Kernel (statistics) - Factbites

Kernel (statistics) - Factbites
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Topic: Kernel (statistics)

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	Directory of Academic Statisticians 2005
		Biometry; cluster analysis; stochastic population processes; psychological applications of statistics; multivariate analysis; simulation; analysis of quantal assay data; medical statistics; ecological statistics; over- dispersion; estimation using transforms.
		Stochastic simulation; optimisation; Markov chain Monte Carlo; Bayesian statistics; applications in ecology, sociology, archaeology, medicine and biology.
		Stochastic analysis, mathematical physics, infinite dimensional analysis, stochastic processes, large deviations, quantum field theory, functional analysis, nonstandard analysis, complex analysis, financial mathematics.
	www.swan.ac.uk /statistics/das/dirint7.htm

	EKU - DMSCS WWW Server
		Dr. Dirk Schlingmann is Chair of the Department of Mathematics and Statistics.
		Supports the Department of Mathematics and Statistics by providing a variety of tutoring services to students in a supportive learning environment.
		The M.S. degree in Mathematical Sciences with options in mathematics, statistics, and computer science.
	www.math.eku.edu (333 words)

	Earliest Known Uses of Some of the Words of Mathematics (K)
		Kernel entered Statistics with the use of Fourier theory in describing estimates for spectral density and probability density functions.
		Earlier "Fejér kernel" was used in U. Grenander and M.Rosenblatt�s "Statistical Spectral Analysis of Time Series Arising from Stationary Stochastic Processes," Annals of Mathematical Statistics, 24, (1953), 537-558.
		Kernel occurs in English in 1909 in M. Bôcher's Introduction to the Study of Integral Equations : "K is called the kernel of these equations." (OED2).
	members.aol.com /jeff570/k.html (333 words)

	Earliest Known Uses of Some of the Words of Mathematics (K)
		Kernel entered Statistics with the use of Fourier theory in describing estimates for spectral density and probability density functions.
		Earlier "Fejér kernel" was used in U. Grenander and M.Rosenblatt’s "Statistical Spectral Analysis of Time Series Arising from Stationary Stochastic Processes," Annals of Mathematical Statistics, 24, (1953), 537-558.
		The use of kernel in algebra appears to be unrelated to its use in integral equations and Fourier analysis.
	members.aol.com /jeff570/k.html (1079 words)

	Publications
		An Introduction to Kernel Density Estimation, Weatherburn Lecture series, Department of Mathematics and Statistics, University of Western Australia, Australia, 24 May 2001.
		Applications of bivariate kernel density estimators (PDF 212 K) Macquarie University, Sydney, Australia, 2 December 2003.
		Bandwidth selectors for multivariate kernel density estimation (PDF 620 K) Université de Montréal, Montréal, Canada, 16 August 2004 and Université Laval, Québec, Canada, 19 August 2004.
	www.maths.uwa.edu.au /~duongt/research/index.html (290 words)

	Machine Learning (Theory) » Organization
		Kernel learning approaches have a few standard kernels which often work on simple problems, although sometimes significant kernel engineering is required.
		One way to organize learning theory is by assumption (in the assumption = axiom sense), from no assumptions to many assumptions.
		This was the sixth Machine Learning Summer School, and the second one that used a wiki.
	hunch.net /index.php?cat=3 (3331 words)

	Yakov Nikitin. Personal Home Page. List of most important publications
		Large deviations of quadratic statistics with degenerate kernel.Abstracts of the conference in Probability and Statistics dedicated to 75 years jubilee of acad.S.Kh.Sira- zhdinov, Fergana,27-29.09.95,Tashkent,1995, p.87-88.
		Asymptotic efficiency in Bahadur sense of omega-square type statistics in case of several samples, Notes of Scient.
		Probability and Statistics: A R.R.Bahadur Festschrift, Wiley Eastern Ltd,New Delhi,1993,p.1-12 (jointly with V.L.Abbakumov).
	www.math.spbu.ru /user/nikitin/pub2002.html (2202 words)

	Probability Abstract Service
		We review a new estimator for estimating the variance components and derived the distribution of the pedigree statistics used in testing for outlying observations.
		This structure is realized via Markov process with transition kernel that is a mixture of Gaussians with non-constant, state dependent, class probabilities.
		Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation.
	www.economia.unimi.it /PAS/Letters/letter_46.shtml (2202 words)

