optimal estimation of a general regression function let e be a convex subset of rd and for each 0 e e let f 0 dt be a probability on the line for any vector an an an2 ann where anl e e let xn1 xnn be independent observations the distribution of xn being f an dt the main results give a method of estimating the unknown regression function an based on a minimum distance recipe under regularity assumptions the proposed estimators are shown in an appropriate framework to be asymptotically normal locally asymptotically minimax and robust the abstract results are illustrated by application to the linear model and to exponential response models in general nothing at all is assumed about the form of the regression function accordingly this forces the limiting normal distributions of the proposed estimators to be located on infinite dimensional linear spaces

parallel approximation algorithms for bin packing we study the parallel complexity of polynomial heuristics for the bin packing problem we show that some well known and simple moethods like first fit decreasing are p complete and it is hence very unlikely that they can be efficiently parallelized on the other hand we exhibit an optimal nc algorithm that achieves the same performance bound as does ffd finally we discuss parallelization of polynomial approximation algorithms for bin packing based on discretization

nonparametric estimates of regression quantiles and their local bahadur representation let x y be a random vector such that x is d dimensional y is real valued and y theta x varepsilon where x and varepsilon are independent and the alpha th quantile of varepsilon is 0 alpha is fixed such that 0 0 and set r p m 2p d where m is a nonnegative integer smaller than p let t theta denote a derivative of theta of order m it is proved that there exists a pointwise estimate hat t n of t theta based on a set of i i d observations x 1 y 1 cdots s n y n that achieves the optimal nonparametric rate of convergence n r under appropriate regularity conditions further a local bahadur type representation is shown to hold for the estimate hat t n and this is used to obtain some useful asymptotic results

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

a frequentist view on cycle transitivity of reciprocal relations we establish a connection between two transitivity frameworks the transitivity of fuzzy relations based on a commutative quasi copula and the cycle transitivity of reciprocal relations w r t the dual quasi copula as an upper bound function loosely speaking it turns out that the latter can be characterized by imposing a lower bound on the relative frequency with which the former is fulfilled when applied to reciprocal relations we provide two compelling cases the 4 6 theorem expressing that the winning probability relation of a set of independent random variables is at least 66 66 product transitive and the 5 6 theorem expressing that the mutual rank probability relation associated with a given poset is at least 83 33 product transitive moreover these lower bounds turn out be rather conservative illustrating that from a frequentist point of view transitivity is abundant

asymptotically efficient estimation of the index of regular variation we propose a conditional mle of the index of regular variation when the functional form of a slowly varying function is assumed known in the tail and we study its asymptotic properties we prove asymptotic normality of p theta k n a probability measure whose density is the product of the joint conditional density of the k n largest order statistics from f theta x given z n k the n k th order statistic and a density of z n k with parameter theta based on this result we show that this conditional mle is asymptotically normal and asymptotically efficient in many senses whenever k n is o n we also propose an iterative estimator of theta given only partial knowledge of l theta x this estimator is asymptotically normal asymptotically unbiased and asymptotically efficient

fully dynamic algorithms for bin packing being mostly myopic helps the problem of maintaining an approximate solution for one dimensional bin packing when items may arrive and depart dynamically is studied in accordance with various work on fully dynamic algorithms and in contrast to prior work on bin packing it is assumed that the packing may be arbitrarily rearranged to accommodate arriving and departing items in this context our main result is a fully dynamic approximation algorithm for bin packing mmp that is frac 5 4 competitive and requires theta log n time per operation i e for an insert or a delete of an item this competitive ratio of frac 5 4 is nearly as good as that of the best practical off line algorithms our algorithm utilizes the technique introduced here whereby the packing of an item is done with a total disregard for already packed items of a smaller size this myopic packing of an item may then cause several smaller items to be repacked in a similar fashion with a bit of additional sophistication to avoid certain bad cases the number of items either individual items or bundles of very small items treated as a whole that needs to be repacked is bounded by a constant

