segmented concave least squares a nonparametric piecewise linear regression abstract in this paper segmented concave least squares scls is introduced scls is a nonparametric piecewise linear regression problem in which the estimated function is monotonic concave and the number of linear segments k is pre specified ordinary least squares k 1 and concave least squares k n the number of observations are two extreme cases of this problem an application of scls is to estimate a hedonic function using this method observations are categorized into k groups and a piecewise linear hedonic function is estimated such that there is one linear segment for every group the estimated hedonic function holds the principle of diminishing marginal utility in this paper scls is used to categorize hotels in finland into three groups a trade off between the number of groups and the goodness of fit measure is used to determine the number of groups based on the similarities of the pricing methods hotels in the sample are endogenously classified and the shadow prices for each group are calculated the results reveal that the hotels do not value hotel attributes similarly and there are significant differences among groups hedonic pricing model via scls provides a novel categorization of hotels that cannot be obtained by using ordinary least squares

noncanonical quantization of gravity i foundations of affine quantum gravity the nature of the classical canonical phase space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations prior to the introduction of constraints a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel hilbert space constraints are introduced following the projection operator method which involves no gauge fixing no complicated moduli space nor any auxiliary fields the result which is only qualitatively sketched in the present paper involves another reproducing kernel with which inner products are defined for the physical hilbert space and which is obtained through a reduction of the original reproducing kernel several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one dimensional quantum mechanical models these toy models help in motivating and understanding the analysis in the case of gravity

estimating a changepoint boundary or frontier in the presence of observation error a range of problems in economics and statistics involve calculation of the boundary or frontier of the support of a distribution several practical and attractive solutions exist if the sampled distribution has a sharp discontinuity at the frontier but accuracy can be greatly diminished if the data are observed with error indeed if the error is additive and has variance 2 then inaccuracies are usually of order for small in this article we suggest an elementary method for reducing the effect of error to o 2 and show that refinements can improve accuracy still further to o 3 or less the problem is inherently ill posed however to such an extent that the frontier is generally not even identifiable unless the error distribution is known the latter assumption is unreasonable in most practical settings not in the least because the error is often asymmetrically distributed for example in the context of productivity analysis the error distribution tends to have a longer tail in the directi

multivariate periodic arma 1 1 processes the main objective of this paper is to investigate the properties of multivariate periodic autoregressive moving average arma l 1 processes such properties include the covariance structure the parameter space and estimation the parameter space of such periodic processes is derived by aggregation for instance monthly models will aggregate to annual models in particular the parameter space and estimation are analyzed for contemporaneous arma carma models it is shown that in general the aggregation of a multivariate periodic arma 1 1 model leads to a stationary multivariate arma 1 1 model however not always a periodic carma 1 1 model aggregates into a stationary carma 1 1 model furthermore it is shown that in estimating the aggregated model parameters the method based on the periodic model and corresponding parameters is superior to that based on the aggregated series

diffusion determines the manifold we prove under a weak smoothness condition that two riemannian manifold are isomorphic if and only there exists an order isomorphism which intertwines with the dirichlet type heat semigroups on the manifolds

feynman formulae and phase space feynman path integrals for tau quantization of some levy khintchine type hamilton functions evolution semigroups generated by pseudo differential operators are considered these operators are obtained by different parameterized by a number procedures of quantization from a certain class of functions or symbols defined on the phase space this class contains hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the levy khintchine formula the considered semigroups are represented as limits of n fold iterated integrals when n tends to infinity such representations are called feynman formulae some of these representations are constructed with the help of another pseudo differential operator obtained by the same procedure of quantization such representations are called hamiltonian feynman formulae some representations are based on integral operators with elementary kernels these are called lagrangian feynman formulae langrangian feynman formulae provide approximations of evolution semigroups suitable for direct computatio

aggregation and estimation for low order periodic arma models the aggregated time series resulting from summing over the seasons of a seasonal time series which is assumed to follow either an ar 1 or arma 1 1 model having periodic seasonal parameters is shown to follow an arma 1 1 model parameter estimation for such models is investigated analytically and via simulation significant gain in parameter estimation efficiency at the aggregated level is demonstrated when the seasonal data and their model is utilized rather than the aggregated annual data and their model

noncanonical quantization of gravity ii constraints and the physical hilbert space the program of quantizing the gravitational field with the help of affine field variables is continued for completeness a review of the selection criteria that singles out the affine fields the alternative treatment of constraints and the choice of the initial before imposition of the constraints ultralocal representation of the field operators is initially presented as analogous examples demonstrate the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear to achieve this introduction and enforcement of the constraints a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical hilbert space is developed and extensively analyzed

