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Topic: Sufficient statistics

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	Encyclopedia: Sufficient statistics (Site not responding. Last check: 2007-11-07)
		In statistics, one often considers a family of probability distributions for a random variable X (and X is often a vector whose components are scalar-valued random variables, frequently independent) parameterized by a scalar- or vector-valued parameter, which let us call θ.
		Sir Ronald Fisher tried to make precise the intuitive idea that a statistic may capture all of the information in X that is relevant to the estimation of θ.
		A statistic T(X) is sufficient for θ precisely if the conditional probability distribution of the data X given the statistic T(X) does not depend on θ.
	www.nationmaster.com /encyclopedia/Sufficient-statistics (543 words)

	Sufficient and Necessary Statistics, W van der Linden (Site not responding. Last check: 2007-11-07)
		The property of sufficiency becomes interesting only if we are able to reduce the number of response vectors, combining them into a statistic without losing any information about the parameters.
		The other day, in a statistical textbook by Casella and Berger (1990) that is now my latest favorite, I found a reference to a paper by Dynkin (1951) that gives an answer to the question: "Are there any necessary statistics?" Dynkin defines a statistic as "necessary", if it is a function of every sufficient statistic.
		Necessary and sufficient statistics for a family of probability distributions.
	www.rasch.org /rmt/rmt63d.htm (431 words)

	IUPUI Department of Mathematical Sciences - Course Information (Site not responding. Last check: 2007-11-07)
		Intended to familiarize the student with basic statistical concepts and some of their applications in public and health policies as well as in social and behavioral sciences.
		Descriptive statistics; elementary probability; random variables and their distributions; expectation; normal, binomial, Poisson, and hypergeometric distributions; sampling distributions; estimation and testing of hypotheses; one-way analysis of variance; correlation and regression.
		Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-Pearson lemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, sequential probability ratio test.
	www.math.iupui.edu /programs/courses/stat.html (1711 words)

	Sufficient, Complete and Ancillary Statistics (Site not responding. Last check: 2007-11-07)
		Show that the sufficient statistics given above for the Bernoulli, Poisson, normal, gamma, and beta families are minimally sufficient for the given parameters.
		Sufficiency is related to several of the methods of constructing estimators that we have studied.
		Thus, the notion of an ancillary statistic is complementary to the notion of a sufficient statistics (which contains all information about the parameter that is contained in the sample).
	www.ds.unifi.it /VL/VL_EN/point/point6.html (675 words)

	[No title]
		The purpose of this is to allow you to perform analyses from summary statistics when summary statistics are all you know and summary statistics are sufficient to obtain results.
		For example, summary statistics are sufficient for performing t-tests, anova, principal components, regression, and factor analyses.
		If the statistical results differ beyond what is attributable to roundoff error, then use of {cmd:corr2data} is inappropriate.
	www.stata.com /updates3/ado.old/corr2data.hlp (940 words)

	Department of Statistics - Texas A&M University
		Introduction to probability, probability distributions, and statistical inference; hypotheses testing using t and F tests; introduction to methods of analysis such as tests of independence, regression, analysis of variance with some consideration of planned experimentation.
		Transformations of statistics; statistical functionals including influence curves and M, L, and R estimators; asymptotic properties of estimators; asymptotic properties of tests; U-statistics; Edgeworth expansions and the bootstrap.
		Statistical theories pertinent to solution of engineering problems in reliability introduced, established, and applied; distribution and failure theory including exponential, log normal, gamma, and Weibull; parameters studied include mean time to failure, failure rate, variances, and standard deviations, confidence limits, and tests of hypotheses.
	stat.tamu.edu /page.php?graduate_course_descriptions (1414 words)

	AD-trees: Cached Sufficient Statistics for fast Counting and Data Mining queries on Massive Sky Surveys (Site not responding. Last check: 2007-11-07)
		There are devastating computational and statistical difficulties; manual analysis of such data sources is now passing from being simply tedious into a new, fundamentally impossible realm where the data sources are just too large to assimilate by humans.
		More importantly, many statistical operations are based on performing a large number of counts: for example there are many correlation measures based on taking a matrix of counts and performing certain significance tests on rows and columns of the matrices.
		More advanced statistical operations involve aggresive searches to find which subsets of attributes (also known as fields of the database) are most predictive of which other subsets., and most do many thousands of these correlations, which in turn involve dozens of counts.
	www.cfht.hawaii.edu /ADASS/Abstracts/P1.13 (1341 words)

	UT Department of Statistics Graduate Courses
		Prereq: 4 courses in graduate-level statistics or consent of statistics department director of graduate studies.
		Prereq: 2 courses in statistics and consent of the statistics department director of graduate studies.
		Statistical computing, numerical methods for linear models and generalized linear models, nonlinear statistical methods, matrix computations and special matrices, essentials of Monte Carlo simulation, and resampling techniques.
	bus.utk.edu /stat/ms/gradcourses.html (1173 words)

