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

some small unipotent representations of indefinite orthogonal groups abstract we study a family of small unitary representations of indefinite orthogonal groups these representations arise as analytic continuations of the discrete series and were studied extensively by knapp in k3 we complete knapp s analysis by proving that they are irreducible in order to do so we prove that the representations are unipotent and have irreducible associated cycles in which all multiplicities are exactly one moreover we prove that the k type structure of each representation matches up to a shift the k type structure of the ring of functions on the closure a nilpotent k c orbit on p

robust estimation via minimum distance methods given a fixed parametric family p it is desired to estimate however due to contaminations of various sorts the data actually collected by the statistician follow a distribution that is close to but possibly distinct from thep s it is proved that under these conditions and in an appropriate asymptotic framework the minimum distance estimators of the cramer von mises type are robust specification of a cramer von mises weight functionh defines a notion of distance each such choice ofh then delineates the kind of contamination possible and leads to an estimator which defends optimally against it when the theory is specialized to location models various choices ofh lead to estimators asymptotically equivalent to such familiar ones as trimmed mean median hodges lehmann estimator and so forth the framework developed herein provides some guidelines for choosing among the possible estimators and suggests that the standard cramer von mises estimator of location is probably as good a robust estimator as any

0 1 matrices which are extreme points of the generalized transitive tournament polytope abstract following brualdi and hwang given a generalized transitive tournament gtt matrix t of order n we consider the graph of t that is the undirected graph with vertices 1 2 n in which there is an edge i j between vertices i and j if and only if 0 ij we characterize the graphs of the extreme gtt 0 1 matrices of order n using this characterization we obtain for n 6 7 the complete list of extreme gtt 0 1 matrices of order n

some calculations of the lusztig vogan bijection for classical nilpotent orbits abstract in this manuscript we compute explicitly the lusztig vogan bijection for local systems of some classical special nilpotent orbits using these results we prove a conjecture of achar and sommers on regular functions of some covers of classical nilpotent orbits

cubic unipotent arthur parameters and multiplicities of square integrable automorphic forms l g f g a ld g f g a lcont g f g a into the direct sum of its discrete spectrum and its continuous spectrum the theory of eisenstein series reduces the description of lcont g f g a to that of the discrete spectrum of certain reductive subgroups of g and thus the basic question is the understanding of the discrete spectrum ld g f g a the discrete spectrum has a further orthogonal decomposition

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

general transitivity conditions for fuzzy reciprocal preference matrices a reciprocal fuzzy matrix relation is a non negative matrix q qij such that qij qji 1 for all i j 1 2 n we define general transitivity conditions named fg transitivities for fuzzy reciprocal preference relations and show that they generalize some well known transitivities we also study relationships of these conditions with two models of rational preferences the so called utility model and the multidimensional model

minimum distance estimators for location and goodness of fit abstract a weighted cramer von mises distance between the empirical distribution function and the assumed model f0 x is minimized to produce estimators n that are asymptotically normal if the weight function is taken proportional to ln f 0 f 0 then n is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom special attention is focused on the limiting distribution of this latter goodness of fit statistic in both null and alternative situations

a paley wiener theorem for real reductive groups le groupe sl 3 r prequantification des orbites de dimension minimale parmi celles non triviales dans la representation co adjointe de sl 3 r noyaux de blattner kostant steinberg irreductibilite et unicite du prolongement de certaines representations de p 3 a sl 3 r etude du prolongement des representations e a sl 3 r la representation type s s 2 minimal parametres de langlands et operateur d entrelacement avec la serie principale pour les representations e et

