set identification via quantile restrictions in short panels this paper studies the identifying power of conditional quantile restrictions in short panels with flxed efiects in contrast to classical flxed efiects models with conditional mean restrictions conditional quantile restrictions are not preserved by taking difierences in the regression equation over time this paper shows however that a conditional quantile restriction in conjunction with a weak conditional independence restriction provides bounds on quantiles of difierences in time varying unobservables across periods these bounds carry observable implications for model parameters which generally result in set identiflcation the analysis of these bounds includes conditions for point identiflcation of the parameter vector as well as weaker conditions that result in identiflcation of individual parameter components

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

semiparametric analysis of random effects linear models from binary panel data andersen 1970 considered the problem of inference on random effects linear models from binary response panel data he showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution and if the observed explanatory variables vary over time a conditional maximum likelihood estimator consistently estimates the model parameters up to scale the present paper shows that inference remains possible if the disturbances for each panel member are known only to be time stationary with unbounded support and if the explanatory variables vary enough over time a conditional version of the maximum score estimator manski 1975 1985 consistently estimates the model parameters up to scale

identifying preferences in networks with bounded degree this paper provides a framework for identifying preferences in a large network under the assumption of pairwise stability of network links network data present difficulties for identification especially when links between nodes in a network can be interdependent e g where indirect connections matter given a preference specification we use the observed proportions of various possible payoff relevant local network structures to learn about the underlying parameters we show how one can map the observed proportions of these local structures to sets of parameters that are consistent with the model and the data our main result provides necessary conditions for parameters to belong to the identified set and this result holds for a wide class of models we also provide sufficient conditions and hence a characterization of the identified set for two empirically relevant classes of specifications an interesting feature of our approach is the use of the economic model under pairwise stability as a vehicle for effective dimension reduction the paper then provides a quadratic programming algorithm that can be used to construct the identified sets this algorithm is illustrated with a pair of simulation exercises

self tuning density estimation based on bayesian averaging of adaptive kernel density estimations yields state of the art performance abstract non parametric probability density function pdf estimation is a general problem encountered in many fields a promising alternative to the dominating solutions kernel density estimation kde and gaussian mixture modeling is adaptive kde where kernels are given individual bandwidths adjusted to the local data density traditionally the bandwidths are selected by a non linear transformation of a pilot pdf estimate containing parameters controlling the scaling but identifying parameters values yielding competitive performance has turned out to be non trivial we present a new self tuning parameter free pdf estimation method called adaptive density estimation by bayesian averaging adeba that approximates pdf estimates in the form of weighted model averages across all possible parameter values weighted by their bayesian posterior calculated from the data adeba is shown to be simple robust competitive in comparison to the current practice and easily generalize to multivariate distributions an implementation of the method for r is publicly available

an econometric model of network formation with degree heterogeneity i introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics homophily as well as unrestricted agent level heterogeneity in link surplus degree heterogeneity like in fixed effects panel data analyses the joint distribution of observed and unobserved agent level characteristics is left unrestricted two estimators for the common homophily parameter 0 are developed and their properties studied under an asymptotic sequence involving a single network growing large the first tetrad logit tl estimator conditions on a sufficient statistic for the degree heterogeneity the second joint maximum likelihood jml estimator treats the degree heterogeneity a i0 i 1 super n as additional incidental parameters to be estimated the tl estimate is consistent under both sparse and dense graph sequences whereas consistency of the jml estimate is shown only under dense graph sequences

drcw ovo one vs one strategy is a common and established technique in machine learning to deal with multi class classification problems it consists of dividing the original multi class problem into easier to solve binary subproblems considering each possible pair of classes since several classifiers are learned their combination becomes crucial in order to predict the class of new instances due to the division procedure a series of difficulties emerge at this stage such as the non competence problem each classifier is learned using only the instances of its corresponding pair of classes and hence it is not competent to classify instances belonging to the rest of the classes nevertheless at classification time all the outputs of the classifiers are taken into account because the competence cannot be known a priori the classification problem would be solved on this account we develop a distance based combination strategy which weights the competence of the outputs of the base classifiers depending on the closeness of the query instance to each one of the classes our aim is to reduce the effect of the non competent classifiers enhancing the results obtained by the state of the art combinations for one vs one strategy we carry out a thorough experimental study supported by the proper statistical analysis showing that the results obtained by the proposed method outperform both in terms of accuracy and kappa measures the previous combinations for one vs one strategy highlightsthe non competence is an important problem in one vs one strategy we develop a distance based combination strategy based on dynamic classifier weighting strategies weights are settled depending on the closeness of the test instance to each one of the classesthe effect of the non competent classifiers is reduced the new strategy enhances the results obtained w r t the state of the art aggregations