semiparametric efficient estimation of ar 1 panel data models this study focuses on the semiparametric efficient estimation of random effect panel models containing ar 1 disturbances we also consider such estimators when the effects and regressors are correlated hausman and taylor 1981 we introduce two semiparametric efficient estimators that make minimal assumptions on the distribution of the random errors effects and the regressors and that provide semiparametric efficient estimates of the slope parameters and of the effects our estimators extend the previous work of park and simar j amer statist assoc 89 1994 929 park et al j econometrics 84 1998 273 and adams et al j business econom statist 17 1999 349 theoretical derivations are supplemented by monte carlo simulations we also provide an empirical illustration by estimating relative efficiencies from a stochastic distance function for the u s banking industry over the 1980s and 1990s in markets where regulatory constraints have been lessened or done away with the deregulatory dynamic market shocks may not be adjusted to immediately and may induce a serial correlation pattern in firm s use of best practice banking technologies our semiparametric estimators have an important role in providing robust point estimates and inferences of the productivity and efficiency gains due to such economic reforms

solution giving formula to cauchy problem for multidimensional parabolic equation with variable coefficients we present a general method of solving the cauchy problem for multidimensional parabolic diffusion type equation with variable coefficients which depend on spatial variable but do not change over time we assume the existence of the c0 semigroup this is a standard assumption in the evolution equations theory which guarantees the existence of the solution and then find the representation based on the family of translation operators of the solution in terms of coefficients of the equation and initial condition it is proved that if the coefficients of the equation are bounded infinitely smooth and satisfy some other conditions then there exists a solution giving c0 semigroup of contraction operators we also represent the solution as a feynman formula i e as a limit of a multiple integral with multiplicity tending to infinity with generalized functions appearing in the integral kernel we present a general method of solving the cauchy problem for multidimensional parabolic diffusion type equation with variable coefficients which depend on spatial variable but do not change over time we assume the existence of the c0 semigroup this is a standard assumption in the evolution equations theory which guarantees the existence of the solution and then find the representation based on the family of translation operators of the solution in terms of coefficients of the equation and initial condition it is proved that if the coefficients of the equation are bounded infinitely smooth and satisfy some other conditions then there exists a solution giving c0 semigroup of contraction operators we also represent the solution as a feynman formula i e as a limit of a multiple integral with multiplicity tending to infinity with generalized functions appearing in the integral kernel

impulse output rapid stabilization for heat equations abstract the main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain with dirichlet boundary condition two constraints will be compulsory first the controls are active in a subdomain of and at discrete time points second the observations are made in another subdomain and at different discrete time points our strategy consists in linking an observation estimate at one time minimal norm impulse control approximate inverse source problem and rapid output stabilization

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

the dimensionality reduction principle for generalized additive models soit x y une paire de variables aleatoires telles que x x 1 x j s etende sur c 0 1 j la distribution conditionnelle de y etant donne x x est supposee appartenir a une famille exponentielle appropriee ayant pour parametre r f x denote la dependance de vis a vis de x et f l approximation additive de f ayant la log vraisemblance esperee maximum possible

a rigorous path integral for quantum spin using flat space wiener regularization adapting ideas of daubechies and klauder j math phys 26 2239 1985 we derive a rigorous continuum path integral formula for the semigroup generated by a spin hamiltonian more precisely we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable schrodinger semigroup on the hilbert space l2 r2 of lebesgue square integrable functions on the euclidean plane r2 the path integral formula emerges from the standard feynman kac ito formula for the schrodinger semigroup in the ultradiffusive limit of the underlying brownian bridge on r2 in a similar vein a path integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin hamiltonian

constructing measures for spin variable path integrals by exploiting the overcompleteness of the spin coherent states we derive expressions for spin kinematics path integrals specifically for spin 1 2 and spin 1 in terms of genuine wiener measures on continuous paths lying on the unit sphere and for certain dynamical systems which when projected onto the subspace spanned by the proper spin coherent state matrix elements yield the appropriate quantum mechanical propagator

estimation of arma models with seasonal parameters the yule walker equations for arma p q models with periodic parameters are derived from which moment estimates can be obtained specifically for the case of arma p 1 models the periodic autoregressive parameters can be found by solving a system of linear equations while the periodic moving average parameters satisfy a system of equations which can be solved iteratively particular examples are given and comparisons are made between the proposed moment estimates and estimates given previously

phase space feynman path integrals a rigorous mathematical formulation of the phase space feynman path integral is given in a general setting this is then applied to yield a representation of solutions of the schrodinger equation with potential depending both on the position and momentum variables

