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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 119 (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.
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 14 (5 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.
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.
Optimal testing in a fixedeffects functional analysis of variance model
 International Journal of Wavelets, Multiresolution and Information Processing
, 2004
"... We consider the testing problem in a fixedeffects functional analysis of variance model. We test the null hypotheses that the functional main effects and the functional interactions are zeros against the composite nonparametric alternative hypotheses that they are separated away from zero in L 2no ..."
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Cited by 6 (4 self)
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We consider the testing problem in a fixedeffects functional analysis of variance model. We test the null hypotheses that the functional main effects and the functional interactions are zeros against the composite nonparametric alternative hypotheses that they are separated away from zero in L 2norm and also possess some smoothness properties. We adapt the optimal (minimax) hypothesis testing procedures for testing a zero signal in a Gaussian “signal plus noise ” model to derive optimal (minimax) nonadaptive and adaptive hypothesis testing procedures for the functional main effects and the functional interactions. The corresponding tests are based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize different types of smoothness conditions assumed on the response function by means of its wavelet coefficients for a wide range of function classes. In order to shed some light on the theoretical results obtained, we carry out a simulation study to examine the finite sample performance of the proposed functional hypothesis testing procedures. As an illustration, we also apply these tests to a reallife data example arising from physiology. Concluding remarks and hints for possible extensions of the proposed methodology are also given.
Variance Function Estimation in Multivariate Nonparametric Regression
, 2006
"... Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, an ..."
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Cited by 4 (0 self)
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Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, and very much contrary to the common practice, it is often not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean. Instead it is desirable to use estimators of the mean with minimal bias. Another important conclusion is that the first order differencebased estimator that achieves minimax rate of convergence in onedimensional case does not do the same in the high dimensional case. Instead, the optimal order of differences depends on the number of dimensions.
Estimating Linear Functionals of the Error Distribution in Nonparametric Regression
"... This paper addresses estimation of linear functionals of the error distribution in nonparametric regression models. It derives an i.i.d. representation for the empirical estimator based on residuals, using undersmoothed estimators for the regression curve. Asymptotic eciency of the estimator is p ..."
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Cited by 4 (2 self)
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This paper addresses estimation of linear functionals of the error distribution in nonparametric regression models. It derives an i.i.d. representation for the empirical estimator based on residuals, using undersmoothed estimators for the regression curve. Asymptotic eciency of the estimator is proved. Estimation of the error variance is discussed in detail.
ASSIST: A suite of S functions implementing spline smoothing techniques. http://www.pstat.ucsb.edu/faculty/yuedong/software.html[3
, 2004
"... We present a suite of user friendly S functions for fitting various smoothing spline models including (a) nonparametric regression models for independent and correlated Gaussian data, and for independent binomial, Poisson and Gamma data; (b) semiparametric linear mixedeffects models; (c) nonpara ..."
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Cited by 2 (1 self)
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We present a suite of user friendly S functions for fitting various smoothing spline models including (a) nonparametric regression models for independent and correlated Gaussian data, and for independent binomial, Poisson and Gamma data; (b) semiparametric linear mixedeffects models; (c) nonparametric nonlinear regression models; (d) semiparametric nonlinear regression models; and (e) semiparametric nonlinear mixedeffects models. The general form of smoothing splines based on reproducing kernel Hilbert spaces is used to model nonparametric functions. Thus these S functions deal with many different situations in a unified fashion. Some well known special cases are polynomial splines, periodic splines, spherical splines, thinplate splines, lsplines, generalized additive models, smoothing spline ANOVA models, projection pursuit models, multiple index models, varying coefficient models, functional linear models, and selfmodeling nonlinear regression models. These nonparametric/semiparametric linear/nonlinear fixed/mixed models are widely used in practice to analyze data arising in many areas of investigation such as medicine, epidemiology, pharmacokinetics, econometrics and social science. This manual describes technical details behind these S functions and illustrate their applications using several examples. 1
NONPARAMETRIC LEAST SQUARES ESTIMATION IN DERIVATIVE FAMILIES
, 2008
"... ABSTRACT. Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose seriestype estimators which incorporate various derivat ..."
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ABSTRACT. Cost function estimation often involves data on a function and a family of its derivatives. It is known that by using such data the convergence rates of nonparametric estimators can be substantially improved. In this paper we propose seriestype estimators which incorporate various derivative data into a single, weighted, nonparametric, leastsquares procedure. Convergence rates are obtained, with particular attention being paid to cases in which rootn consistency can be achieved. For lowdimensional cases, it is shown that much of the beneficial impact on convergence rates is realized even if only data on ordinary firstorder partials are available. For example, if one incorporates data on factor demands, a two or three–input cost function can be estimated at rates only slightly slower than if it were a function of a single nonparametric variable. In instances where the rootn rate is attained (possibly up to a logarithmic factor), the smoothing parameter can often be chosen very easily, without resort to empirical methods. Moreover, the fact that the optimal rate is rootn can be determined from knowledge of which derivatives are observed, and does not require complex empirical arguments. In other cases, standard crossvalidation can be employed. Applications to cost and production function estimation are used to illustrate the methodology.
Nonparametric Regression for Problems Involving Lognormal Distributions
"... First of all, I wish to devote my sincere thanks and deep appreciation to my dissertation advisor, Professor Lawrence D. Brown, for his tremendous amount of encouragement, guidance and financial support during the development of my research. It is he who has brought me into the wonderful world of St ..."
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First of all, I wish to devote my sincere thanks and deep appreciation to my dissertation advisor, Professor Lawrence D. Brown, for his tremendous amount of encouragement, guidance and financial support during the development of my research. It is he who has brought me into the wonderful world of Statistics. It is him that I will keep learning from and living up to through the rest of my life. Special thanks are due to all those people who had advised and helped me at important steps of my life, among whom are Noah Gans, Jianhua Huang, Paul Shaman