gelfand numbers of operators with values in a hilbert space in the paper we prove two inequalities involving gelfand numbers of operators with values in a hilbert space the first inequality is a rademacher version of the main result in pa to 1 which relates the gelfand numbers of an operator from a banach spacex intol 2 n with a certain rademacher average for the dual operator the second inequality states that the gelfand numbers of an operatoru froml 1 n into a hilbert space satisfy the inequality k 1 2 c k u leqq c parallel u parallel log 1 n k 1 2 wherec is a universal constant several applications of these inequalities in the geometry of banach spaces are given

donsker classes of sets we study the central limit theorem clt and the law of large numbers lln for empirical processes indexed by a countable class of sets c the main result of purely measure theoretical nature relates different ways to measure the size of c it relies on a new rearrangement inequality that has been inspired by techniques used in the local theory of banach spaces as an application we give sharp necessary conditions for the clt that are in some sense the best possible we also obtain a way to compute the rate of convergence in the lln

inference on counterfactual distributions counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics in this article we develop modeling and inference tools for counterfactual distributions based on regression methods the counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates for either of these scenarios we derive joint functional central limit theorems and bootstrap validity results for regression based estimators of the status quo and counterfactual outcome distributions these results allow us to construct simultaneous confidence sets for function valued effects of the counterfactual changes including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals these confidence sets can be used to test functional hypotheses such as no effect positive effect or stochastic dominance our theory applies to general counterfactual changes and covers the main regression methods including classical quantile duration and distribution regressions we illustrate the results with an empirical application to wage decompositions using data for the united states as a part of developing the main results we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution we show that distribution regression encompasses the cox duration regression and represents a useful alternative to quantile regression we establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals publication abstract

pairwise difference estimators of censored and truncated regression models abstract this paper proposes a class of estimators of the semiparametric censored regression model under the assumption that the error terms are i i d and independent of the covariates the estimators exploit the fact that for a pair of observations a particular transformation of the censored variables depending upon the parameter vector and both covariate vectors will be identically distributed therefore the difference in the transformed dependent variables will be symmetrically distributed around zero when the transformation is evaluated at the true parameter vector an analogous class of estimators for the truncated regression model includes the bhattacharya chernoff and yang 1983 estimator as a special case the estimators are defined as minimizers of u processes so the large sample theory for classical m estimators is extended to this case conditions are given to ensure root n consistency and asymptotic normality of the estimators and a small scale simulation study for the censored regression estimator suggest that it will be well behaved in finite samples

combining predictions in pairwise classification an optimal adaptive voting strategy and its relation to weighted voting weighted voting is the commonly used strategy for combining predictions in pairwise classification even though it shows good classification performance in practice it is often criticized for lacking a sound theoretical justification in this paper we study the problem of combining predictions within a formal framework of label ranking and under some model assumptions derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers we call this strategy adaptive voting and show that it is optimal in the sense of yielding a map prediction of the class label of a test instance moreover we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction this result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that even though adaptive voting is sometimes able to achieve consistent improvements weighted voting is in general quite competitive all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met in this sense weighted voting appears to be a more robust aggregation strategy

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

approximating the inverse of a symmetric positive definite matrix abstract it is shown for an n n symmetric positive definite matrix t t i j with negative off diagonal elements positive row sums and satisfying certain bounding conditions that its inverse is well approximated uniformly to order l n 2 by a matrix s s i j where s i j i j t i j 1 t i j being the kronecker delta function and t being the sum of the elements of t an explicit bound on the approximation error is provided

sequential complexities and uniform martingale laws of large numbers we establish necessary and sufficient conditions for a uniform martingale law of large numbers we extend the technique of symmetrization to the case of dependent random variables and provide sequential non i i d analogues of various classical measures of complexity such as covering numbers and combinatorial dimensions from empirical process theory we establish relationships between these various sequential complexity measures and show that they provide a tight control on the uniform convergence rates for empirical processes with dependent data as a direct application of our results we provide exponential inequalities for sums of martingale differences in banach spaces