sur le theoreme de paley wiener d arthur the fourier transform of a c function f with compact support on a real reductive lie group g is given by a collection of operators o p e ip e f for a suitable family of representations of g which depends on a family indexed by p in a finite set of parabolic subgroups of g of pairs of parameters e varying in a set of discrete series e lying in a complex finite dimensional vector space the ip e are generalized principal series induced from p it is easy to verify the holomorphy of the fourier transform in the complex parameters also it satisfies some growth properties moreover an intertwining operator between two representations ip e ip e of the family implies an intertwining property for o p e and o p e there is also a way to introduce hsuccessive partial derivatives h of the family of representations ip e along the parameter e and intertwining operators between subquotients of these successive derivatives imply the intertwining property for the successive derivatives of the fourier transform o we show that these properties characterize the collections of operators p e o p e which are fourier transforms of a c function with compact support for g linear the proof which uses harish chandra fs plancherel formula rests on a similar result for left and right k finite functions which is due to j arthur we give also a proof of arthur fs result purely in term of representations involving the work of a knapp and e stein on intertwining integrals and langlands and vogan fs classifications of irreducible representations of g

a quadraticity limit theorem useful in linear models this paper proves an asymptotic uniform quadraticity of certain statistics based on randomly weighted residual empirical processes under fairly general conditions this result is useful in many statistical inference problems pertaining to linear models including the correlation and autoregression models some applications to the goodness of fit tests and minimum distance estimation in linear models are given

quadratic unipotent arthur parameters and residual spectrum of symplectic groups the purpose of this paper is to study certain quadratic unipotent arthur parameters in the sense of moeglin and use them to parametrize a part of the residual spectrum of symplectic groups over number fields coming from the conjugacy class of borel subgroups in particular using certain identities satisfied by local intertwining operators arthur s multiplicity formula is established for them which remarkably enough appears by itself in the corresponding residue of the eisenstein series introduction in this paper we study certain quadratic unipotent arthur

theoreme de type paley wiener pour les groupes de lie semi simples reels avec une seule classe de conjugaison de sous groupes de cartan abstract in this article we characterize the space of fourier transforms of the smooth compactly supported functions on a semisimple lie group with one conjugacy class of cartan subgroups cf th 6 we get also results on the space of fourier transforms of the elements of the enveloping algebra of the lie algebra of such a group cf th 1 2 and 3

characterizations of character sheaves for complex reductive algebraic groups character sheaves are geometric objects associated to a reductive algebraic group they are closely related to irreducible characters of finite chevalley groups the existence of character sheaves was conjectured by g lusztig in the book characters of reductive groups over finite fields 1984 there he described what one should expect character sheaves to be for complex reductive groups a definition of character sheaves for an arbitrary characteristic quite different from this description was given by him later 1985 it is shown in this thesis in particular that the original 1984 lusztig s suggestion for describing character sheaves is equivalent to the later definition we use alternative characterizations of character sheaves for a connected complex reductive algebraic group g that are obtained in this thesis and also the one conjectured by g lusztig and g laumon that was obtained in 1988 by v ginsburg and independently by i mirkovic and k vilonen these characterizations involve microsupport and microlocalization of a sheaf a microsupport ss cal f of a complex cal f of sheaves on g is a closed conic subset of t sp g g times bf g it tells us about singularities of cal f a microlocalization mu sb m cal f of cal f along a submanifold m of g is a complex of sheaves on the conormal bundle t sbsp m g which allows us to analyze cal f on the infinitesimally small neighbourhood of m theorem let g be a complex connected reductive algebraic group cal f be a g equivariant for conjugation irreducible perverse sheaf on g let cal n be the nilpotent cone of the lie algebra g of g s may denote either g or the set of all semisimple elements of g the following are equivalent i cal f is a character sheaf ii ss cal f vert sb s subset s times cal n iii supp mu sb cal o cal f subset cal o times cal n where cal o subset s is a conjugacy class iv supp mu sb x cal f subset cal n x in s characterization ii when s g is the one given by ginsburg mirkovic and vilonen characterization iii with s being the set of semisimple elements was conjectured by j bernstein for arbitrary characteristic this kind of characterizations essentially simplifies the development and our understanding of the theory currently there is still no such description for positive characteristic an important intermediate result is the description of the microsupport of a doubc constructible sheaf cal f on a manifold x in terms of microlocalizations to the points of this manifold ss cal f overline bigcup limits sb x in x rm supp mu sb x cal f