	Earliest Known Uses of Some of the Words of Mathematics (K)
		Earlier "Fejér kernel" was used in U. Grenander and M.Rosenblatt’s "Statistical Spectral Analysis of Time Series Arising from Stationary Stochastic Processes," Annals of Mathematical Statistics, 24, (1953), 537-558.
		The use of kernel in algebra appears to be unrelated to its use in integral equations and Fourier analysis.
		A JSTOR search found the "Fejér kernel" and "Dirichlet kernel" in Charles N. Moore's "On the Application of Borel's Method to the Summation of Fourier's Series" (Proceedings of the National Academy, 11, (1925), 284-287) but it is unlikely that this was the first published use of these terms.
	members.aol.com /jeff570/k.html (2202 words)

	Earliest Known Uses of Some of the Words of Mathematics (K)
		Earlier "Fejér kernel" was used in U. Grenander and M.Rosenblatt’s "Statistical Spectral Analysis of Time Series Arising from Stationary Stochastic Processes," Annals of Mathematical Statistics, 24, (1953), 537-558.
		The use of kernel in algebra appears to be unrelated to its use in integral equations and Fourier analysis.
		Kernel occurs in English in 1909 in M. Bôcher's Introduction to the Study of Integral Equations: "K is called the kernel of these equations." (OED2).
	members.aol.com /jeff570/k.html (2202 words)

	HEC Montréal - CREF - SEMINAR
		However, many kernels give a higher power than the BP/LB test statistics or the truncated uniform kernel based test statistic.
		With the L2 norm and the truncated uniform kernel, we retrieve a generalized BP test statistic applied to the estimated standardized residuals.
		One member of the class provides a generalized version of the BP test statistic, using the truncated uniform kernel and the L2 norm.
	www.hec.ca /cref/sem/resumes/031001.html (2202 words)

	NEMS Kernel Regression Technical Note
		and H. Müller (1984): "Estimating regression functions and their derivatives by the kernel method," Scandinavian Journal of Statistics, 11, pp.
		For the Uniform kernel all sufficiently close solutions are treated the same and the approximated value (as shown below) is the simple average of all of the pseudo database values from the sufficiently close solutions.
		Given the values of the kernel functions (for the sufficiently close solutions with indices SC), the estimate of an out-of-sample endogenous variable is constructed as,
	www.eia.doe.gov /smg/asa_meeting_2004/fall/files/exe/KernSumHelp.htm (2202 words)

	NEMS Kernel Regression Technical Note
		and H. Müller (1984): "Estimating regression functions and their derivatives by the kernel method," Scandinavian Journal of Statistics, 11, pp.
		For the Uniform kernel all sufficiently close solutions are treated the same and the approximated value (as shown below) is the simple average of all of the pseudo database values from the sufficiently close solutions.
		Given the values of the kernel functions (for the sufficiently close solutions with indices SC), the estimate of an out-of-sample endogenous variable is constructed as,
	www.eia.doe.gov /smg/asa_meeting_2004/fall/files/exe/KernSumHelp.htm (2202 words)

	Cornell Department of Statistics
		One-year, intensive, professional degree in applied statistics and statistical computing.
		We illustrate the Hastings Coupling method by presenting a particular case: the Normal Kernel Coupler (NKC).
		This information sharing allows algorithms that have improved efficiency, particularly in problems where mixing is difficult, such as multi-modal posterior distributions.
	www.stat.cornell.edu (361 words)

	RePEc
		Kernel Estimation of Partial Means and a General Variance Estimator.
		Kernel and Bandwidth Selection, Prewhitening, and the Performance of the Fully Modified Least Squares Estimation Method.
		Testing the Goodness of Fit of a Parametric Density Function by Kernel Method.
	www.inomics.com /cgi/repec?handle=RePEc:cup:etheor (361 words)

	Nonparametric Spatial Rainfall Characterization Using Adaptiv...
		KEYWORDS: nonparametric statistics, Kth nearest neighbor, kernel estimator, nonstationarity, cross validation.
		In this method, observations closer to the point of estimate are weighted higher using kernel function with a prescribed bandwidth.
		The kernel bandwidth is local and it extends only to the Kth Nearest Neighbor, KNN, observation.
	www.ai-geostats.org /papers/_papers/00000010.htm (361 words)

	Stochastic Approaches to Fracture Modelling
		Following a brief review of the application of the kernel density estimation method to the analysis of spatial point patterns we propose an integrated approach to bandwidth selection based on K-function and distance statistics.
		Of the methods available, non-parametric estimation using kernel functions is straightforward, computationally efficient and honours, locally and globally, the original data.
		One way of modelling the spatial characteristics of fractures is by marked point processes, the first step of which is the estimation of point intensity.
	www.ai-geostats.org /papers/_papers/000000ac.htm (361 words)

	Analysis of M-mode Echocardiogram
		First and second derivatives are calculated with the standard kernel function
		Load the data manipulation, descriptive statistics, and graphics standard packages.
		Note: Due to the use of quartic polynomials for interpolation, the result of the second derivative will be a quadratic polynomial.
	library.wolfram.com /examples/echocardiogram/analysis.html (361 words)

	IngentaConnect Kernel deconvolution of stochastic volatility models
		Then an adaptation of the deconvolution kernel estimator proposed by Fan and Truong [ Annals of Statistics, 21, (1993) 1900] estimates the function m with the optimal rate, which depends on the distribution of the measurement error.
		The rates vary from powers of n to powers of ln( n) depending on the rate of decay near infinity of the characteristic function of this noise.
		In this paper, we study the problem of the nonparametric estimation of the function m in a stochastic volatility model h
	www.ingentaconnect.com /content/bpl/jtsa/2004/00000025/00000004/art00008 (361 words)

	Programming Tutorials - Books : Information Theory, Inference & Learning Algorithms
		Information Theory and Statistics (Dover Books on Mathematics)
		Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
		The importance of this book is it answers why people have been going into new directions into coding theory and provides good information about LDPC codes, turbo codes and decoding algorithms.
	www.programmertutorials.com /ItemId/0521642981 (332 words)

	Research: Statistical Learning Theory
		This problem hinges upon fundamental issues of statistics and science in general, such as the problems of complexity of explanations, a priori knowledge, and representation of data.
		This project aims at studying (theoretically) the possibility of learning (or tuning) the kernel of a support vector machine from the data, and designing statistically efficient algorithms for doing so.
		Statistical learning theory studies the process of inferring regularities from empirical data.
	www.kyb.tuebingen.mpg.de /projects?ra=23&printversion=1 (261 words)

	Nonparametric Spatial Rainfall Characterization Using Adaptiv...
		KEYWORDS: nonparametric statistics, Kth nearest neighbor, kernel estimator, nonstationarity, cross validation.
		In this method, observations closer to the point of estimate are weighted higher using kernel function with a prescribed bandwidth.
		A nonparametric statistical tool based on kernel function estimation is developed for spatial rainfall characterization.
	www.ai-geostats.org /papers/_papers/00000010.htm (118 words)

	Kernel Density Plot
		"Kernel Density Estimation using the Fast Fourier Transform", B. Silverman, Applied Statistics, Royal Statistical Society, (1982), Vol.
		where K is the kernel function h is the smoothing parameter or window width.
		The kernel density estimate, f(n), of a set of n points from a density f is defined as:
	www.itl.nist.gov /div898/software/dataplot/refman1/auxillar/kernplot.htm (742 words)

	FERNANDO PEREZ-CRUZ WEB PAGE
		Keywords: Machine learning, probabilistic modelling, Neural Networks, Bayesian Statistics, Learning Theory, Support Vector Machines, Kernel Methods and Reinforcement Learning.
		Bernhard Schölkopf and Alexander J. Smola (2002) Learning with Kernels.
		Prerequisites: A good background in statistics, calculus, linear algebra, and computer science.
	www.gatsby.ucl.ac.uk /~fernando/SupLearn.html (450 words)