a random forests quantile classifier for class imbalanced data abstract extending previous work on quantile classifiers q classifiers we propose the q classifier for the class imbalance problem the classifier assigns a sample to the minority class if the minority class conditional probability exceeds 0

uniform limit theorems for harris recurrent markov chains we study uniform limit theorems for regenerative processes and get strong law of large numbers and central limit theorem of this type then we apply those results to harris recurrent markov chains based on some ideas of k athreya p ney and e nummelin

a note on the problem of reporting maximal cliques reporting the maximal cliques of a graph is a fundamental problem arising in many areas this note bridges the gap between three papers addressing this problem the original paper of bron kerbosh c bron j kerbosch algorithm 457 finding all cliques of an undirected graph communication of acm 16 9 1973 575 577 and two papers recently published in tcs namely that of tomita et al tomita a tanaka h takahashi the worst case time complexity for generating all maximal cliques and computational experiments theoretical computer science 363 1 2006 28 42 and that of koch i koch fundamental study enumerating all connected maximal common subgraphs in two graphs theoretical computer science 250 1 2 2001 1 30 in particular we show that the strategy of tomita et al is a simple modification of the bron kerbosch algorithm based on an un exploited observation raised in koch s paper

asymptotics for panel quantile regression models with individual effects this paper studies panel quantile regression models with individual fixed effects we formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals n and the number of time periods t jointly go to infinity the estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature nevertheless due to the non smoothness of the objective function we had to impose a more restrictive condition on t to prove asymptotic normality than that usually found in the literature the finite sample performance of the estimator is evaluated by monte carlo simulations

the worst case time complexity for generating all maximal cliques and computational experiments we present a depth first search algorithm for generating all maximal cliques of an undirected graph in which pruning methods are employed as in the bron kerbosch algorithm all the maximal cliques generated are output in a tree like form subsequently we prove that its worst case time complexity is o 3n 3 for an n vertex graph this is optimal as a function of n since there exist up to 3n 3 maximal cliques in an n vertex graph the algorithm is also demonstrated to run very fast in practice by computational experiments

classification by pairwise coupling we discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes and then coupling the estimates together the coupling model is similar to the bradley terry method for paired comparisons we study the nature of the class probability estimates that arise and examine the performance of the procedure in real and simulated data sets classifiers used include linear discriminants nearest neighbors adaptive nonlinear methods and the support vector machine

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

panel data discrete choice models with lagged dependent variables in this paper we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables lags of the endogenous dependent variable as well as unobservable individual specific effects for the binary logit model with the dependent variable lagged only once chamberlain 1993 gave conditions under which the model is not identified we present a stronger set of conditions under which the parameters of the model are identified the identification result suggests estimators of the model and we show that these are consistent and asymptotically normal although their rate of convergence is slower than the inverse of the square root of the sample size we also consider identification in the semiparametric case where the logit assumption is relaxed we propose an estimator in the spirit of the conditional maximum score estimator manski 1987 and we show that it is consistent in addition we discuss an extension of the identification result to multinomial discrete choice models and to the case where the dependent variable is lagged twice finally we present some monte carlo evidence on the small sample performance of the proposed estimators for the binary response model

nonparametric identification in panels using quantiles abstract this paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity the effects of interest are derivatives of the average and quantile structural functions of the model we find that these derivatives are identified with two time periods for stayers i e for individuals with the same regressor values in two time periods we show that the identification results carry over to models that allow location and scale time effects we propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identified effects the bootstrap proposed allows inference for function valued parameters such as quantile effects uniformly over a region of quantile indices and or regressor values an empirical application to engel curve estimation with panel data illustrates the results

