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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.
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 35 (8 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.
Simultaneous Confidence Bands For Linear Regression And Smoothing
 Journal of the American Statistical Association
, 1992
"... Suppose we observe Y i = f(x i ) + ffl i ; i = 1; . . . ; n. We wish to find approximate 1 \Gamma ff simultaneous confidence regions for ff(x);x 2 Xg. Our regions will be centered around linear estimates f(x) of parametric or nonparametric f(x). There is a large amount of previous work on this sub ..."
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Cited by 32 (6 self)
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Suppose we observe Y i = f(x i ) + ffl i ; i = 1; . . . ; n. We wish to find approximate 1 \Gamma ff simultaneous confidence regions for ff(x);x 2 Xg. Our regions will be centered around linear estimates f(x) of parametric or nonparametric f(x). There is a large amount of previous work on this subject. Substantial restrictions have been usually placed on some or all of the dimensionality of x, the class of functions f that can be considered, the class of linear estimates f and the region X . The method we present is an approximation to the tube formula and can be used for multidimensional x and a wide class of linear estimates. By considering the effect of bias we are able to relax assumptions on the class of functions f which are considered. Simulations and numerical computations are used to illustrate the performance. 1 Research is supported in part by the National Science Foundation under grant DMS8902188. AMS 1991 subject classifications. Primary 62F25; Secondary 60G15, 62G0...
GoodnessofFit Tests for Parametric Regression Models
 JOUR. AMERI. STATIST. ASSOC
, 2001
"... Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric ts is negligible by using the adaptive Neyman test and other methods. The testing procedures ..."
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Cited by 19 (5 self)
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Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric ts is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consistently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies show that the new testing procedures are indeed powerful and omnibus. The power of the proposed tests is comparable to the Ftest statistic even in the situations where F test is known to be suitable and can be far more powerful than the Ftest statistic in other situations. An application to testing linear models versus additive models are discussed.
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.
Inference of Trends in Time Series
 J. the Royal Statistical Society: Series B (Statistical Methodology
, 2007
"... Summary. We consider statistical inference of trends in mean nonstationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically cor ..."
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Cited by 14 (4 self)
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Summary. We consider statistical inference of trends in mean nonstationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years.
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.
Testing For Monotonicity Of A Regression Mean Without Selecting A Bandwidth
, 1998
"... . A new approach to testing for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of `running gradients' over short intervals, although from some viewpoints it may be regarded as an analogue for monotonicity test ..."
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Cited by 4 (3 self)
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. A new approach to testing for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of `running gradients' over short intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almostflat parts of the target function. In fact, it is calibrated so as to work well for flat response curves, and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders. In this respect, as well as in its construction, the `running gradients' approach differs from alternative techniques based on the notion of a critical bandwidth. KEYWORDS. Bootstrap, calibration, curve estimation, Monte Carlo, response curve, running gradient. SHORT TITLE. Testing for monotonicity. 1 The man...