brown s paradox in the estimated confidence approach a widely held notion of classical conditional theory is that statistical inference in the presence of ancillary statistics should be independent of the distribution of those ancillary statistcs in this paper ancillary paradoxes which contradict this notion are presented for two scenarios involving confidence estimation these results are related to brown s ancillary paradox in point estimation moreover the confidence coefficient the usual constant coverage probability estimator is shown to be inadmissible for confidence estimation in the multiple regression model with random predictor variables if the dimension of the slope parameters is greater than five some estimators better than the confidence coefficient are provided in this paper these new estimators are constructed based on empirical bayes estimators

the geometry of the moduli space of curves of genus 23 the problem of describing the birational geometry of the moduli space mg of complex curves of genus g has a long history severi already knew in 1915 thatmg is unirational for g 10 cf sev see also ac1 for a modern proof in the same paper severi conjectured thatmg is unirational for all genera g then for a long period this problem seemed intractable mumford writes in mu p 51 whether more mg s g 11 are unirational or not is a very interesting problem but one which looks very hard too especially if g is quite large the breakthrough came in the eighties when eisenbud harris and mumford proved that mg is of general type as soon as g 24 and that the kodaira dimension of m23 is 1 see hm eh3 we note that mg is rational for g 6 see dol for problems concerning the rationality of various moduli spaces severi s proof of the unirationality of mg for small g was based on representing a general curve of genus g as a plane curve of degree d with nodes this is possible when d 2g 3 2 when the number of nodes is small i e d 1 d 2 6 the dominant map from the variety of plane curves of degree d and genus g to mg yields a rational parametrization of the moduli space the two conditions involving d and can be satisfied only when g 10 so severi s argument cannot be extended for other genera however using much more subtle ideas chang ran and sernesi proved the unirationality of mg for g 11 12 13 see cr1 se1 while for g 15 16 they proved that the kodaira dimension is see cr2 4 the remaining cases g 14 and 17 g 23 are still quite mysterious harris and morrison conjectured in hmo that mg is uniruled precisely when g 23 all these facts indicate that m23 is a very interesting transition case our main result is the following

dimension theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes introduction let k be an algebraically closed ground field of characteristic zero the following result is well known see severi 1 anhang f p 317 if en d is a complete i e maximal irreducible algebraic system defined over k of plane algebraic not necessarily irreducible curves of a given order n such that the general curve c of en d k has d nodes and no other singularities then the dimension of en d is equal to 3n p 1 where p n 1 n 2 2 d is the effective genus of c we note that 3n p 1 is equal to n n 3 2 d here n n n 3 2 is the dimension of the linear system of all plane curves of order n this is in agreement with the intuitive expectation that the requirement that a curve of order n possess d nodes in non assigned position imposes d independent algebraic non linear conditions on the curve the above result is easily proved and will be included by us in a more general theorem the proof of which is the main object of this paper theorem 2 section 3 and which deals with irreducible algebraic systems e of curves of order n in which the general curve c of e k has arbitrary singularities but is free from multiple components equivalently c is a reduced curve this theorem asserts that if p is the effective genus of c the definition of the effective genus of a reducible but reduced curve is given in section 3 formula 2 then dim e c 3n p 1 with equality if and only if c has only nodes as singularities it is easily seen see severi loc cit that if 0 c d n n 1 2 then there always exists curves of order n having d nodes the maximum

valid post selection inference it is common practice in statistical data analysis to perform data driven variable selection and derive statistical inference from the resulting model such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori we propose to produce valid post selection inference by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention intervals simultaneity is required for all linear functions that arise as coefficient estimates in all submodels by purchasing simultaneity insurance for all possible submodels the resulting post selection inference is rendered universally valid under all possible model selection procedures this inference is therefore generally conservative for particular selection procedures but it is always less conservative than full scheffe protection importantly it does not depend on the truth of the selected submodel and hence it produces valid inference even in wrong models we describe the structure of the simultaneous inference problem and give some asymptotic results

an ancillarity paradox in the estimation of multinomial probabilities abstract let x be a multinomial n p variable where n is an ancillary statistic in section 2 it is shown that the minimax estimator of p for fixed sample size n is not minimax for squared error loss in section 3 it is shown that the minimax estimator of p for fixed sample size n is still minimax for relative squared error loss

plane curves of minimal degree with prescribed singularities we prove that there exists a positive such that for any integer d 3 and any topological types s1 sn of plane curve singularities satisfying

on line predictive linear regression gauss linear model independent identically distributed observations multivariate analysis on line protocol prequential statistics regression we consider the on line predictive version of the standard problem of linear regression the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations the standard treatment of prediction in linear regression analysis has two drawbacks 1 the usual prediction intervals guarantee that the probability of error is equal to the nominal significance level but this property per se does not imply that the long run frequency of error is close to 2 it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters we state a general result showing that in the on line protocol the frequency of error does equal the nominal significance level up to statistical fluctuations and we describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters one of these models which only assumes that the observations are independent and identically distributed is popular in machine learning but greatly underused in the statistical theory of regression