learning valued preference structures for solving classification problems this paper introduces a new approach to classification which combines pairwise decomposition techniques with ideas and tools from fuzzy preference modeling more specifically our approach first decomposes a polychotomous classification problem involving m classes into an ensemble of binary problems one for each ordered pair of classes the corresponding classifiers are trained on the relevant subsets of the transformed original training data in the classification phase a new query is submitted to every binary learner the output of each classifier is interpreted as a fuzzy degree of preference for the first in comparison with the second class by combining the outputs of all classifiers one thus obtains a fuzzy preference relation which is taken as a point of departure for the final classification decision this way the problem of classification is effectively reduced to a problem of decision making based on a fuzzy preference relation corresponding techniques which have been investigated quite intensively in the field of fuzzy set theory hence become amenable to the task of classification in particular by decomposing a preference relation into a strict preference an indifference and an incomparability relation this approach allows one to quantify different types of uncertainty in classification and thereby supports sophisticated classification and postprocessing strategies

the central limit theorem for empirical processes under local conditions the case of radon infinitely divisible limits without gaussian component on obtient des resultats de convergence faible pour des processus empiriques indices par des classes f de fonctions dans le cas de limites de radon purement de poisson infiniment divisibles

individual and time effects in nonlinear panel models with large n t fixed eects estimators of nonlinear panel data models can be severely biased because of the well known incidental parameter problem we develop analytical and jackknife bias corrections for nonlinear models with both individual and time eects under asymptotic sequences where the time dimension t grows with the cross sectional dimension n the time eects introduce additional incidental parameter bias as the existing bias corrections apply to models with only individual eects we derive the appropriate corrections the basis for the corrections are general asymptotic expansions of xed eects estimators with incidental parameters in multiple dimensions we apply the expansions to m estimators with concave objective functions in parameters for panel models with additive individual and time eects these estimators cover xed eects estimators of the most popular limited dependent variable models such as logit probit ordered probit tobit and poisson models our analysis therefore extends the use of large t bias adjustments to an important class of models we also develop bias corrections for functions of the data parameters and individual and time eects including average partial eects in this case the incidental parameter bias is asymptotically of second order in general but the corrections improve nite sample properties

a quantile correlated random coefficients panel data model abstract we propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data specifically we extend the correlated random coefficients representation of linear quantile regression e g koenker 2005 section 2 6 we show that panel data allows the econometrician to i introduce dependence between the regressors and the random coefficients and ii weaken the assumption of comonotonicity across them i e to enrich the structure of allowable dependence between different coefficients we adopt a fixed effects approach leaving any dependence between the regressors and the random coefficients unmodeled we motivate different notions of quantile partial effects in our model and study their identification for the case of discretely valued covariates we present analog estimators and characterize their large sample properties when the number of time periods t exceeds the number of random coefficients p identification is regular and our estimates are n consistent when t p our identification results make special use of the subpopulation of stayers units whose regressor values change little over time in a way which builds on the approach of graham and powell 2012 in this just identified case we study asymptotic sequences which allow the frequency of stayers in the population to shrink with the sample size one purpose of these discrete bandwidth asymptotics is to approximate settings where covariates are continuously valued and as such there is only an infinitesimal fraction of exact stayers while keeping the convenience of an analysis based on discrete covariates when the mass of stayers shrinks with n identification is irregular and our estimates converge at a slower than n rate but continue to have limiting normal distributions we apply our methods to study the effects of collective bargaining coverage on earnings using the national longitudinal survey of youth 1979 nlsy79 consistent with prior work e g chamberlain 1982 vella and verbeek 1998 we find that using panel data to control for unobserved worker heterogeneity results in sharply lower estimates of union wage premia we estimate a median union wage premium of about 9 percent but with in a more novel finding substantial heterogeneity across workers the 0 1 quantile of union effects is insignificantly different from zero whereas the 0 9 quantile effect is of over 30 percent our empirical analysis further suggests that on net unions have an equalizing effect on the distribution of wages

consistency under sampling of exponential random graph models the growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure typically however these are models for the entire network while the data consists only of a sampled sub network parameters for the whole network which is what is of interest are estimated by applying the model to the sub network this assumes that the model is consistent under sampling or in terms of the theory of stochastic processes that it defines a projective family focusing on the popular class of exponential random graph models ergms we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models and that satisfying it drastically limits ergm s expressive power these results are actually special cases of more general results about exponential families of dependent random variables which we also prove using such results we offer easily checked conditions for the consistency of maximum likelihood estimation in ergms and discuss some possible constructive responses