	HEC Montréal - CREF - SEMINAR
		The class of tests for the adequacy of an ACD model is obtained by comparing a kernel-based spectral density estimator of the estimated standardized residuals and the null hypothesis of adequacy using a norm.
		The tests for ACD effects of the first class are obtained by comparing a kernel-based normalized spectral density estimator and the normalized spectral density under the null hypothesis of no ACD effects, using a norm.
		The asymptotic distributions of the test statistics in the two classes are N (0;1) under the null hypothesis of no ACD effects.
	www.hec.ca /cref/sem/resumes/031001.html (450 words)

	biblio26.txt
		SILVERMAN B 86 T The Effects of Kernel Choices in Density- T Estimation with Biased Data A WU CO K MATHEMATICAL SCIENCES - Statistics U STAT PROB L 34(4): 373-383,JUL 16 1997 W CO Wu, Johns Hopkins Univ,Dept W Math Sci, Baltimore, MD 21218 W.
		SILVERMAN B 86 T Order-Restricted Bayesian-Estimation of the Age T Composition of a Population of Atlantic Cod A NANDRAM B A SEDRANSK J A SMITH SJ K MATHEMATICAL SCIENCES - Statistics U J AM STAT A 92(437): 33-40,MAR 1997 W B Nandram, Worcester Polytech W Inst,Dept Math Sci, Worcester, MA W 01609 W.
		SILVERMAN B 86 T A Region-based Segmentation Method for T Multichannel Image Data A BOSE S A OSULLIVA.F K MATHEMATICAL SCIENCES - Statistics U J AM STAT A 92(437): 92-106,MAR 1997 W S Bose, Ohio State Univ,Dept Stat, W Columbus, OH 43210 W.
	main.cs.qub.ac.uk /~fmurtagh/class/csna/re_CD/CD2002/data/original/biblio26.txt (450 words)

	Computing correlations between global brain mean intensity and the task
		The group mask is the intersection between the individual subjects' masks, which means that even if only subject's mask was missing a certain region, this region will not be included in the group statistics.
		I have found it useful to define this explicit mask using the subject's normalised inplane anatomical image, by segmenting out the gray and the white matter from it, then combining them, and then smoothing it with a large kernel (20mm), in order to be really lenient as to which voxels would be included.
		The mask image that was used for model estimation can be viewed after statistics have been computed by displaying the mask.img file in the results directory.
	www-psych.stanford.edu /~kalina/SPM99/Tools/glm_specmask.html (729 words)

	Empirical orthogonal functions
		The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the location of the data (see Mercer's theorem and the kernel trick for more information).
		A more advanced technique is to form a kernel matrix out of the data, using a fixed kernel.
		In statistics and signal processing, the method of empirical orthogonal functions is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data.
	www.freeglossary.com /Empirical_orthogonal_functions (729 words)

	citi-tr-95-4.txt
		/ #endif / KERNEL / { rpc_ss_ndr_marsh_interp(3, / number of [out] parameters / 104, / type vector index of first [out] parameter / IDL_param_vec, &IDL_ms); #ifndef KERNEL* curtime(&now); /* Obtain current time.
		/ #endif / KERNEL / rpc_ss_ndr_unmar_interp(2, / number of [in] parameters / 88, / type vector index of first [in] parameter / IDL_param_vec, &IDL_ms); #ifndef KERNEL* curtime(&now); /* Obtain current time.
		The values are actually collected by an asynchronous thread (described in more detail be- low) and the desire was to ensure that the statistics were always consistent so that, for example, dividing total elapsed time by the number of calls would always generate a correct average.
	www.citi.umich.edu /techreports/trash/TXT/citi-tr-95-4.txt (3035 words)

	Citations: Statistical Estimation and Optimal recovery - Donoho (ResearchIndex)
		Sacks and Ylvisaker (1981) showed that for estimating a function at a point, with squared error loss and a quasi Holder class F(C) the linear minimax estimate is a kernel estimate with specially chosen kernel and specially chosen bandwidth; this estimate is within 17 of asymptotically....
		Many of the tools used to study inverse problems in statistics and applied mathematics are the same, too: functional analysis, convex analysis, optimization theory, nonsmooth analysis, approximation theory, harmonic analysis, and measure theory.
		Donoho, D. (1994b), `Statistical estimation and optimal recovery', Annals of Statistics 22, 238--270.
	citeseer.ist.psu.edu /context/136178/0 (1457 words)

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