evaluating contextual variables affecting productivity using data envelopment analysis a dea based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one sided inefficiency deviations as well as two sided random noise conditions are identified under which a two stage procedure consisting of dea followed by ordinary least squares ols regression analysis yields consistent estimators of the impact of contextual variables conditions are also identified under which dea in the first stage followed by maximum likelihood estimation mle in the second stage yields consistent estimators of the impact of contextual variables this requires the contextual variables to be independent of the input variables but the contextual variables may be correlated with each other monte carlo simulations are carried out to compare the performance of our two stage approach with one stage and two stage parametric approaches simulation results indicate that dea based procedures with ols maximum likelihood or even tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity simulation results also indicate that dea based procedures perform better than parametric methods in the estimation of individual decision making unit dmu productivity overall the results establish dea as a nonparametric stochastic frontier estimation sfe methodology

a canonical process for estimation of convex functions the invelope of integrated brownian motion t4 a process associated with integrated brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities respectively we call this process the invelope and show that it is an almost surely uniquely defined function of integrated brownian motion its role is comparable to the role of the greatest convex minorant of brownian motion plus a parabolic drift in the problem of estimating monotone functions an iterative cubic spline algorithm is introduced that solves the constrained least squares problem in the limit situation and some results obtained by applying this algorithm are shown to illustrate the theory

comment on semiclassical dynamics of a spin in an arbitrary magnetic field in a recent paper alscher and grabert claim to prove that a dominant tree level stationary phase approximation to the wiener regularized continuum su 2 coherent state path integral for the quantum propagator zf t exp i 0 h ds zi becomes exact provided h is a linear combination of the su 2 generators with arbitrary time dependent coefficients i find the derivation of this in fact obvious result unduly complicated and somewhat obscure the authors start from a classical spin action inconsistent with necessary boundary conditions and therefore are forced to invoke a nontrivial regularization of the action to render the latter meaningful alternatively when a su 2 symplectic potential consistent with the boundary conditions is employed no regularization is required to obtain the leading quasiclassical asymptotics

recent results regarding affine quantum gravity recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non classical modification of the ground state wave function leads to a result that eliminates term by term divergences that arise in a conventional perturbation analysis after a brief review of both the scalar field story and the affine quantum gravity program examination of the procedures used in the latter surprisingly shows an analogous formulation which already implies that affine quantum gravity is not plagued by divergences that arise in a standard perturbation study additionally guided by the projection operator method to deal with quantum constraints trial reproducing kernels are introduced that satisfy the diffeomorphism constraints furthermore it is argued that the trial reproducing kernels for the diffeomorphism constraints may also satisfy the hamiltonian constraint as well

constructing measures for path integrals the overcompleteness of the coherent states for the heisenberg weyl group implies that many different integral kernels can be used to represent the same operator within such an equivalence class we construct an integral kernel to represent the quantum mechanical evolution operator for certain dynamical systems in the form of a path integral that involves genuine wiener measures on continuous phase space paths to achieve this goal it is necessary to employ an expression for the classical action different from the usual one

dose finding using the biased coin up and down design and isotonic regression we are interested in finding a dose that has a prespecified toxicity rate in the target population in this article we investigate five estimators of the target dose to be used with the up and down biased coin design bcd introduced by durham and flournoy 1994 statistical decision theory and related topics these estimators are derived using maximum likelihood weighted least squares sample averages and isotonic regression a linearly interpolated isotonic regression estimate is shown to be simple to derive and to perform as well as or better than the other target dose estimators in terms of mean square error and average number of subjects needed for convergence in most scenarios studied

non parametric efficiency estimation using richardson lucy blind deconvolution abstract we propose a non parametric three stage strategy for efficiency estimation in which the richardson lucy blind deconvolution algorithm is used to identify firm specific inefficiencies from the residuals corrected for the expected inefficiency the performance of the proposed algorithm is evaluated against the method of moments under 16 scenarios assuming 0 the results show that the richardson lucy blind deconvolution method does not generate null or zero values due to wrong skewness or low kurtosis of inefficiency distribution that it is insensitive to the distributional assumptions and that it is robust to data noise levels and heteroscedasticity we apply the richardson lucy blind deconvolution method to finnish electricity distribution network data sets and we provide estimates for efficiencies that are otherwise inestimable when using the method of moments and correct ranks of firms with similar efficiency scores

testing procedures for detection of linear dependencies in efficiency models the validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of or uncorrelated with technical efficiency however few studies have attempted to test these assumptions in a recent paper wilson 2003 investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes in this study we discuss the implications of these assumptions in three situations i bootstrapping non parametric efficiency models ii estimating stochastic frontier models and iii obtaining aggregate measures of industry efficiency we propose a semi parametric hausmann type asymptotic test for linear independence uncorrelation and use a monte carlo experiment to show that it has good size and power properties in finite samples we also describe how the test can be generalized in order to detect higher order dependencies such as heteroscedasticity so that the test can be used to test for full independence when the efficiency distribution has a finite number of moments finally an empirical illustration is provided using data on us electric power generation

quantization of systems with a general phase space equipped with a riemannian metric quantization on phase spaces of general geometry devoid of any special symmetry properties is discussed on the basis of phase spaces endowed with a symplectic structure a riemannian geometry and a structure using techniques from differential geometry and especially exploiting the dirac operator we are able to offer a fully geometric quantization procedure for a wide class of symmetry free phase spaces our procedure leads to the conventional results in cases where the phase space is a symmetric space for which alternative quantization techniques suffice

periodic covariance stationarity of multivariate periodic autoregressive moving average processes periodic covariance stationarity conditions for multivariate periodic autoregressive moving average parma processes are investigated it follows from a previous work that a necessary and sufficient condition for the periodic stationarity of a multivariate periodic process is the covariance stationarity of the lumped vector process which contains the periodic vectors as its elements it is shown that for univariate and multivariate parma processes even with periodically varying orders the lumped process is a multivariate autoregressive moving average arma process the stationarity conditions of which are readily available periodic stationarity conditions for the multivariate parma 1 1 process are explicitly obtained which apply for all parma 1 q processes it is shown that the periodic stationarity of a periodic process always implies the stationarity of the aggregated process the sum of the periodic vectors the reverse is yet to be proved or disproved however it is shown to be true for par 1 and parma 1 1 processes

an analysis of a second order time accurate scheme for a finite volume method for parabolic equations on general nonconforming multidimensional spatial meshes the present work is an extension of our previous work bradji and fuhrmann 2011 4 which dealt with error analysis of a finite volume scheme of first order both in time and space for parabolic equations on general nonconforming multidimensional spatial meshes introduced recently in eymard et al 2010 12 we aim in this paper to get a higher order time accurate scheme for a finite volume method for parabolic equations using the same class of spatial generic meshes stated above we derive a finite volume scheme approximating the heat equation as a model for parabolic equations in which the discretization in time is performed using the crank nicolson method we derive an a priori estimate for the discrete problem and we prove that the error estimate of the finite volume scheme is of order two in time and it is of optimal order in space the error estimate is analysed in several norms which allow us to derive approximations for the exact solution and its first derivatives both spatial and temporal whose the convergence order is two in time and it is optimal in space we prove in particular when the discrete flux is calculated using a stabilized discrete gradient that the convergence order is k 2 h d where h d resp k is the mesh size of the spatial resp time discretization these estimates are valid under the regularity assumption u c 3 0 t c 2 w for the exact solution u the proof of these error estimates is based essentially on a new a priori estimate for the discrete problem and a comparison between the finite volume approximate solution and an auxiliary finite volume approximation

nonparametric efficiency analysis a multivariate conditional quantile approach this paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup multiple inputs and multiple outputs it introduces quantile efficiency scores a nonparametric estimator is proposed achieving strong consistency and asymptotic normality then if increases to one as a function of the sample size we recover the properties of the fdh estimator but our estimator is more robust to the perturbations in data since it attains a finite gross error sensitivity environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed numerical examples illustrate the usefulness of the approach

semiclassical dynamics of a spin in an arbitrary magnetic field the spin coherent state path integral describing the dynamics of a spin system in a magnetic field of arbitrary time dependence is considered defining the path integral as the limit of a wiener regularized expression the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints the resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator a nonlinear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary value problem the semiclassical spin dynamics is thus readily amenable to numerical methods

weak coherent state path integrals weak coherent states share many properties of the usual coherent states but do not admit a resolution of unity expressed in terms of a local integral they arise e g in the case that a group acts on an inadmissible fiducial vector motivated by the recent affine quantum gravity program the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time evolution operator since weak coherent states do not admit a resolution of unity it is clear that the standard way of constructing a path integral by time slicing is predestined to fail instead a well defined path integral with wiener measure based on a continuous time regularization is used to approach this problem the dynamics is rigorously established for linear hamiltonians and the difficulties presented by more general hamiltonians are addressed