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

estimation of censored quantile regression for panel data with fixed effects this article investigates estimation of censored quantile regression qr models with fixed effects standard available methods are not appropriate for estimation of a censored qr model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity motivated by these limitations the article proposes estimators that are obtained by applying fixed effects qr to subsets of observations selected either parametrically or nonparametrically we derive the limiting distribution of the new estimators under joint limits and conduct monte carlo simulations to assess their small sample performance an empirical application of the method to study the impact of the 1964 civil rights act on the black white earnings gap is considered supplementary materials for this article are available online

a non parametric approach to extending generic binary classifiers for multi classification ensemble methods which combine generic binary classifier scores to generate a multi classification output are commonly used in state of the art computer vision and pattern recognition systems that rely on multi classification in particular we consider the one vs one decomposition of the multi class problem where binary classifier models are trained to discriminate every class pair we describe a robust multi classification pipeline which at a high level involves projecting binary classifier scores into compact orthogonal subspaces followed by a non linear probabilistic multi classification step using kernel density estimation kde we compare our approach against state of the art ensemble methods dcs drcw on 16 multi class datasets we also compare against the most commonly used ensemble methods vote nest on 6 real world computer vision datasets finally we measure the statistical significance of our approach using non parametric tests experimental results show that our approach gives a statistically significant improvement in multi classification performance over state of the art highlightsensemble methods combine binary classifiers to yield a multi classification output one vs one ensemble binary classifiers trained to discriminate each class pair we propose a robust non parametric probabilistic one vs one ensemble method kdemrp kdemrp improves classification performance over state of the art dcs drcw kdemrp improvements are statistically significant

a central limit theorem in the β model for undirected random graphs with a diverging number of vertices chatterjee diaconis and sly 2011 recently established the consistency of the maximum likelihood estimate in the beta model when the number of vertices goes to infinity by approximating the inverse of the fisher information matrix we obtain its asymptotic normality under mild conditions simulation studies and a data example illustrate the theoretical results

reducing multiclass to binary a unifying approach for margin classifiers we present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin based binary learning algorithm the proposed framework unifies some of the most popular approaches in which each class is compared against all others or in which all pairs of classes are compared to each other or in which output codes with error correcting properties are used we propose a general method for combining the classifiers generated on the binary problems and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms the scheme and the corresponding bounds apply to many popular classification learning algorithms including support vector machines adaboost regression logistic regression and decision tree algorithms we also give a multiclass generalization error analysis for general output codes with adaboost as the binary learner experimental results with svm and adaboost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms

in defense of one vs all classification we consider the problem of multiclass classification our main thesis is that a simple one vs all scheme is as accurate as any other approach assuming that the underlying binary classifiers are well tuned regularized classifiers such as support vector machines this thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification we support our position by means of a critical review of the existing literature a substantial collection of carefully controlled experimental work and theoretical arguments

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

approximation to stable law by the lindeberg principle abstract by the lindeberg principle we develop in this paper an approximation to one dimensional possibly asymmetric stable distributions with 0 2 in the smooth wasserstein distance it is the first time that the general stable central limit theorem is proved by the lindeberg principle and that this theorem with 0 1 is proved by a new method other than fourier analysis our main tools are a taylor like expansion and a kolmogorov forward equation

a clt for empirical processes involving time dependent data for stochastic processes xt t e we establish sufficient conditions for the empirical process based on ixt y pr xt y t e y r to satisfy the clt uniformly in t e y r corollaries of our main result include examples of classical processes where the clt holds and we also show that it fails for brownian motion tied down at zero and e 0 1

entropy and the combinatorial dimension we solve talagrand s entropy problem the l2 covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension this extends dudley s theorem on classes of 0 1 valued functions for which the shattering dimension is the vapnik chervonenkis dimension in convex geometry the solution means that the entropy of a convex body k is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of k this has a number of consequences including the optimal elton s theorem and estimates on the uniform central limit theorem in the real valued case

clique detection models in computational biochemistry and genomics abstract many important problems arising in computational biochemistry and genomics have been formulated in terms of underlying combinatorial optimization models in particular a number have been formulated as clique detection models the proposed article includes an introduction to the underlying biochemistry and genomic aspects of the problems as well as to the graph theoretic aspects of the solution approaches each subsequent section describes a particular type of problem gives an example to show how the graph model can be derived summarizes recent progress and discusses challenges associated with solving the associated graph theoretic models clique detection models include prescribing a a maximal clique b a maximum clique c a maximum weighted clique or d all maximal cliques in a graph the particular types of biochemistry and genomics problems that can be represented by a clique detection model include integration of genome mapping data nonoverlapping local alignments matching and comparing molecular structures and protein docking

