trapping aspects in enhanced diffusion we study the superlinear diffusion x2 t t 1 in layered media containing random velocity fields the superlinear behavior holds in the case of random velocities along thex direction accompanied by diffusional motion in the space transverse to it the transverse space can be either euclidean fractal or ultrametric for a one dimensional transverse space we derive exact expressions for the higher moments of the displacement furthermore we investigate the propagatorp x t along thex direction and establish its scaling behavior our analysis highlights the resemblance between the stretched gaussian behavior of the propagator and the stretched exponential form of the survivial probability in the trapping problem both show late crossover behavior

the traveling salesman problem with distances one and two we present a polynomial time approximation algorithm with worst case ratio 7 6 for the special case of the traveling salesman problem in which all distances are either one or two we also show that this special case of the traveling salesman problem is max snp hard and therefore it is unlikely that it has a polynomial time approximation scheme

seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

superdiffusive transport due to random velocity fields the motion of a random walk in a medium containing random but spatially correlated velocity fields is discussed this type of disorder generally leads to superdiffusive behavior in which the mean square displacement x2 t grows faster than linearly with time for a two dimensional medium with layers of random velocities in the x direction x2 t is found to increase as t2v with 2v 32 the probability distribution of displacements appears to fit the form p x t t 34 exp x t34 with 1 7 however a lifshitz argument for the tail of the distribution suggests that 43 this discrepancy is yet to be fully resolved we also discuss some intriguing properties in a model with isotropic velocity fields in two dimensions we find v 43 while 3 these values obey the general scaling relation 1 v 1

the laurent series approach to structural modeling abstract caves and christensen 1980 have provided a procedure for displaying the regular regions of a flexible functional form in the 2 good homothetic and nonhomothetic cases and in the 3 good homothetic case we extend the procedure to the nonhomothetic 3 good case and we apply the extended procedure to the translog generalized leontief and minflex laurent flexible functional forms in addition we acquire the regular regions for the minflex laurent model in the 2 good nonhomothetic case and superimpose the resulting regions on those already found by caves and christensen for the translog and generalized leontief models we find that the new minflex laurent model generally has the largest regular regions of the three flexible functional forms in addition the regular region of the minflex laurent model is found to expand as real income increases as a result that model is particularly well suited for use with time series data which typically is characterized by positive long term growth trends in real income in such applications all recent data and future forecasts can be expected to lie within the regular region of the minflex laurent model although it is possible for some of the earliest data to fall outside that regular region the model s regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets the regular region of each of the three models moves when the model s parameters are changed with the generalized leontief or translog model the regular region s shape location and size are unpredictable without prior knowledge of the model s parameters with either of those models the intersection of the model s regular regions as the parameters are changed is contained within a very small neighborhood of the one point at which we require the model to be regular with the minflex laurent model the primary properties of the regular regions are invariant to the values of the parameters and the intersection of the displayed regular regions is a very large unbounded set the width of that intersection increases without limit as real income increases

generalized quadratic revenue functions abstract in this paper we focus on the specification of revenue functions in their dual price space we consider two distance functions the shephard output distance function and the directional output distance function and define both in price space the former is multiplicative in nature and satisfies homogeneity whereas the latter is additive and satisfies the translation property functional equation methods yield the translog specification in the case of the shephard distance function and a quadratic specification in the case of the directional distance function monte carlo evidence suggests that the quadratic specification outperforms the translog in large samples and in true models with plenty of curvature