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

efficient bootstrap simulation on donne deux idees pour renforcer une simulation la premiere est d equilibrer les echantillons simules la seconde est de faire un usage explicite des approximations qui ne demandent pas de simulation

limit linear series basic theory in this paper we introduce techniques for handling the degeneration of linear series on smooth curves as the curves degenerate to a certain type of reducible curves curves of compact type the technically much simpler special case of 1 dimensional series was developed by beauville 2 knudsen 21 23 harris and mumford 17 in the guise of admissible covers it has proved very useful for studying the moduli space of curves the above papers and harris 16 and the simplest sorts of weierstrass points diaz 4 with our extended tools we are able to prove for example that in this paper we present the basic theory of limit linear series necessary for proving these results the results themselves will be taken up in our forthcoming papers 8 12 simpler applications not requiring the tools developed in this paper but perhaps clarified by them have already been given in our papers 5 7

conditioning likelihood and coherence a review of some foundational concepts 2000 conditioning likelihood and coherence a review of some foundational concepts journal of the american statistical association vol 95 no 452 pp 1340 1346

irreducibility of equisingular families of curves in 1985 joe harris proved the long standing claim of severi that equisingular families of plane nodal curves are irreducible whenever they are nonempty for families with more complicated singularities this is no longer true given a divisor d on a smooth projective surface it thus makes sense to look for conditions which ensure that the family v irr d s 1 s r of irreducible curves in the linear system d l with precisely r singular points of types s 1 s r is irreducible considering different surfaces including general surfaces in p 3 c and products of curves we produce a sufficient condition of the type r i 1 deg x s i 2 d k 2 where is some constant and x s i some zero dimensional scheme associated to the singularity type our results carry the same asymptotics as the best known results in this direction in the plane case even though the coefficient is worse for most of the surfaces considered these are the only known results in that direction

on the variety of plane curves of degree with nodes and cusps let pn be the projective space which parametrizes all plane curves of degree d and v d k the subvariety of pn consisting of all reduced and irreducible plane curves of degree d with 3 nodes and k cusps as their only singularities in this paper we prove that v d k is irreducible if k 3 except possibly when k 3 and d 5 or 6

analytic order of singular and critical points we deal with the following closely related problems i for a germ of a reduced plane analytic curve what is the minimal degree of an algebraic curve with a singular point analytically equivalent isomorphic to the given one ii for a germ of a holomorphic function in two variables with an isolated critical point what is the minimal degree of a polynomial equivalent to the given function up to a local holomorphic coordinate change classically known estimates for such a degree d in these questions are 1 d 1 where is the milnor number our result in both the problems is d a with an absolute constant a as a corollary we obtain asymptotically proper sufficient conditions for the existence of algebraic curves with prescribed singularities on smooth algebraic surfaces

existence of curves with prescribed topological singularities throughout this paper we study the existence of irreducible curves c on smooth projective surfaces with singular points of prescribed topological types s 1 s r there are necessary conditions for the existence of the type r i 1 s i c 2 c k for some fixed divisor k on and suitable coefficients and and the main sufficient condition that we find is of the same type saying it is asymptotically proper ten years ago general results of this quality were not known even for the case e p 2 c an important ingredient for the proof is a vanishing theorem for invertible sheaves on the blown up e of the form o d r i 1 m i e i deduced from the kawamata vieweg vanishing theorem its proof covers the first part of the paper while the middle part is devoted to the existence theorems in the last part we investigate our conditions on ruled surfaces products of elliptic curves surfaces in p 3 c and k3 surfaces

conditional inference for treatment and error in multivariate analysis summary directional methods of conditional inference are applied to the multivariate analysis of variance exact and easily implemented tests are derived for treatment effect error variance matrix and treatment improvement each test provides a physical measure of the magnitude of the departure from expectation under the hypothesis and is conditional on the indicated direction of departure for treatment effect the test provides a geometrically understandable alternative to tests such as the largest root the trace and others for treatment improvement the test attempts to take account reasonably of coordinates that contain no apparent effect

ideals associated to deformations of singular plane curves we consider in this paper the geometry of certain loci in deformation spaces of plane curve singularities these loci are the equisingular locus es which parametrizes equisingular or topologically trivial deformations the equigeneric locus eg which parametrizes deformations of constant geometric genus and the equiclassical locus ec which parametrizes deformations of constant geometric genus and class the class of a reduced plane curve is the degree of its dual it was previously known that the tangent space to es corresponds to an ideal called the equisingular ideal and that the support of the tangent cone to eg corresponds to the conductor ideal we show that the support of the tangent cone to ec corresponds to an ideal which we call the equiclassical ideal by studying these ideals we are able to obtain information about the geometry and dimensions of es ec and eg this allows us to prove some theorems about the dimensions of families of plane curves with certain specified singularities

covariate assisted ranking and screening for large scale two sample inference author s cai t tony sun wenguang wang weinan abstract two sample multiple testing has a wide range of applications the conventionalpractice first reduces the original observations to a vector of p values and then chooses a cutoffto adjust for multiplicity however this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures we introduce a new framework fortwo sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power a data driven multiple testing procedure is developed by employinga covariate assisted ranking and screening cars approach that optimally combines the informationfrom both the primary and the auxiliary variables the proposed cars procedureis shown to be asymptotically valid and optimal for false discovery rate control the procedureis implemented in the r package cars numerical results confirm the effectiveness of carsin false discovery rate control and show that it achieves substantial power gain over existingmethods cars is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection