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30
Flexible smoothing with Bsplines and penalties
 STATISTICAL SCIENCE
, 1996
"... Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots ..."
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Cited by 395 (6 self)
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Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent Bsplines. We show connections to the familiar spline penalty on the integral of the squared second derivative. A short overview of Bsplines, their construction, and penalized likelihood is presented. We discuss properties of penalized Bsplines and propose various criteria for the choice of an optimal penalty parameter. Nonparametric logistic regression, density estimation and scatterplot smoothing are used as examples. Some details of the computations are presented.
Properties of realized variance under alternative sampling schemes
 Journal of Business and Economic Statistics
, 2006
"... This paper investigates the statistical properties of realized variance in the presence of market microstructure noise. Different from the existing literature, the analysis relies on a pure jump process for high frequency security prices and explicitly distinguishes among alternative sampling schem ..."
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Cited by 50 (1 self)
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This paper investigates the statistical properties of realized variance in the presence of market microstructure noise. Different from the existing literature, the analysis relies on a pure jump process for high frequency security prices and explicitly distinguishes among alternative sampling schemes, including calendar time sampling, business time sampling, and transaction time sampling. The main finding of this paper is that transaction time sampling is generally superior to the common practice of calendar time sampling in that it leads to a lower mean squared error of realized variance. The benefits of sampling in transaction time are particularly pronounced when the trade intensity pattern is volatile. Based on IBM transaction data over the period 2000– 2004 the empirical analysis finds (i) an average optimal sampling frequency of about 3 minutes with a steady downward trend and significant daytoday variation related to market liquidity and (ii) a consistent reduction in mean squared error of realized variance due to sampling in transaction time that is about 5 % on average but
Properties of Bias Corrected Realized Variance Under Alternative Sampling Schemes
"... grateful to Michael Boldin for providing the TAQ data used in this paper. ..."
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Cited by 25 (1 self)
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grateful to Michael Boldin for providing the TAQ data used in this paper.
A reproducing kernel Hilbert space framework for spike train signal processing
 Neural Comp
, 2009
"... This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical descr ..."
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Cited by 22 (11 self)
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This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, called the crossintensity (CI) kernels, is further analyzed in detail. This particular inner product family encapsulates the statistical description from conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provides an interesting perspective to other works presented in the literature, as will be illustrated in terms of spike train distance measures. Finally, as an application example, the presented RKHS framework is used to derive from simple principles a clustering algorithm for spike trains.
Bootstrap Confidence Regions For The Intensity Of A Poisson Point Process
 Journal of the American Statistical Association
, 1996
"... . We develop bootstrap methods for constructing confidence regions, including intervals and simultaneous bands, in the context of estimating the intensity function of a nonstationary Poisson process. Several different resampling algorithms are suggested, ranging from resampling a Poisson process wi ..."
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Cited by 11 (1 self)
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. We develop bootstrap methods for constructing confidence regions, including intervals and simultaneous bands, in the context of estimating the intensity function of a nonstationary Poisson process. Several different resampling algorithms are suggested, ranging from resampling a Poisson process with intensity equal to that estimated nonparametrically from the data, to resampling the data points themselves in much the same way one would use the bootstrap in problems involving independent and identically distributed observations. For each different bootstrap method a variety of percentilet ways of constructing confidence bands is described, producing bands whose width varies in proportion to standard deviation, or is approximately constant, depending on the application. The effectiveness of these different approaches is demonstrated both theoretically and numerically, for real and simulated data. Issues such as bias correction are addressed. KEY WORDS. Bootstrap, confidence band, con...
Detection of spatial clustering with average likelihood ratio test statistics
 Annals of Statistics
, 2009
"... ar ..."
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Reproducing Kernel Hilbert Spaces for Point Processes, with Applications to Neural Activity Analysis
, 2008
"... having accepted me as his student, and for his experienced guidance and advice. His incentive to creativity, breath of knowledge, and critical reaching thinking are, I believe, some of the most valuable lessons I will retain from my doctoral education. Without him, this dissertation would not have b ..."
