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253
PROBABILITY INEQUALITIES FOR SUMS OF BOUNDED RANDOM VARIABLES
, 1962
"... Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the s ..."
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Cited by 1767 (2 self)
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Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the smumands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.
Nonparametric analysis of a generalized regression model: the maximum rank correlation estimator
 Journal of the Royal Statistical Society
, 1977
"... The paper considers estimation of a model.b; = D F ( x//3,, u,), where the composite transformation D. F is only specified that D: W * R is nondegenerate monotonic and F: R * + R is strictly monotonic in each of its variables. The paper thus generalizes standard data analysis which assumes tha ..."
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Cited by 124 (0 self)
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The paper considers estimation of a model.b; = D F ( x//3,, u,), where the composite transformation D. F is only specified that D: W * R is nondegenerate monotonic and F: R * + R is strictly monotonic in each of its variables. The paper thus generalizes standard data analysis which assumes that the functional form of II. F is known and additive. The estimator which it proposes is the maximum rank correlation estimator which is nonparametric in the functional form of D. F and nonparametric in the distribution of the error terms, a,. The estimator is shown to be strongly consistent for the parameters /?a up to a scale coefficient. 1.
Integrating structured biological data by kernel maximum mean discrepancy
 IN ISMB
, 2006
"... Motivation: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernelbased statistical test for this problem, based on the fact that two distributions are different if and only if the ..."
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Cited by 71 (17 self)
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Motivation: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernelbased statistical test for this problem, based on the fact that two distributions are different if and only if there exists at least one function having different expectation on the two distributions. Consequently we use the maximum discrepancy between function means as the basis of a test statistic. The Maximum Mean Discrepancy (MMD) can take advantage of the kernel trick, which allows us to apply it not only to vectors, but strings, sequences, graphs, and other common structured data types arising in molecular biology. Results: We study the practical feasibility of an MMDbased test on three central data integration tasks: Testing crossplatform comparability of microarray data, cancer diagnosis, and datacontent based schema matching for two different protein function classification schemas. In all of these experiments, including highdimensional ones, MMD is very accurate in finding samples that were generated from the same distribution, and outperforms its best competitors. Conclusions: We have defined a novel statistical test of whether two samples are from the same distribution, compatible with both multivariate and structured data, that is fast, easy to implement, and works well, as confirmed by our experiments.
A kernel method for the two sample problem
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 19
, 2007
"... We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert ..."
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Cited by 61 (17 self)
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We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg. a Banach space). We apply our twosample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.
Everything you always wanted to know about copula modeling but were afraid to ask
 Journal of Hydrologic Engineering
, 2007
"... Abstract: This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using co ..."
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Cited by 57 (1 self)
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Abstract: This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented for selecting an appropriate model, estimating its parameters, and checking its goodnessoffit. A larger, realistic application of the methodology to hydrological data is then presented.
Aggregate Poverty Measures
 36 Dynamics in Algeria By Laabas Belkacem, Ph.D
, 1997
"... Abstract. The way poverty is measured is important for an understanding of what has happened to poverty as well as for antipoverty policy evaluation. Sen’s (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should ..."
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Cited by 37 (2 self)
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Abstract. The way poverty is measured is important for an understanding of what has happened to poverty as well as for antipoverty policy evaluation. Sen’s (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should satisfy certain properties or axioms and the desirability of a poverty measure should be evaluated by these axioms. During the last two decades, many researchers have adopted the axiomatic approach pioneered by Sen to propose additional axioms and develop alternative poverty measures. The objective of this survey is to provide a clarification on the extensive literature of aggregate poverty measures. In this survey, we first examine the desirability of each axiom, the properties of each poverty measure, and the interrelationships among axioms. The desirability of an axiom cannot be evaluated in isolation, and some combination of axioms may make it impossible to devise a satisfactory poverty measure; some axioms can be implied by other axioms combined and so are not independent; some others are ad hoc and are disqualified as axioms for poverty measurement. Based on the interactions among axioms, we identify the ‘core ’ axioms which together have a strong implication on the functional form of a poverty measure. We then review poverty measures that have appeared in the literature, evaluating the interrelationships among different measures, and examining the properties of each measure. The axioms each measure satisfies�violates are also summarized in a tabular form. Several ‘good ’ poverty measures, which have not been documented by previous surveys, are also included.
On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted
, 1997
"... This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic setup provided by a Markov structure that suggests natural coupling variables. More specifically ..."
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Cited by 32 (1 self)
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This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic setup provided by a Markov structure that suggests natural coupling variables. More specifically, given a stationary Markov chain X�t � , and a function U = U�X�t��, we propose a way to study the proximity of U to a normal random variable when the state space is large. We apply the general method to the study of two problems. In the first, we consider the antivoter chain X�t � =�X �t� i �i∈ � � t = 0 � 1���� � where � is the vertex set of an nvertex regular graph, and X �t� i =+1or−1. The chain evolves from time t to t + 1 by choosing a random vertex i, and a random neighbor of it j, and setting X �t+1� i =−X �t� j and X�t+1� k = X �t� k for all k = i. For a stationary antivoter chain, we study the normal approximation of Un = U �t� n = ∑ i X �t� i for large n and consider some conditions on sequences of graphs such that Un is asymptotically normal, a problem posed by Aldous and Fill. The same approach may also be applied in situations where a Markov chain does not appear in the original statement of a problem but is constructed as an auxiliary device. This is illustrated by considering weighted Ustatistics. In particular we are able to unify and generalize some results on normal convergence for degenerate weighted Ustatistics and provide rates. 1. Introduction and
Generalized entropy power inequalities and monotonicity properties of information
 IEEE Trans. Inform. Theory
, 2007
"... New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary ..."
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Cited by 31 (6 self)
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New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary collection of subsets. As a consequence, a simple proof of the monotonicity of information in central limit theorems is obtained, both in the setting of i.i.d. summands as well as in the more general setting of independent summands with variancestandardized sums. 1