nonparametric stochastic frontiers a local maximum likelihood approach this paper proposes a new approach to handle nonparametric stochastic frontier sf models it is based on local maximum likelihood techniques the model is presented as encompassing some anchorage parametric model in a nonparametric way first we derive asymptotic properties of the estimator for the general case local linear approximations then the results are tailored to a sf model where the convoluted error term efficiency plus noise is the sum of a half normal and a normal random variable the parametric anchorage model is a linear production function with a homoscedastic error term the local approximation is linear for both the production function and the parameters of the error terms the performance of our estimator is then established in finite samples using simulated data sets as well as with a cross sectional data on us commercial banks the methods appear to be robust numerically stable and particularly useful for investigating a production process and the derived efficiency scores

quasiclassical path integral in coherent state manifolds quantization of classical dynamical systems with a poisson structure on homogeneous kahler manifolds is considered the quantization follows the method invented by berezin and represents the unitary transition operator as a quasiclassical path integral in the coherent state basis in case the coherent state manifold appears as a degenerate rank one co adjoint orbit of the symmetry group an explicit representation of the transition amplitude in terms of classical data can be derived for large values of the highest weight which corresponds to the quasiclassical approximation this representation is further shown to perfectly agree in contrast to some earlier approaches with the known exact results and may provide non trivial asymptotics of physical relevance

efficient estimation of monotone boundaries let g 0 1 0 1 be a monotone nondecreasing function and let g be the closure of the set x y is an element of 0 1 x 0 1 0 less than or equal to y less than or equal to g x we consider the problem of estimating the set g from a sample of i i d observations uniformly distributed in g the estimation error is measured in the hausdorff metric we propose the estimator which is asymptotically efficient in the minimax sense

quasi feynman formulas a method of obtaining the evolution operator for the schrodinger equation abstract for a densely defined self adjoint operator h in hilbert space f the operator exp i t h is the evolution operator for the schrodinger equation i t h i e if 0 x 0 x then t x exp i t h 0 x for x q the space f here is the space of wave functions defined on an abstract space q the configuration space of a quantum system and h is the hamiltonian of the system in this paper the operator exp i t h for all real values of t is expressed in terms of the family of self adjoint bounded operators s t t 0 which is chernoff tangent to the operator h one can take s t exp t h or use other simple families s that are listed in the paper the main theorem is proven on the level of semigroups of bounded operators in f so it can be used in a wider context due to its generality two examples of application are provided

oscillatory integrals on hilbert spaces and schrodinger equation with magnetic fields the theory of oscillatory integrals on hilbert spaces the mathematical version of feynman path integrals is extended to cover more general integrable functions preserving the property of the integrals to have converging finite dimensional approximations an application to the representation of solutions of the time dependent schrodinger equation with a scalar and a magnetic potential by oscillatory integrals on hilbert spaces is given a relation with ramer s functional in the corresponding probabilistic setting is found

wiener measures for path integrals with affine kinematic variables the results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp ith can be written as a well defined wiener integral involving wiener measure on the lobachevsky half plane in the limit that the diffusion constant diverges this approach works for a wide class of hamiltonians including e g d2 dx2 v x on l2 r with v sufficiently singular at x 0

quantum mechanical path integrals with wiener measure for all polynomial hamiltonians ii the coherent state representation of quantum mechanical propagators as well defined phase space path integrals involving wiener measure on continuous phase space paths in the limit that the diffusion constant diverges is formulated and proved this construction covers a wide class of self adjoint hamiltonians including all those which are polynomials in the heisenberg operators in fact this method also applies to maximal symmetric hamiltonians that do not possess a self adjoint extension this construction also leads to a natural covariance of the path integral under canonical transformations an entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin operator hamiltonian as well defined path integrals involving wiener measure on the unit sphere again in the limit that the diffusion constant diverges

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

smooth approximations to monotone concave functions in production analysis an alternative to nonparametric concave least squares abstract estimation of banking efficiency and productivity is essential for regulatory purposes and for testing various theories in the context of banking such as the quiet life hypothesis the bad management hypothesis etc in such studies it is therefore important to place as few restrictions as possible on the functional forms subject to global satisfaction of the theoretical properties relating to monotonicity and concavity in this paper we propose an alternative to nonparametric segmented concave least squares we use a differentiable approximation to an arbitrary functional form based on smoothly mixing cobb douglas anchor functions over the data space estimation is based on bayesian techniques organized around markov chain monte carlo the approximation properties of the new functional form are investigated in a monte carlo experiment where the true functional form is a symmetric generalized mcfadden the new techniques are applied to a large u s banking data set as well as a global banking data set

the joint measurement of technical and allocative inefficiencies an application of bayesian inference in nonlinear random effects models this article estimates technical and allocative inefficiencies and increase in costs therefrom of individual firms using a translog cost system consisting of the cost function and the cost share equations we call it a nonlinear random effects system because technical and allocative inefficiencies are random hence the term random effects and are separated from the random noise terms appearing in each equation of the system and because the inefficiency terms appear in the system in a highly nonlinear fashion which helps in separating them from random errors we use bayesian inference procedures based on markov chain monte carlo mcmc techniques to estimate the proposed system inferences on firm specific technical inefficiency and both input specific and firm specific allocative inefficiencies are developed using mcmc techniques we apply the new methods to a sample of 500 u s commercial banks we focus on input allocation problem based on the assumption that banks minimize cost empirical results sh

