal bin width. Rules proposed by, for example, Scott lead to better large sample performance of the histogram, but are not consistent themselves. In this paper we extend the bin width rules of Scott to those that achieve rootn rates of convergence to the L2optimal bin width, thereby providing firm scientific justification for their use. Moreover, the proposed rules are simple, easy and fast to compute, and perform well in simulations. KEY WORDS: Binning; Data analysis; Density estimation; Kernel functional estimator; Smoothing parameter selection. 1.
Preprint Number 15–26 A WEIGHTED LEASTSQUARES CROSSVALIDATION BANDWIDTH SELECTOR FOR KERNEL DENSITY ESTIMATION
"... Abstract: Since the late eighties several methods have been considered in the literature to reduce the sample variability of the leastsquares crossvalidation bandwidth selector for kernel density estimation. In this paper a weighted version of this classical method is proposed and its asymptotic ..."
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Abstract: Since the late eighties several methods have been considered in the literature to reduce the sample variability of the leastsquares crossvalidation bandwidth selector for kernel density estimation. In this paper a weighted version of this classical method is proposed and its asymptotic and finite sample behaviour is studied. The simulation results attest that the weighted crossvalidation bandwidth performs quite well presenting a better finite sample performance than the standard crossvalidation method for “easytoestimate ” densities, and retaining the good finite sample performance of the standard crossvalidation method for “hardtoestimate ” ones.
Information Bound For Bandwidth Selection In Kernel Estimation Of Density Derivatives
"... Based on a random sample of size n from an unknown density f on the real line, several datadriven methods for selecting the bandwidth in kernel estimation of f (k) , k = 0; 1; 2; \Delta \Delta \Delta , have recently been proposed which have a very fast asymptotic rate of convergence to the optim ..."
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Based on a random sample of size n from an unknown density f on the real line, several datadriven methods for selecting the bandwidth in kernel estimation of f (k) , k = 0; 1; 2; \Delta \Delta \Delta , have recently been proposed which have a very fast asymptotic rate of convergence to the optimal bandwidth, where f (k) denotes the kth derivative of f . In particular, for all k and sufficiently smooth f , the best possible relative rate of convergence is O p (n \Gamma1=2 ). For k = 0, Fan and Marron (1992) employed semiparametric arguments to obtain the best possible constant coefficient, that is, an analog of the usual Fisher information bound, in this convergence. The purpose of this paper is to show that, with sufficient additional effort, their arguments can be extended to general k and establish the information bounds for all k. The extension from the special case k = 0 to the case of general k requires some more work which is not trivial. This gives a significant benchma...