a multivariate statistical approach to reducing the number of variables in data envelopment analysis abstract the usefulness of data envelopment analysis dea depends on its ability to calculate the relative efficiency of decision making units dmus using multiple inputs and outputs unfortunately the greater the number of input and output variables the less discerning the analysis in practice the input and output variables are usually highly correlated with one another often reflecting no more than the relative size of each dmu to counteract the limited distinction provided by a dea with many variables analysts for many years have taken the approach of retaining only some of the variables originally planned for the analysis omitting on an ad hoc basis variables that are highly correlated with those retained in this paper we describe a systematic statistical method for deciding which of the original correlated variables can be omitted with least loss of information and which should be retained results on a number of published datasets reveal that even omitting variables that are highly correlated and thereby contain little additional information on performance can have a major influence on the computed efficiency measures

s adic l functions attached to the symmetric square of a newform in order to apply the ideas of iwasawa theory to the symmetric square of a newform we need to be able to define non archimedean analogues of its complex l series the interpolated p adic l function is closely connected via a main conjecture with certain selmer groups over the cyclotomic bbb z p extension of bbb q in the p ordinary case these functions are well understood in this article we extend the interpolation to an arbitrary set s of good primes not necessarily satisfying ordinarity conditions the corresponding s adic functions can be characterised in terms of certain admissibility criteria we also allow interpolation at particular primes dividing the level of the newform one interesting application is to the symmetric square of a modular elliptic curve e defined over bbb q our constructions yield p adic l functions at all primes of stable or semi stable reduction if p is ordinary or multiplicative the corresponding analytic function is bounded if p is supersingular our function behaves like log 2 1 t 1991 mathematics subject classification 11f67 11f66 11f33 11f30

a formula for the derivative of the p adic l function of the symmetric square of a finite slope modular form let f be a modular form of weight k and nebentypus psi by generalizing a construction of dabrowski and delbourgo we construct a p adic l function interpolating the special values of the l function l s rm sym 2 f otimes xi where xi is a dirichlet character when s k 1 and xi psi 1 this p adic l function vanishes due to the presence of a so called trivial zero we give a formula for the derivative at s k 1 of this p adic l function when the form f is steinberg at p if the weight of f is even the conductor is even and squarefree and the nebentypus is trivial this formula implies a conjecture of benois

critical p adic l functions we attach p adic l functions to critical modular forms and study them we prove that those l functions fit in a two variables p adic l function defined locally everywhere on the eigencurve

testing for two regime threshold cointegration in vector error correction models this paper examines a two regime vector error correction model with a single cointegrating vector and a threshold effect in the error correction term we propose a relatively simple algorithm to obtain maximum likelihood estimation of the complete threshold cointegration model for the bivariate case we propose a suplm test for the presence of a threshold we derive the null asymptotic distribution show how to simulate asymptotic critical values and present a bootstrap approximation we investigate the performance of the test using monte carlo simulation and find that the test works quite well applying our methods to the term structure model of interest rates we find strong evidence for a threshold effect

scaling units via the canonical correlation analysis in the dea context abstract this paper deals with the evaluation of decision making units which have multiple inputs and outputs a new method cca dea is developed where the canonical correlation analysis cca is utilized to provide a full rank scaling for all the units rather than a categorical classification for efficient and inefficient units as done by the data envelopment analysis dea the cca dea approach is an attempt to bridge the gap between the frontier approach of dea and the average tendencies of statistics econometrics nonparametric statistical tests are employed to validate the consistency between the classification from the dea and the postclassification that was generated by the cca dea

two variable p adic l functions attached to eigenfamilies of positive slope consider a classical cusp eigenform f n 1 a n f q n of weight k 2 for 0 n with a dirichlet character mod n and let l f s n 1 n a n f n s denote the l function of f twisted with an arbitrary dirichlet character for a prime number p 5 consider a family of cusp eigenforms f k of weight k k f k n 1 a n f k q n containing f f k such that the fourier coefficients a n f k are given by certain p adic analytic functions k a n f k the purpose of this paper is to construct a two variable p adic l function attached to coleman s family f k of cusp eigenforms of a fixed positive slope v p p 0 where p p k is an eigenvalue which depends on k of the atkin operator u u p our p adic l function interpolates the special values l f k s at points s k with s 1 2 k 1 we give a construction using the rankin selberg method and the theory of p adic integration on a profinite group y with values in an affinoid k algebra a where k is a fixed finite extension of q p our p adic l functions are p adic mellin transforms of certain a valued measures in their turn such measures come from eisenstein distributions with values in certain banach a modules m m n a of families of overconvergent forms over a