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

approximations to the solution of cauchy problem for a linear evolution equation via the space shift operator second order equation example abstract we present a general method of solving the cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two one and zero the method is based on the chernoff approximation procedure applied to a specially constructed shift operator it is proven that approximations converge uniformly to the exact solution

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

maximum likelihood consistency and data envelopment analysis a statistical foundation this paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis dea dea estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function while the best practice frontier estimator is biased below the theoretical frontier for a finite sample size the bias approaches zero for large samples the dea estimators exhibit the desirable asymptotic property of consistency and the asymptotic distribution of the dea estimators of inefficiency deviations is identical to the true distribution of these deviations this result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions

finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions abstract we give an approach to the theory of oscillatory integrals in infinite dimensions starting from finite dimensional oscillatory integrals we also provide detailed asymptotic expansions by a method of stationary phase in infinite dimensions with convergence and estimates for the remainder provided by a strong control on finite dimensional approximations

dea with efficiency classification preserving conditional convexity abstract we propose to relax the standard convexity property used in data envelopment analysis dea by imposing additional qualifications for feasibility of convex combinations we specifically focus on a condition that preserves the koopmans efficiency classification this yields an efficiency classification preserving conditional convexity property which is implied by both monotonicity and convexity but not conversely substituting convexity by conditional convexity we construct various empirical dea approximations as the minimal sets that contain all dmus and are consistent with the imposed production assumptions imposing an additional disjunctive constraint to standard convex dea formulations can enforce conditional convexity computation of efficiency measures relative to conditionally convex production set can be performed through disjunctive programming dp

existence of solutions to heat equations with singular lower order terms abstract this paper is concerned with the solvability for the cauchy problem of heat equations in r n n 2 with singular lower order terms u t x t u x t x x 2 u x t c x 2 u x t f x t in r n 0 t u x 0 u 0 x in r n where r c n 2 2 4 u 0 is an initial value f is an inhomogeneous term and t 0 is arbitrarily given in particular u 0 and f are taken from a weighted l p space the result generalizes the one of baras and goldstein 1984 2 from 0 to 0 and improves the one of arendt goldstein and goldstein 2006 1 which deals with an m accretive realization of the linear part in a weighted l p space under the stronger condition c n 2 2 p 1 p 2 moreover this paper clarifies some regularities of solutions

semiparametric stochastic frontier models a generalized additive model approach abstract the choice of the functional form of the frontier into a stochastic frontier model is typically neglected in applications and canonical functions are usually considered this paper introduces a semiparametric approach for stochastic frontier estimation that extends previous works based on pseudo likelihood estimators allowing flexibility in model selection and capability of imposing monotonicity and concavity constraints for these purposes the present work introduces a generalized additive framework that moreover permits to model the influence of contextual environmental factors to the hypothesized production process by the relative extension given by generalized additive models for location scale and shape through some monte carlo simulations and an application to european agricultural data the flexibility of the proposed framework in analyzing efficiency is illustrated

feynman path integrals for polynomially growing potentials abstract a general class of infinite dimensional oscillatory integrals with polynomially growing phase functions is studied a representation formula of the parseval type is proved as well as a formula giving the integrals in terms of analytically continued absolutely convergent integrals these results are applied to provide a rigorous feynman path integral representation for the solution of the time dependent schrodinger equation with a quartic anharmonic potential the borel summability of the asymptotic expansion of the solution in power series of the coupling constant is also proved

null controllability for a heat equation with a singular inverse square potential involving the distance to the boundary function this article is devoted to the analysis of control properties for a heat equation with a singular potential 2 defined on a bounded c2 domain rn where is the distance to the boundary function more precisely we show that for any 1 4 the system is exactly null controllable using a distributed control located in any open subset of while for 1 4 there is no way of preventing the solutions of the equation from blowing up the result is obtained applying a new carleman estimate