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Cited by 3 (1 self)
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having accepted me as his student, and for his experienced guidance and advice. His incentive to creativity, breath of knowledge, and critical reaching thinking are, I believe, some of the most valuable lessons I will retain from my doctoral education. Without him, this dissertation would not have been possible. I also thank Dr. John G. Harris, for serving as my committee member, his interest in my research, and providing an essential practical perspective to much of my work. I also thank Dr. Justin C. Sanchez for his valuable time to read and comment on many of the results shown here. His expertise on neural activity analysis and often complementary perspective can be encountered throughout this dissertation. I also thank Dr. Jianbo Gao for all the advice and interest in serving in my committee. I am forever indebted to Dr. Francisco Vaz, for first creating the opportunity for me to come to CNEL and for all the help in obtaining funding from FCT. I will never forget that without Dr. Vaz’s assistance, I would have missed the wonderful opportunity to get a Ph.D. at the University of Florida. My friends and colleagues at CNEL deserve credit for many of the joys and for
An Efficient Algorithm for Continuoustime Cross Correlogram of Spike Trains Abstract
"... We propose an efficient algorithm to compute the smoothed correlogram for the detection of temporal relationship between two spike trains. Unlike the conventional histogram based correlogram estimations, the proposed algorithm operates on continuous time without binning the spike train nor the corre ..."
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Cited by 3 (3 self)
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We propose an efficient algorithm to compute the smoothed correlogram for the detection of temporal relationship between two spike trains. Unlike the conventional histogram based correlogram estimations, the proposed algorithm operates on continuous time without binning the spike train nor the correlogram. Hence it can be more precise in detecting the effective delay between two recording sites. Moreover, it can take advantage of the higher temporal resolution of the spike times provided by the current recording methods. The Laplacian distribution kernel for smoothing enables efficient computation of the algorithm. We also provide the basic statistics of the estimator and a guideline for choosing the kernel size. This new technique is demonstrated by estimating the effective delays in a neuronal network from synthetic data and recordings of dissociated cortical tissue. ($Id: cipogram.tex 298 20071022 19:04:45Z arpaiva $) Key words: cross correlation, correlogram, delay estimation, kernel intensity estimation, point process 1
Optimization in reproducing kernel Hilbert spaces of spike trains
 IN COMPUTATIONAL NEUROSCIENCE
, 2010
"... This paper presents a framework based on reproducing kernel Hilbert spaces (RKHS) for optimization with spike trains. To establish the RKHS for optimization we start by introducing kernels for spike trains. It is shown that spike train kernels can be built from ideas of kernel methods, or from the i ..."
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Cited by 2 (2 self)
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This paper presents a framework based on reproducing kernel Hilbert spaces (RKHS) for optimization with spike trains. To establish the RKHS for optimization we start by introducing kernels for spike trains. It is shown that spike train kernels can be built from ideas of kernel methods, or from the intensity functions underlying the spike trains. However, the later approach shall be the main focus of this study. We introduce the memoryless crossintensity (mCI) kernel as an example of an inner product of spike trains, which defines the RKHS bottomup as an inner product of intensity functions. Being defined in terms of the intensity functions, this approach towards defining spike train kernels has the advantage that points in the RKHS incorporate a statistical description of the spike trains, and the statistical model is explicitly stated. Some properties of the mCI kernel and the RKHS it induces will be given to show that this RKHS has the necessary structure for optimization. The issue of estimation from data is also addressed. We finalize with an example of optimization in the RKHS by deriving an algorithm for principal component analysis (PCA) of spike trains.
A Kernel Estimator For Stochastic Subsurface Characterization
"... A nonparametric statistical methodology based on kernel function estimation is developed for assessing the probability that a particular location in the aquifer has high or low hydraulic conductivity using bore hole information. The approach presented is an alternative to indicator Kriging. Soils ar ..."
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A nonparametric statistical methodology based on kernel function estimation is developed for assessing the probability that a particular location in the aquifer has high or low hydraulic conductivity using bore hole information. The approach presented is an alternative to indicator Kriging. Soils are classified through a binary indicator function defined as 0 for a low and as 1 for a high conductivity soil. Estimates of the probability of occurrence of a high or low conductivity soil are made on a three dimensional grid. Each such estimate is formed as a local weighted average of the indicator function values that lie within an averaging interval or bandwidth of the point of estimate. A different vertical bandwidth is chosen at each borehole log. Horizontal bandwidths are selected independently at each horizontal level. These bandwidths are chosen by cross validation. Observations closer to the point of estimate are weighted higher using a kernel or weight function. Unlike Kriging, th...