non cuspidal hida theory for siegel modular forms and trivial zeros of p adic l functions we study the derivative of the standard p adic l function associated with a p ordinary siegel modular form for p a parabolic subgroup of mathrm gl n when it presents a semi stable trivial zero this implies part of greenberg s conjecture on the order and leading coefficient of p adic l functions at such trivial zero we use the method of greenberg stevens for the construction of the improvedp adic l function we develop hida theory for non cuspidal siegel modular forms

factorization of p adic rankin l series we prove that the p adic l series of the tensor square of a p ordinary modular form factors as the product of the symmetric square p adic l series of the form and a kubota leopoldt p adic l series this establishes a generalization of a conjecture of citro greenberg s exceptional zero conjecture for the adjoint follows as a corollary of our theorem our method of proof follows that of gross who proved a factorization result for the katz p adic l series associated to the restriction of a dirichlet character whereas gross s method is based on comparing circular units with elliptic units our method is based on comparing these same circular units with a new family of units called beilinson flach units that we construct the beilinson flach units are constructed using bloch s intersection theory of higher chow groups applied to products of modular curves we relate these units to special values of classical and p adic l functions using work of beilinson as generalized by lei loeffler zerbes in the archimedean case and bertolini darmon rotger as generalized by kings loeffler zerbes in the p adic case central to our method are two compatibility theorems regarding bloch s intersection pairing and the classical and p adic beilinson regulators defined on higher chow groups

dea and the discriminant analysis of ratios for ranking units the purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the data envelopment analysis dea in order to rank all the units on the same scale this new method discriminant data envelopment analysis of ratios dr dea presents a further post optimality analysis of dea for organizational units when their multiple inputs and outputs are given we construct the ratio between the composite output and the composite input where their common weights are computed by a new non linear optimization of goodness of separation between the two pregiven groups a practical use of dr dea is that the common weights may be utilized for ranking the units on a unified scale dr dea is a new use of a two group discriminant criterion that has been presented here for ratios rather than the traditional discriminant analysis which applies to a linear function moreover non parametric statistical tests are employed to verify the consistency between the classification from dea efficient and inefficient units and the post classification as generated by dr dea

a generalization of greenberg s l invariant using the theory of phi gamma modules we generalize greenberg s construction of the cal l invariant to p adic representations which are semistable at p this allows us to formulate a quite general conjecture about the behavior of p adic l functions at trivial zeros

p adic banach spaces and families of modular forms let p be a prime cp the completion of an algebraic closure of the p adic numbers qp and k a nite extension of qp contained in cp let v be the valuation on cp such that v p 1 and let be the absolute value on cp such that x p v x for x cp suppose n is a positive integer prime to p let x1 np denote the modular curve over k which represents elliptic curves with 1 np structure and let up be the hecke operator on modular forms on x1 np which takes a form with q expansion n anq n to the modular form with q expansion n anpq n a modular form f is said to have slope q if there is a polynomial r t over cp such that r up f 0 and such that the newton polygon of r t has only one side and its slope is

p adic l functions and p adic periods of modular forms let e be an elliptic curve which is defined over q and has stable reduction modulo a given prime p assuming that e is modular one can associate to e a p adic l function lp e s see mz swd a v vi mz t t for its construction in various cases this function is defined by a certain interpolation property and is analytic for sezp in this paper we will assume that e has split multiplicative reduction at p under this assumption the interpolation property implies that lp e 1 0 we will prove a formula for ep e 1 which was discovered experimentally by mazur tate and teitelbaum mz t t by tate s p adic urfiformization theory there is a p adic integer q epzp which we refer to as the tate period for e and a p adic analytic isomorphism