wiener and poisson process regularization for coherent state path integrals by introducing a suitable continuous time regularization into a formal phase space path integral it follows that the propagator is given by the limit of well defined functional integrals involving standard stochastic processes and their associated probability measures such regularizations require pinning of both coordinate and momenta variables and automatically lead to coherent state representations it is found that each standard independent increment process involving a superposition of a wiener and a poisson process is associated with a specific generally non gaussian fiducial vector with which the coherent states are defined

hamiltonian feynman path integrals via the chernoff formula the main aim of the present paper is using a chernoff theorem i e the chernoff formula to formulate and to prove some rigorous results on representations for solutions of schrodinger equations by the hamiltonian feynman path integrals feynman integrals over trajectories in the phase space the corresponding theorem is related to the original feynman approach to feynman path integrals over trajectories in the phase space in much the same way as the famous theorem of nelson is related to the feynman approach to the feynman path integral over trajectories in the configuration space we also give a representation for solutions of some schrodinger equations by a series which represents an integral with respect to the complex poisson measure on trajectories in the phase space

data envelopment analysis as nonparametric least squares regression data envelopment analysis dea is known as a nonparametric mathematical programming approach to productive efficiency analysis in this paper we show that dea can be alternatively interpreted as nonparametric least squares regression subject to shape constraints on the frontier and sign constraints on residuals this reinterpretation reveals the classic parametric programming model by aigner and chu aigner d s chu 1968 on estimating the industry production function amer econom rev 58 826 839 as a constrained special case of dea applying these insights we develop a nonparametric variant of the corrected ordinary least squares cols method we show that this new method referred to as corrected concave nonparametric least squares c2nls is consistent and asymptotically unbiased the linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis

estimation of a convex function characterizations and asymptotic theory we study nonparametric estimation of convexregression and density functions by methods of least squares in the regression and density cases and maximum likelihood in the density estimation case we provide characterizations of these estimators prove that they are consistent and establish their asymptotic distributions at a fixed point of positive curvature of the functions estimated the asymptotic distribution theory relies on the existence of an invelope function for integrated two sided brownian motion t 4 which is established in a companion paper by groeneboom jongbloed and wellner

on p values for smooth components of an extended generalized additive model the problem of testing smooth components of an extended generalized additive model for equality to zero is considered confidence intervals for such components exhibit good across the function coverage probabilities if based on the approximate result hat f i n f i v f i i where f is the vector of evaluated values for the smooth component of interest and v f is the covariance matrix for f according to the bayesian view of the smoothing process based on this result a wald type test of f 0 is proposed it is shown that care must be taken in selecting the rank used in the test statistic the method complements previous work by extending applicability beyond the gaussian case while considering tests of zero effect rather than testing the parametric hypothesis given by the null space of the component s smoothing penalty the proposed p values are routine and efficient to compute from a fitted model without requiring extra model fits or null distribution simulation

coherent state path integral calculation of the wigner function we consider a set of operators 1 n with diagonal representatives p n in the space of generalized coherent states n d n p n nn we regularize the coherent state path integral as a limit of a sequence of averages l over polygonal paths with l vertices n1 l the distribution of the path centroid 1 l l 1lp nl tends to the wigner function w x the joint distribution for the operators w x lim l n x l this result is proved in the case where the hamiltonian commutes with the wigner function is non positive if the dominant paths with path centroid in a certain region have berry phases close to odd multiples of for finite l the path centroid distribution is a wigner function convolved with a gaussian of variance inversely proportional to l the results are illustrated by numerical calculations of the spin wigner function from su 2 coherent states the relevance to the quantum monte carlo sign problem is also discussed

a mathematical theory of the phase space feynman path integral of the functional an essentially different description of quantization from the heisenberg description and the schrodinger one was proposed by feynman in 1948 it is called the description by means of the feynman path integral in the same paper and his book in 1965 it was studied in detail how his so called transition elements described by the feynman path integral of the functional look in the conventional notation of wave functions and operators to help us to relate the results of path integral calculations to the results in the heisenberg theory and the schrodinger one then some formulas were obtained heuristically for it but it seems that rigorous results for these formulas obtained little except for the special cases in the author s preceding paper in the present paper these formulas are proved rigorously and more generally than his formulas by means of the phase space feynman path integral introduced by the author in the preceding paper not the configuration space feynman path integral it is also proved that an assumption is necessary for the functional in order that the feynman path integral of the functional can be defined this assumption seems to reflect the uncertainty principle in quantum mechanics