	List of selected publications of Tom Snijders
		As an elaboration and practical implementation of this point, a statistical model for the dynamics of networks, expressed as digraphs with a fixed vertex set, is proposed in which the outdegree distribution is governed by parameters that are not connected to the parameters for the structural dynamics.
		A statistical approach to a posteriori blockmodeling for graphs is proposed.The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong.
		Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only.
	stat.gamma.rug.nl /snijders/publ.htm (11082 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The method of VanTrees was all or nothing: either you have the raw data or you have a single scalar sufficient statistic: the likelihood ratio.
		The advantage was that the dimension of the sufficient statistics for the individual binary tests are lower in dimension than the dimension of any common feature set.
		Subsequently, Kay [kay2000] showed that simple sufficient statistics can exist for the binary tests even if no common sufficient statistic exists for differentiating the two classes.
	www.npt.nuwc.navy.mil /csf/hist.html (675 words)

	Sufficiency (statistics) (Site not responding. Last check: 2007-11-07)
		In statistics, one often considers a family of probability distributions for a random variable
		Sir Ronald Fisher tried to make precise the intuitive idea that a statistic may capture all of the information in
		If g(X) is any kind of estimator of θ, then typically the conditional expectation of g(X) given T(X) is a better estimator of θ ; one way of making that statement precise is called the Rao-Blackwell theorem.
	www.sciencedaily.com /encyclopedia/sufficiency__statistics_ (548 words)

	[No title]
		Informally, we assume that the sufficient sequence may be generated as the output of a discrete-time system whose input is the sequence of ob- served random variables.
		This statistic is also necessary in the sense of Dynkin [41, as noted by Arato 151; hence it is a minimal sufficient statistic, meaning that it is a function of every other sufficient statistic.
		The sufficient statistic for such a class is minimal sufficient, and under the Jacobian condition described above, it may be used as the state vector in a minimal-dimension realization of the sufficient sequence.
	www.math.rutgers.edu /pub/sontag/bd-suft-seq.txt (5099 words)

	Title page for ETD etd-92297-162126
		A statistic that summarizes an entire data set without losing any information about the family of distributions or the model is often called a sufficient statistic.
		The new method is used to evaluate the expected efficiency of a statistic in discriminating between any two values of the parameter as compared to a sufficient statistic.
		Several card-counting statistics are compared by the amount of information each provides in discriminating between different deck compositions as compared to a sufficient statistic.
	scholar.lib.vt.edu /theses/available/etd-92297-162126 (296 words)

	Statistics (STAT) - Course Descriptions - University Catalog 2005-06: George Mason University
		Topics include descriptive statistics, probability, distributions, sampling, inference, estimation and hypothesis testing; linear regression and correlation; the analysis of variance; multiple regression; and the analysis of association between categorical variables.
		Topics include limiting distributions and stochastic convergence, sufficient statistics, exponential families, statistical decision theory and opti-mality for point estimation, Bayesian methods, maximum likelihood, asymptotic results, interval estimation, optimal tests of statistical hypotheses, and likelihood ratio tests.
		Statistical methods essential to the analysis of rates and proportions from data associated with clinical trials, case-control, prospective and cross-sectional studies in the health care sector.
	www.gmu.edu /catalog/courses/stat.html (3032 words)

	Course Descriptions for Mathematics and Statistics
		The statistical software package Minitab will be used to reinforce these principles and to introduce students to the use of the computer in statistical analysis.
		Statistical methods are taught with the aim of utilizing the SAS programs to arrive at outputs and their interpretation.
		A study of the multivariate normal distribution, statistical inference on multivariate data, multivariate analysis of covariance, canonical correlation, principal component analysis and cluster analysis.
	www.rit.edu /~932www/ugrad_bulletin/courses/cos/maths.html (4239 words)

	Sufficient Statistics (Site not responding. Last check: 2007-11-07)
		Fortunately, spotting sufficient statistics can be made easier by the Fisher-Neyman Factorization Theorem.
		Minimal sufficient statistics are, roughly speaking, sufficient statistics that cannot be compressed any more without losing information about the unknown parameter.
		Further examples of sufficient statistics may be found in the module on the Fisher-Neyman Factorization Theorem.
	cnx.rice.edu /content/m11481/latest (693 words)

	Statistics Courses
		This course presents regression analysis and related techniques, and is recommended for students throughout the natural and social sciences who are interested in applying regression analysis in their research and/or understanding the statistical concepts underlying the methodology.
		The topics include simple and multiple linear regression, matrix representation of the regression model, statistical inferences for regression model, diagnostics and remedies for multicollinearity, outlier and influential cases, polynomial regression and interaction regression models, model selection, weighted least square procedure for unequal error variances, and ANOVA model and test.
		Statistical software SAS will be used throughout the course to demonstrate how to apply the techniques on real data.
	www.stat.unc.edu /courses.html (1271 words)

	VFML: ExampleGroupStats.h File Reference
		Tracks and maintains the sufficient statistics needed to calculate Entropy and Gini of discrete and continuous attributes, as well as make some queries about the probability of events in the data.
		Frees all the memory that was being used by the structure.
		Creates a structure to track the statistics needed to cacluate several common machine metrics for the attributes that are active in the AttributeTracker.
	www.cs.washington.edu /dm/vfml/ExampleGroupStats_8h.html (1531 words)

	Connexions - Content - Search Repository (Site not responding. Last check: 2007-11-07)
		Learn what descriptive statistics are and see several applications of them.
		In order to find a solution to the basic reqursion equations, the scaling filter must satisfy a set of sufficient conditions.
		This module describes the various ways the term "statistics" is used.
	cnx.rice.edu /content/search?words=sufficient+statistic (104 words)

	STAT 713 - Mathematical Statistics II
		STAT 713 - Mathematical Statistics II 713—Mathematical Statistics II (3) (Prereq: STAT 712) Further development of estimation theory and tests of hypotheses, including an introduction to Bayesian estimation, sufficiency, minimum variance principles, uniformly most powerful and likelihood ratio tests, and sequential probability ratio tests.
		Purpose: To acquaint beginning graduate students in statistics and other disciplines with the mathematical development of statistical inference.
		To provide a foundation for further study in statistical theory at both the master's and doctoral levels.
	www.stat.sc.edu /curricula/courses/713 (203 words)

	[MBC-Rasch] sufficient statistics (Site not responding. Last check: 2007-11-07)
		In this paper, the meaning of sufficient statistics for the parameters is also explained.
		However, I do not understand as to what the 'Location' statistic is referring in this case.
		Could someone please confirm whether my first 2 assumptions are correct, and help me out with the understanding of the 'Location' statistic.
	lists.wu-wien.ac.at /pipermail/rasch/2003q4/000180.html (269 words)

	Multiple Signals, Statistical Sufficiency, and Pareto Orderings of Best Agency Contracts (Site not responding. Last check: 2007-11-07)
		Abstract: In this study we identify necessary and sufficient conditions for sufficient statistics to strictly (Pareto) dominate all nonsufficient statistics as information for contracting in agencies with moral hazard.
		We first observe that strict dominance requires that an optimal compensation scheme itself be a sufficient statistic.
		Since this can occur only in settings where the family of distributions parameterized by the agent's hidden effort admits one-dimensional sufficient statistics, strict dominance is the exceptional case.
	www.rje.org /abstracts/abstracts/1989/Spring_1989._pp._102_112.html (152 words)

	Efficient Learning using Constrained Sufficient Statistics (Site not responding. Last check: 2007-11-07)
		This approach use constraints imposed by the statistics already collected from the data to guide the learning algorithm.
		This allows us to reduce the number of statistics collected during learning and thus speed up the learning time.
		The basic technique that we introduce is general and can be used to improve learning performance in many settings where sufficient statistics must be computed.
	www.eecs.harvard.edu /~nir/Abstracts/FGe1.html (160 words)

	Graphical Models
		Many of the classical multivariate probabalistic systems studied in fields such as statistics, systems engineering, information theory, pattern recognition and statistical mechanics are special cases of the general graphical model formalism -- examples include mixture models, factor analysis, hidden Markov models, Kalman filters and Ising models.
		Here the savings are minimal, but in general, if we had n binary nodes, the full joint would require O(2^n) space to represent, but the factored form would require O(n 2^k) space to represent, where k is the maximum fan-in of a node.
		In statistics, this is known as Berkson's paradox, or "selection bias".
	www.cs.ubc.ca /~murphyk/Bayes/bayes.html (6598 words)

	Amazon.com: Books: Introduction to Mathematical Statistics (5th Edition) (Site not responding. Last check: 2007-11-07)
		Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics.
		Offering a strong background for those who wish to go on to study statistical applications or more advanced theory, this text presents the most thorough treatment of the mathematics of statistics of any competing text.
		I feel that statistics and mathematics is best learned by doing lots of problems and in the case of statistics practicing on real world data.
	www.amazon.com /exec/obidos/tg/detail/-/0023557222?v=glance (1309 words)

	On the Efficient Gathering of Sufficient Statistics for Classification from Large SQL Databases
		For a wide variety of classification algorithms, scalability to large databases can be achieved by observing that most algorithms are driven by a set of sufficient statistics that are significantly smaller than the data.
		By relying on a SQL backend to compute the sufficient statistics, we leverage the query processing system of SQL databases and avoid the need for moving data to the client.
		We present a new SQL operator (Unpivot) that enables efficient gathering of statistics with minimal changes to the SQL backend.
	research.microsoft.com /research/pubs/view.aspx?msr_tr_id=MSR-TR-98-39 (208 words)

	On Discrete Sufficient Statistics for Asynchronous Band-limited CDMA Systems - Mantravadi, Veeravalli (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: The problem of generating discrete sufficient statistics for statistical signal processing in Code Division Multiple Access (CDMA) systems is considered in context of the underlying channel bandwidth restrictions.
		In most analyses of CDMA systems, the derivation of discrete sufficient statistics is facilitated by first relaxing the bandwidth constraints on the noise and the signaling waveforms in the corresponding continuoustime system model.
		On discrete sufficient statistics for asynchronous band-limited CDMA systems.
	citeseer.lcs.mit.edu /mantravadi98discrete.html (588 words)

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