i o efficient algorithms for the minimum cut problem on unweighted undirected graphs the problem of finding the minimum cut of an undirected unweighted graph is studied on the external memory model first a lower bound of e v sort v on the number of i os is shown for the problem where v is the number of vertices and e is the number of edges then the following are presented for m b 2 1 a minimum cut algorithm that uses o c log e rm msf v e frac v b rm sort v i os here msf v e is the number of i os needed to compute a minimum spanning tree of the graph and c is the value of the minimum cut the algorithm performs better on dense graphs than the algorithm of 7 which requires o e c 2 v log v c i os when executed on the external memory model for a fat graph for 0 the maximum tree packing of the graph is at least 1 c 2 our algorithm computes a minimum cut in o c loge msf v e sort e i os 2 a randomized algorithm that computes minimum cut with high probability in o c log e cdot rm msf v e rm sort e log 2 v frac v b rm sort v log v i os 3 a 2 e minimum cut algorithm that requires o e v msf v e i os and performs better on sparse graphs than our exact minimum cut algorithm

on the estimation of the extreme value index and large quantile estimation l article se constitue de deux parties on donne une preuve simple de la convergence faible de l estimation de pickand pour le parametre principal d une loi de valeurs extremes on donne d autres conditions naturelles pour la convergence forte et pour la normalite asymptotique de l estimation ensuite une grande quantile d une loi est estimee par une combinaison de statistiques d ordre intermediaires ou extremes ceci mene a un intervalle de confiance asymptotique

convex linear t s functions a generalization of frank s equation abstract the main purpose of this paper is to solve the functional equation t s min max for 0 and a pair t s of a t norm t and a t conorm s this equation arises when we consider a convex linear combination of a t norm and a t conorm and set out the problem of finding the intersection of the segments determined by the pairs min max and t s

on a conjecture about the frank copula family it is shown that any member of the frank copula family fulfills a family of functional inequalities which arises as a family of sufficient conditions that allow to characterize the transitivity of reciprocal relations expressing the winning probabilities among random variables artificially coupled by a same copula the inequalities are parameterized by a single integer parameter the first of these inequalities expresses symmetry of the copula while the second one expresses an upper bound on its volume subsequent inequalities are increasingly restrictive

the iterated mod problem abstract the iterated mod problem is this given a b1 b2 bn all integers or all polynomials in q x is a mod b1 mod b2 mod bn 0 when the inputs are integers we prove the problem p complete with respect to log space reductions whereas in the polynomial case we prove the problem is in nc the significance of these results lies primarily in the similarity between the iterated mod problem and the euclidean algorithm we also show that the superincreasing knapsack problem is p complete using a very similar proof

a test for extreme value domain of attraction abstract a simple statistic is proposed to test the hypothesis that a sample comes from a distribution in the domain of attraction of the gumbel distribution it is based on the top k order statistics and is a generalization of the shapiro wilk goodness of fit statistic the critical region of the test and its power against the alternative that the sample comes from a distribution in another domain of attraction are studied theoretically and by simulation the power turns out to be superior to that of other tests previously proposed

global sufficiency of extreme order statistics in location models of weibull type in janssen and reiss 1988 it was shown that in a location model of a weibull type sample with shape parameter 1 a 1 thek n lower extremes are asymptotically local sufficient in the present paper we show that even global sufficiency holds moreover it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line

asymptotically optimal tests for conditional distributions let xl y1 xn yn be independent replicates of the random vector x y e rd m where x is rd valued and y is rm valued we assume that the conditional distribution p y e ix x qii of y given x x is a member of a parametrie family where the parameter space 0 is an open subset of rh with 0 e 0 under suitable regularity conditions we establish upper bounds for the power functions of asymptotic level a tests for the problem 0 against a sequence of contiguous alternatives as weil as asymptotically optimal tests which attain these bounds since the testing problem involves the joint density of x y as an infinite dimensional nuisance parameter its solution is not standard a monte carlo simulation exemplifies the influence of this nuisance parameter as a main tool we establish local asymptotic normality lan of certain poisson point processes which approximately describe our initial sampie

