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46
Spatially adaptive wavelet thresholding with context modeling for image denoising
 IEEE Trans. Image Proc
, 2000
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2002a), “Statistical Analysis of a Telephone Call Center: A Queueing Science Perspective,” technical report, University of Pennsylvania, downloadable at http://iew3.technion.ac.il/serveng/References/references.html
"... A call center is a service network in which agents provide telephonebased services. Customers who seek these services are delayed in telequeues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking cal ..."
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Cited by 126 (19 self)
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A call center is a service network in which agents provide telephonebased services. Customers who seek these services are delayed in telequeues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.
Efficient Estimation of Conditional Variance Functions in Stochastic Regression
 Biometrika
, 1998
"... this paper is to derive an ecient fullyadaptive procedure for estimating ..."
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Cited by 79 (7 self)
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this paper is to derive an ecient fullyadaptive procedure for estimating
A selective overview of nonparametric methods in financial econometrics
 Statist. Sci
, 2005
"... Abstract. This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of timehomogeneous and timedependent diffusion processes, and estimation ..."
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Cited by 34 (7 self)
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Abstract. This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of timehomogeneous and timedependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline the main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.
Local Polynomial Variance Function Estimation
, 1997
"... The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametr ..."
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Cited by 16 (4 self)
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The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The effect of preliminary estimation of the mean is studied, and a "degrees of freedom" is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence model computations. KEY WORDS: Bandwidth; Heteroscedasticity; Kernel Smoothing; Nonparametric Regression; Smoother Matrix. 1. Introduction In regression analysis it is often the...
Variance Estimation in Nonparametric Regression via the Difference Sequence Method
 Ann. Statist
, 2006
"... Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of differencebased kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwid ..."
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Cited by 12 (4 self)
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Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of differencebased kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.
Adaptive estimation of mean and volatility functions in (auto) regressive models
 Stochastic Processes and their Applications 97
"... In this paper, we study the problem of non parametric estimation of the mean and variance functions b and σ 2 in a model: Xi+1 = b(Xi) + σ(Xi)εi+1. For this purpose, we consider a collection of finite dimensional linear spaces. We estimate b using a mean squares estimator built on a data driven sele ..."
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Cited by 10 (5 self)
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In this paper, we study the problem of non parametric estimation of the mean and variance functions b and σ 2 in a model: Xi+1 = b(Xi) + σ(Xi)εi+1. For this purpose, we consider a collection of finite dimensional linear spaces. We estimate b using a mean squares estimator built on a data driven selected linear space among the collection. Then an analogous procedure estimates σ 2, using a possibly different collection of models. Both data driven choices are performed via the minimization of penalized mean squares contrasts. The penalty functions are random in order not to depend on unknown variancetype quantities. In all cases, we state non asymptotic risk bounds in IL2 empirical norm for our estimators and we show that they are both adaptive in the minimax sense over a large class of Besov balls. Lastly, we give the results of intensive simulation experiments which show the good performances of our estimator.
Estimating residual variance in nonparametric regression using least squares, Biometrika 92: 821–830
, 2005
"... We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as ..."
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Cited by 8 (4 self)
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We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. Our method can be applied to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points. No ordering is required for our method. We develop methods for selecting the bandwidth. For the special case of one dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite sample performance of our method and compare it with existing methods. We illustrate our method using a real data set.
Effect of mean on variance function estimation in nonparametric regression
, 2006
"... Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results indicate that, contrary to the common practice, it is not de ..."
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Cited by 8 (1 self)
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Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results indicate that, contrary to the common practice, it is not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean when the mean function is not smooth. Instead it is more desirable to use estimators of the mean with minimal bias. On the other hand, when the mean function is very smooth, our numerical results show that the residualbased method performs better, but not substantial better than the firstorderdifferencebased estimator. In addition our asymptotic results also correct the optimal rate claimed
Nonparametric Regression with Additional Measurement Errors in the Dependent Variable
 Universitat Stuttgart
, 2003
"... Estimation of a regression function from data which consists of an independent and identically distributed sample of the underlying distribution with additional measurement errors in the dependent variable is considered. It is allowed that the measurement errors are not independent and have nonzero ..."
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Cited by 6 (3 self)
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Estimation of a regression function from data which consists of an independent and identically distributed sample of the underlying distribution with additional measurement errors in the dependent variable is considered. It is allowed that the measurement errors are not independent and have nonzero mean. It is shown that the rate of convergence of least squares estimates applied to this data is similar to the rate of convergence of least squares estimates applied to an independent and identically distributed sample of the underlying distribution as long as the measurement errors are small. As an application, estimation of the conditional variance from residuals is considered.