semiparametric inference in the proportional odds regression model abstract for fitting the proportional odds regression model with right censored survival times we introduce some weighted empirical odds functions these functions are solutions of some self consistency equations and have a nice martingale representation from these functions several classes of new regression estimators such as the pseudo maximum likelihood estimator martingale residual based estimators and minimum distance estimators are derived these estimators have desirable properties such as easy computation asymptotic normality via a martingale analysis and reliable asymptotic covariance estimation in closed form extensive numerical studies show that the minimum l 2 distance estimators have very good finite sample behaviors compared to existing methods results of some simulation studies and applications to a real dataset are given the weighted odds function based approach also provides inference on the baseline odds function and some measures for lack of fit analysis

on non 0 1 2 1 extreme points of the generalized transitive tournament polytope the acyclic tournaments of order n form the linear ordering polytope pnlo the generalized transitive tournaments of order n form the polytope pnc which contains the linear ordering polytope it is known that the integral extreme points of pnc coincide with those of pnlo dridi showed that pnlo pnc for n 5 while for n 5pnlo pnc borobia gave a complete characterization of the extreme points of pnc with values in 0 1 1 2 it was mentioned by brualdi and hwang that no extreme points of pnc with values not in 0 1 1 2 are known in this paper we present a method for obtaining a family of extreme points of pnc with values not in 0 1 1 2 we also prove that these non half integral extreme points of pnc violate certain diagonal inequalities which are facet defining for pnlo

the unitary dual for complex classical lie groups in this paper we classify the unitary spectrum of the complex classical groups let g be any complex simply connected semisimple lie group there are two well known ways of constructing unitary representations from lower groups unitary induction from a parabolic subgroup and complementary series a reasonable way to describe the unitary dual is to find a distinguished set of representations for each group such that every other unitary representation is obtained from this set by the above constructions from strictly smaller parabolic subgroups this is entirely similar to the classification of admissible modules where the distinguished representations are the discrete series for integral infinitesimal character such a set is provided by the special unipotent representations introduced in bv1 their existence and unitarity was conjectured earlier by a they were shown to have many interesting properties such as the fact that their annihilator is a maximal primitive ideal from this it was possible to obtain character formulas for them however it is clear that this set is not large enough to describe the entire unitary spectrum for example in type c the metaplectic representation is not special unipotent or even one of the larger class of representations considered in a the definition of special unipotent representations suggests that one should consider representations with maximal primitive ideal and infinitesimal character as small as possible it is not clear which of them should be unitary imposing the condition that the annihilator be a completely prime ideal which is necessary for unitarity does not seem to be very helpful either thus one is left with the task of explicitly computing the g invariant form and ruling out the cases when it is indefinite this is an almost impossible calculation a rough estimate says that one needs to compute signatures on the k types in the principal series which have length ii 2p ql

dimensions of irreducible modules over w algebras and goldie ranks the main goal of this paper is to compute two related numerical invariants of a primitive ideal in the universal enveloping algebra of a semisimple lie algebra the first one very classical is the goldie rank of an ideal the second one is the dimension of an irreducible module corresponding to this ideal over an appropriate finite w algebra we concentrate on the integral central character case we prove modulo a conjecture that in this case the two are equal our conjecture asserts that there is a one dimensional module over the w algebra with certain additional properties the conjecture is proved for the classical types also modulo the same conjecture we compute certain scale factors introduced by joseph this allows to compute the goldie ranks of the algebras of locally finite endomorphisms of simples in the bgg category mathcal o this completes a program of computing goldie ranks proposed by joseph in the 80 s for integral central characters and modulo our conjecture we also provide an essentially kazhdan lusztig type formula for computing the characters of the irreducibles in the brundan goodwin kleshchev category mathcal o for a w algebra again under the assumption that the central character is integral in particular this allows to compute the dimensions of the finite dimensional irreducible modules the formula is based on a certain functor from an appropriate parabolic category mathcal o to the w algebra category mathcal o this functor can be regarded as a generalization of functors previously constructed by soergel and by brundan kleshchev we prove a number of properties of this functor including the quotient property and the double centralizer property we develop several side topics related to our generalized soergel functor for example we discuss its analog for the category of harish chandra modules we also discuss generalizations to the case of categories mathcal o over dixmier algebras the most interesting example of this situation comes from the theory of quantum groups we prove that an algebra that is a mild quotient of luszitg s form of a quantum group at a root of unity is a dixmier algebra for this we check that the quantum frobenius epimorphism splits