comparison of location models of weibull type samples and extreme value processes four different location parameter models are compared within the sufficiency and deficiency concept the starting is a location model of a weibull type sample with shape parameter 1 a 1 here our basic inequality concerns the approximate sufficiency of the k lower extremes in addition the lower extremes are approximately equal in distribution to left s m 1 1 a t right m leqq k where s m is the sum of m i i d standard exponential random variables and t is the location parameter the final step leads us to the model of extreme value processes left s m 1 1 a t right m 1 2 3

on the super additivity and estimation biases of quantile contributions sample measures of top centile contributions to the total concentration are downward biased unstable estimators extremely sensitive to sample size and concave in accounting for large deviations it makes them particularly unfit in domains with power law tails especially for low values of the exponent these estimators can vary over time and increase with the population size as shown in this article thus providing the illusion of structural changes in concentration they are also inconsistent under aggregation and mixing distributions as the weighted average of concentration measures for a and b will tend to be lower than that from a b in addition it can be shown that under such fat tails increases in the total sum need to be accompanied by increased sample size of the concentration measurement we examine the estimation superadditivity and bias under homogeneous and mixed distributions

a p complete graph partition problem abstract the different than majority labelling dtml problem has a simple polynomial time sequential algorithm the labelling given by this algorithm is called the lexicographical first dtml in this paper we show that the lf dtml problem is p complete furthermore we show that even when restricted to planar graphs the lf dtml problem remains p complete

lower bounds in a parallel model without bit operations we define a natural and realistic model of parallel computation called the pram model without bit operations it is like the usual pram model the main difference being that no bit operations are provided it encompasses virtually all known parallel algorithms for weighted combinatorial optimization and algebraic problems in this model we prove that for some large enough constant b the mincost flow problem for graphs with n vertices cannot be solved deterministically or with randomization in sqrt n b expected time using 2 sqrt n b processors this is so even if we restrict every cost and capacity to be an integer nonnegative if it is a capacity of bitlength at most an for some large enough constant a a similar lower bound is also proved for the max flow problem it follows that these problems cannot be solved in our model deterministically or with randomization in omega n c expected time with 2 omega n c processors where c is an appropriate positive constant and n is the total bitlength of the input since these problems were known to be p complete this provides concrete support for the belief that p completeness implies high parallel complexity and for the p not nc conjecture our lower bounds also extend to the pram model with limited bit operations which provides instructions for parity and left or right shift by one bit our proof is based on basic algebraic geometry so we investigate if the algebrogeometric approach could also work for the p versus nc problem our results support this possibility and a close analysis of the limitation of our technique in this context suggests that such a proof of p not nc should somehow use geometric invariant theory in a deep way

on testing the extreme value index via the pot method n alternatives based on the point processes n of the exceedances among y n i over a sequence of thresholds t it turns out that the random number of n exceedances t n over t is the central sequence for the log likelihood n ratio d l n rd l n yielding its local asymptotic normality lan b n b n n 0 this result implies in particular that t n carries asymptotically all the information about the underlying parameter b which is contained in n n we establish sharp bounds for the rate at which t n becomes asymptoti cally sufficient which show however that this is quite a poor rate these results remain true if we add an unknown scale parameter 1 n a model assumption on the upper tail of the underlying d f such as m is for example indispensable if one is interested in extreme quantities of the underlying d f that is such quantities of f which are usually outside the range of the given data y y a typical example is inference about 1 n y1 4 extreme quantiles f p inf t g r f t g p with p being close to 1 this problem is typically tackled by hydrologists for the prediction of large w

on a family of connectives for fuzzy sets abstract in this paper we find the general solution of the functional equation s t x y t x n y x where s is a t conorm t is a t norm and n is a strong negation on the unit interval in particular the result yields a family of connectives for fuzzy sets