a two stage hybrid procedure for estimating an inverse regression function we consider a two stage procedure tsp for estimating an inverse regression function at a given point where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this estimate is used at stage two we establish that the convergence rate of the second stage estimate can attain the parametric n 1 2 rate furthermore a bootstrapped variant of tsp btsp is introduced and its consistency properties studied this variant manages to overcome the slow speed of the convergence in distribution and the estimation of the derivative of the regression function at the unknown target quantity finally the finite sample performance of btsp is studied through simulations and the method is illustrated on a data set

corrections to the coherent state path integral comments upon a speculation of l s schulman intuitively the feynman path integral corresponds to a weighted sum over classical paths an interpretation that fails for the phase space path integral to address the question of whether there exists a path integral expression conforming to a sum over paths in phase space an examination of the discrete coherent state path integral cspi is undertaken via an alternative formulation of the cspi it is shown that the coherent state action for a broad class hamiltonians can be transformed from the variables q p to q q for these hamiltonians such a transformation along with the inclusion of all terms o e zi zi 1 yields an expression which for finite e can be interpreted as a sum over classical paths with gaussian weight the numerical evaluation of this expression through importance sampling monte carlo is demonstrated

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

weak galerkin method with r r 1 r 1 order finite elements for second order parabolic equations in this paper we propose a weak galerkin method with a stabilization term for a model problem of second order parabolic differential equations we establish both the continuous time and the discrete time weak galerkin finite element schemes which allow the use of totally discontinuous piecewise polynomial basis and the finite element partitions on shape regular polygons in addition we adapt the combination of polynomial spaces p r t 0 p r 1 e p r 1 t 2 that reduces the number of unknowns in the numerical scheme without compromising the accuracy of the numerical approximation we show as well that the continuous time weak galerkin finite element method preserves the energy conservation law the optimal convergence order estimates in both discrete h1 and l2 norms are obtained we also present numerical experiments to illustrate the theoretical results

isotonic regression another look at the changepoint problem a test based on isotonic regression is developed for monotonic trends in short range dependent sequences and is applied to argentina rainfall data and global warming data this test provides another perspective for changepoint problems the isotonic test is shown to be more powerful than some existing tests for trend

stochastic non convex envelopment of data applying isotonic regression to frontier estimation abstract isotonic nonparametric least squares inls is a regression method for estimating a monotonic function by fitting a step function to data in the literature of frontier estimation the free disposal hull fdh method is similarly based on the minimal assumption of monotonicity in this paper we link these two separately developed nonparametric methods by showing that fdh is a sign constrained variant of inls we also discuss the connections to related methods such as data envelopment analysis dea and convex nonparametric least squares cnls further we examine alternative ways of applying isotonic regression to frontier estimation analogous to corrected and modified ordinary least squares cols mols methods known in the parametric stream of frontier literature we find that inls is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings in the absence of noise the corrected inls cinls has a higher discriminating power than fdh in the case of noisy data we propose to apply the method of non convex stochastic envelopment of data non convex stoned which disentangles inefficiency from noise based on the skewness of the inls residuals the proposed methods are illustrated by means of simulated examples

the klauder daubechies construction of the phase space path integral and the harmonic oscillator the canonical operator quantisation formulation corresponding to the klauder daubechies construction of the phase space path integral is considered this formulation is explicitly applied and solved in the case of the harmonic oscillator thereby illustrating in a manner complementary to klauder and daubechies original work some of the promising features offered by their construction of a quantum dynamics the klauder daubechies functional integral involves a regularisation parameter eventually taken to vanish which defines a new physical time scale when extrapolated to the field theory context besides providing a new regularisation of short distance divergences keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems comment 18 pages

variable selection in semiparametric regression modeling in this paper we are concerned with how to select significant variables in semiparametric modeling variable selection for semiparametric regression models consists of two components model selection for nonparametric components and select significant variables for parametric portion thus it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel this leads to very heavy computational burden in this paper we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood the newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously this allows us to establish the sampling properties of the resulting estimate we first establish the rate of convergence of the resulting estimate with proper choices of penalty functions and regularization parameters we then establish the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component we investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi squared distribution which is independent of the nuisance parameters extensive monte carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures

solving nonlocal initial boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the adomian decomposition method in this paper we present a new approach to solve nonlocal initial boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations subject to initial and nonlocal boundary conditions of integral type we first transform the given nonlocal initial boundary value problems of integral type for the linear and nonlinear parabolic and hyperbolic partial differential equations into local dirichlet initial boundary value problems and then use a relatively new modified adomian decomposition method adm furthermore we investigate the fourier adomian method which also does not require any a priori assumptions on the solution for the solution of nonlocal initial boundary value problems combined with our new approach several examples are presented to demonstrate the efficiency of the adm