censored median regression using weighted empirical survival and hazard functions abstract for median regression models that regress the median of the survival time or a transform thereof on the covariates some semi parametric estimators that include the intercept component are introduced when the survival time may be censored these new median regression estimators do not require estimating the censoring distributions they can be viewed as an extension of the sample median to the censored regression model these estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal they performed very well in various numerical studies the proposed procedures are illustrated in some real data examples

unipotent representations of complex semisimple groups algebraic group over r or c in this paper we restrict attention to c we generalize arthur s definition slightly or perhaps simply make it more precise all of the resulting representations except for a finite set are then unitarily induced from representations of the same kind on proper parabolic subgroups we call the finite set remaining special unipotent representations a precise definition will be given later definition 1 17 our main result theorem iii of this introduction is a character formula for any special unipotent representation of course such a formula can be deduced from the kazhdan lusztig conjecture cf v3 the advantages of theorem iii are that it is in closed form and that it lends itself to verification of some conjectures of arthur in a so let g be a connected complex semisimple lie group and q its lie algebra choose

generalized transitive tournaments and doubly stochastic matrices abstract we show that a doubly stochastic matrix is a convex combination of nonidentity permutation matrices if and only if it can be written as the sum of a nonnegative matrix and a convex combination of cycle matrices we use this result to give a shorter proof of the theorem of cruse which asserts that a doubly stochastic matrix is a convex combination of nonidentity permutation matrices if and only if its inner product with each generalized transitive tournament matrix is at least 1 the generalized transitive tournaments of order n form a convex polytope t n which contains the convex hull t n also called the linear ordering polytope of the transitive tournaments each transitive tournament matrix of order n is an extreme point of t n but for n 6 there are other extreme points with each generalized tournament matrix t of order n we associate a graph whose edges correspond to the nonintegral entries of t we investigate which graphs can arise from generalized transitive tournaments and which can arise from extreme generalized transitive tournaments we briefly discuss a generalization of the linear ordering polytope to arbitrary posets

doubly stochastic matrices and dicycle covers and packings in eulerian digraphs abstract mirsky 1963 raised the question of characterizing 0 n the convex hull of the nonidentity permutation matrices of order n by a set of linear constraints cruse 1979 solved mirsky s problem by presenting an implicit description of those constraints we associate an eulerian digraph with each doubly stochastic matrix and then restate cruse s characterization of the polytope 0 n in terms of dicycle covers of these digraphs brualdi and hwang 1992 have shown by using cruse s characterization and a result of dridi 1980 an explicit set of linear inequalities that characterize 0 n for n 6 by using our characterization of 0 n we show that their result is valid if and only if n 6 we show as well that if d is an eulerian digraph on n 6 nodes then there is always a minimum dicycle cover which is integral we apply this last result and a result of seymour 1994 to derive a min max relation for eulerian digraphs on n 6 nodes

minimum distance methods based on quadratic distances for transforms in simple linear regression models minimum distance estimators and test statistics based on quadratic distances for transforms are introduced in simple linear regression models asymptotic properties of quadratic distance estimators and tests for the error distributions are derived the modified quadratic distance estimator is shown to be efficient provided that the error distribution is symmetric and the derivative of the logarithm of the error density is a linear combination of the transforms

minimum distance estimation in a linear regression model this paper discusses a class of minimum distance cramer von mises type estimators of the slope parameter in a linear regression model these estimators are obtained by minimizing an integral of squared difference between weighted empiricals of the residuals and their expectations with respect to a large class of integrating measures the estimator corresponding to the weights proportional to the design variable is shown to be asymptotically efficient within the class at a given error distribution the paper also discusses the asymptotic null distribution of a class of minimum cramer von mises type goodness of fit test statistics