on the algorithmic implementation of multiclass kernel based vector machines in this paper we describe the algorithmic implementation of multiclass kernel based vector machines our starting point is a generalized notion of the margin to multiclass problems using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks our notion of margin yields a direct method for training multiclass predictors by using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size we describe an efficient fixed point algorithm for solving the reduced optimization problems and prove its convergence we then discuss technical details that yield significant running time improvements for large datasets finally we describe various experiments with our approach comparing it to previously studied kernel based methods our experiments indicate that for multiclass problems we attain state of the art accuracy

a non parametric entropy based approach to detect changes in climate extremes summary the paper focuses primarily on temperature extremes measured at 24 european stations with at least 90 years of data here the term extremes refers to rare excesses of daily maxima and minima as mean temperatures in this region have been warming over the last century it is automatic that this positive shift can be detected also in extremes after removing this warming trend we focus on the question of determining whether other changes are still detectable in such extreme events as we do not want to hypothesize any parametric form of such possible changes we propose a new non parametric estimator based on the kullback leibler divergence tailored for extreme events the properties of our estimator are studied theoretically and tested with a simulation study our approach is also applied to seasonal extremes of daily maxima and minima for our 24 selected stations

generic inference on quantile and quantile effect functions for discrete outcomes quantile and quantile effect qe functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation existing inference methods for these functions

central limit theorems for stochastic processes under random entropy conditions necessary and sufficient conditions are found for the weak convergence of the row sums of an infinitesimal row independent triangular array nj of stochastic processes indexed by a set s to a sample continuous gaussian process when the array satisfies a random entropy condition analogous to one used by gine and zinn 1984 for empirical processes this entropy condition is satisfied when s is a class of sets or functions with the vapnik ervonenkis property and each nj f fd nj is of the form njc for some reasonable random finite signed measure vnj as a result we obtain necessary and sufficient conditions for the weak convergence of possibly non i i d partial sum processes and new sufficient conditions for empirical processes indexed by vapnik ervonenkis classes special cases include prokhorov s 1956 central limit theorem for empirical processes and shorack s 1979 theorems on weighted empirical processes

enumerating all connected maximal common subgraphs in two graphs we represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem we have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs these algorithms are based on variants of the bron kerbosch algorithm in this paper we explain the transformation of the maximal common subgraph problem into the clique problem we give a short summary of the variants of the bron kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs after introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs the results show the drastical reduction of the runtimes for the new algorithms

lower bounds for the empirical minimization algorithm in this correspondence we present a simple argument that proves that under mild geometric assumptions on the class f and the set of target functions t the empirical minimization algorithm cannot yield a uniform error rate that is faster than 1 radic k in the function learning setup this result holds for various loss functionals and the target functions from t that cause the slow uniform error rate are clearly exhibited

active set algorithms for isotonic regression a unifying framework in this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods the active set approach provides a unifying framework for studying algorithms for isotonic regression simplifies the exposition of existing algorithms and leads to several new efficient algorithms we also investigate the computational complexity of several algorithms

a generalization of the lindeberg principle we generalize lindeberg s proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables the result is applied to get a similar theorem for smooth functions of exchangeable random variables this theorem allows us to identify for the first time the limiting spectral distributions of wigner matrices with exchangeable entries

classification by pairwise coupling of imprecise probabilities we address combining imprecise classifiers in the framework of imprecise probabilities classifier outputs are probability intervals which are large for irrelevant classifiers the combination consists in computing probabilities consistent with the intervals this approach is particularly interesting when combining few classifiers in this paper we are interested in making decisions by combining classifiers providing uncertain outputs in the form of sets of probability distributions more precisely each classifier provides lower and upper bounds on the conditional probabilities of the associated classes the classifiers are combined by computing the set of unconditional probability distributions compatible with these bounds by solving linear optimization problems when the classifier outputs are inconsistent we propose a correcting step that restores this consistency the experiments show the interest of our approach for solving multi class classification problems particularly when information is scarce i e a limited number of classifiers is available in this case modeling the lack of information associated with classifier outputs gives good results even when they are poorly regularized or overfit the data