local asymptotic normality of truncated empirical processes given n iid copies x 1 x n of a random element x in some arbitrary measurable space s we are only interested in those observations that fall into some subset d having but a small probability of occurrence it is assumed that the distribution p x of x belongs on d to a parametric family p x d p v v r d nonlinear regression analysis and the peaks over threshold pot approach in extreme value analysis are prominent examples for the pot approach on s r and p v being a generalized pareto distribution it is known that the complete information about the underlying parameter v 0 is asymptotically contained in the number n of observations in d among x 1 x n but not in their actual values this result is formulated in terms of local asymptotic normality of the log likelihood ratio of the point process of exceedances with n being the central sequence in this paper we establish a necessary and sufficient condition such that n has this property for a general truncated empirical process in an arbitrary sample space and for an arbitrary parametric family the known results are then consequences of this result we can moreover characterize the influence of the actual observations in d on the central sequence if this condition is violated immediate applications are asymptotically optimal tests for testing v 0 and if r asymptotic efficiency of the ml estimator n satisfying p vn d n n where these statistics are based on n only

the complexity of markov decision processes we investigate the complexity of the classical problem of optimal policy computation in markov decision processes all three variants of the problem finite horizon infinite horizon discounted and infinite horizon average cost were known to be solvable in polynomial time by dynamic programming finite horizon problems linear programming or successive approximation techniques infinite horizon we show that they are complete for p and therefore most likely cannot be solved by highly parallel algorithms we also show that in contrast the deterministic cases of all three problems can be solved very fast in parallel the version with partially observed states is shown to be pspace complete and thus even less likely to be solved in polynomial time than the np complete problems in fact we show that most likely it is not possible to have an efficient on line implementation involving polynomial time on line computations and memory of an optimal policy even if an arbitrary amount of precomputation is allowed finally the variant of the problem in which there are no observations is shown to be np complete

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

statistical inference for conditional curves poisson process approach a poisson approximation of a truncated empirical point process enables us to reduce conditional statistical problems to unconditional ones let mathbf x y be a d m dimensional random vector and denote by f cdot mid mathbf x the conditional d f of mathbf y given mathbf x mathbf x applying our approach one may study the fairly general problem of evaluating a functional parameter t f cdot mid mathbf x 1 ldots f cdot mid mathbf x p based on independent replicas mathbf x 1 mathbf y 1 ldots mathbf x n mathbf y n of mathbf x y this will be exemplified in the particular cases of nonparametric estimation of regression means and regression quantiles besides other functionals

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

the maximum flow problem is log space complete for p the space complexity of the maximum flow problem is investigated it is shown that the problem is log space complete for deterministic polynomial time thus the maximum flow problem probably has no algorithm which needs only o logk n storage space for any constant k another consequence is that there is probably no fast parallel algorithm for the maximum flow problem

the frank inequality abstract we investigate a functional inequality for copulas that has emerged from our study of the comparison of a set of random variables pairwisely coupled by a same copula any copula satisfying this inequality is necessarily symmetric and radially symmetric moreover any associative copula satisfying this inequality is a solution to the well known frank equation for this reason the inequality is coined the frank inequality we fully characterize the associative copulas that satisfy the frank inequality they turn out to be either frank copulas or ordinal sums of a same frank copula with equidistant idempotent elements as a by product we observe that frank copulas are super additive on the unit square

transitivity frameworks for reciprocal relations cycle transitivity versus fg transitivity for a reciprocal relation q on a set of alternatives a two transitivity frameworks which generalize both t transitivity and stochastic transitivity are compared the framework of cycle transitivity introduced by the present authors soc choice welf to appear and which is based upon the ordering of the numbers q a b q b c and q c a for all a b c a 3 and the framework of fg transitivity introduced by switalski fuzzy sets and systems 137 2003 85 as an immediate generalization of stochastic transitivity the rules that enable to express fg transitivity in the form of cycle transitivity and cycle transitivity in the form of fg transitivity illustrate that for reciprocal relations the concept of cycle transitivity provides a framework that can cover more types of transitivity than does the concept of fg transitivity

kernel and nearest neighbor estimation of a conditional quantile let x 1 z 1 x 2 z 2 x n z n be iid as x z and for 0 p 1 let p x denote the conditional p quantile of z given x x i e p z p x x x p kernel and near est neighbor estimators of p x are proposed in order to study the asymptotics of these estimates bahadur type representations of the sample conditional quantiles are obtained these representations are used to examine the important issue of choosing the smoothing parameter by a local approach for a fixed x based on weak convergence of these estimators the results lead to asymptotic linear models which motivate certain estimators