donsker classes and random geometry on donne des conditions geometriques aleatoires pour que le processus empirique indice par la classe des fonctions de carre integrable satisfasse le theoreme central limite

coupled samples in simulation assume that we wish to generate two samples of n independent identically distributed random variables x1 xn and y1 yn where x1 and y1 have densities f and g respectively if these samples are used in a simulation and f is close to g it is sometimes desirable to have close simulation results this can be achieved by insisting that both samples agree in most of their components that is xi yi for as many i as possible under the given distributional constraints samples with this property are said to be optimally coupled in this paper we propose and study various methods of coupling two samples a sequence of samples and an infinite family of samples

network and panel quantile effects via distribution regression abstract this paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two way effects strictly exogenous covariates and possibly discrete outcome variables the method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators these fixed effects estimators are debiased to deal with the incidental parameter problem under asymptotic sequences where both dimensions of the data set grow at the same rate the confidence bands for the quantile functions and effects have correct joint coverage in large samples an empirical application to gravity models of trade illustrates the applicability of the methods to network data

probability estimates for multi class classification by pairwise coupling pairwise coupling is a popular multi class classification method that combines all comparisons for each pair of classes this paper presents two approaches for obtaining class probabilities both methods can be reduced to linear systems and are easy to implement we show conceptually and experimentally that the proposed approaches are more stable than the two existing popular methods voting and the method by hastie and tibshirani 1998

asymptotics when the number of parameters tends to infinity in the bradley terry model for paired comparisons we are concerned here with establishing the consistency and asymptotic normality for the maximum likelihood estimator of a merit vector u 0 u t representing the merits of t 1 teams players treatments objects under the bradley terry model as t this situation contrasts with the well known neyman scott problem under which the number of parameters grows with t the amount of sampling and for which the maximum likelihood estimator fails even to attain consistency a key feature of our proof is the use of an effective approximation to the inverse of the fisher information matrix specifically under the bradley terry model when teams i and j with respective merits u i and u j play each other the probability that team i prevails is assumed to be u i u i u j suppose each pair of teams play each other exactly n times for some fixed n the objective is to estimate the merits u i s based on the outcomes of the nt t 1 2 games clearly the model depends on the u i s only through their ratios under some condition on the growth rate of the largest ratio u i u j 0 i j t as t the maximum likelihood estimator of u 1 u 0 u t u 0 is shown to be consistent and asymptotically normal some simulation results are provided

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

the law of the iterated logarithm in uniformly convex banach spaces we give necessary and sufficient conditions for a random vari able x with values in a uniformly convex banach space b to satisfy the law of the iterated logarithm precisely we show that a b valued random vari able x satisfies the compact law of the iterated logarithm if and only if a 2 i2 x oo the family i x 2 x 6 b i 1 is uni formly integrable and sn a n 0 in probability 1 introduction let b be a banach space with topological dual b and norm by random variable with values in b we mean a measurable map x from some probability space 0 7 p into b such that the image of p by x defines a radon probability measure on the borel cr field of b we may assume equivalently that x takes almost surely its values in a separable subspace of b given a b valued random variable x we denote by xn new a sequence of inde pendent copies of x and let as usual sn xx h h xn we write lt to denote the function max l logi and use l2t to denote l lt t g r we set further or 2nl2n 1 2 the random variable x is said to satisfy the bounded law of the iterated logarithm lil if the sequence sn an n s is bounded with probability one and the compact lil if this sequence is almost surely relatively compact in b it is well known that if x satisfies the compact lil there is a compact convex and symmetric set k in b such that

refined pivot selection for maximal clique enumeration in graphs this article re examines the pivoting bron kerbosch algorithm for identifying all maximal cliques within a graph a curious result is presented there exist pivot candidates which may be selected with no penalty to the worst case running time even if these vertices do not satisfy the established conditions for the known complexity bound hence such pivots may be selected eagerly a refined pivot selection process is described and the preservation of the established worst case bound is proved additionally empirical evidence shows that the revised algorithm is notably faster than bron kerbosch with tomita style pivot selection