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

non parametric hypothesis testing procedures and applications to demand analysis abstract this paper proposes a test of the hypothesis that a possibly vector valued regression function g lies in a particular compact family of functions f where f is not necessarily a finite dimensional parametric family under the assumption of a known covariance matrix of the errors the test is shown to be consistent for a broad range of alternatives and an upper bound on the significance level is established it is shown how the test may be used to test the utility maximization hypothesis and homotheticity and the paper indicates how to apply the test to a broad range of other non parametric hypotheses

proof verification and the hardness of approximation problems we show that every language in np has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof if a string is in the language then there exists a proof such that the verifier accepts with probability 1 i e for every choice of its random string for strings not in the language the verifier rejects every provided proof with probability at least 1 2 our result builds upon and improves a recent result of arora and safra 1998 whose verifiers examine a nonconstant number of bits in the proof though this number is a very slowly growing function of the input length as a consequence we prove that no max snp hard problem has a polynomial time approximation scheme unless np p the class max snp was defined by papadimitriou and yannakakis 1991 and hard problems for this class include vertex cover maximum satisfiability maximum cut metric tsp steiner trees and shortest superstring we also improve upon the clique hardness results of feige et al 1996 and arora and safra 1998 and show that there exists a positive e such that approximating the maximum clique size in an n vertex graph to within a factor of n e is np hard

the global properties of the minflex laurent generalized leontief and translog flexible functional forms caves and christensen 16 have provided a procedure for displaying the regular regions of a flexible functional form in the 2 good homothetic and nonhomothetic cases and in the 3 good homothetic case we extend the procedure to the nonhomothetic 3 good case and we apply the extended procedure to the translog generalized leontief and minflex laurent flexible functional forms in addition we acquire the regular regions for the minflex laurent model in the 2 good nonhomothetic case and superimpose the resulting regions on those already found by caves and christensen for the translog and generalized leontief models we find that the new minflex laurent model generally has the largest regular regions of the three fiexible functional forms in addition the regular region of the minflex laurent model is found to expand as real income increases as a result that model is particularly well suited for use with time series data which typically is characterized by positive long term growth trends in real income in such applications all recent data and future forecasts can be expected to lie within the regular region of the minflex laurent model although it is possible for some of the earliest data to fall outside that regular region the model s regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets the regular region of each of three models moves when the model s parameters are changed with the generalized leontief or translog model the regular region s shape location and size are unpredictable without prior knowledge of the model s parameters with either of those two models the intersection of the model s regular regions as the parameters are changed is contained within a very small neighborhood of the one point at which we require the model to be regular with the minflex laurent model the primary properties of the regular regions are invariant to the values of the parameters and the intersection of the displayed regular regions is a very large unbounded set the width of that intersection increases without limit as real income increases

improved algorithms for bipartite network flow in this paper network flow algorithms for bipartite networks are studied a network g v e is called bipartite if its vertex set v can be partitioned into two subsets v 1 and v 2 such that all edges have one endpoint in v 1 and the other in v 2 let n v n 1 v 1 n 2 v 2 m e and assume without loss of generality that n 1 leq n 2 a bipartite network is called unbalanced if n 1 ll n 2 and balanced otherwise this notion is necessarily imprecise it is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks the basic idea in these improvements is a two edge push rule that allows one to charge most computation to vertices in v 1 and hence develop algorithms whose running times depend on n 1 rather than n for example it is shown that the two edge push version of goldberg and tarjan s fifo preflow push algorithm runs in o n 1 m n 1 3 time and that the analogous version of ahuja and orlin s excess scaling algorithm runs in o n 1 m n 1 2 log u time where u is the largest edge capacity these ideas are also extended to dynamic tree implementations parametric maximum flows and minimum cost flows

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

nonparametric and distribution free estimation of the binary threshold crossing and the binary choice models in this paper it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term this identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term the estimator is shown to be strongly consistent and a two step procedure for its calculation is developed the paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results

anomalous diffusion in a unidirectional random velocity field with long range correlations the anomalous diffusion in a unidirectional random velocity field with long range correlations is analysed in directions transverse to the direction of the field or along the field direction critical values of the exponents which characterize the power like falloff of the correlations in the transverse and longitudinal directions and the critical dimension of space are determined the anomalous dimension of the longitudinal diffusion coefficient is also calculated in the first order of the in expansion for several cases of a long range correlated random velocity field

stratified disordered media exact solutions for transport parameters and their self averaging properties we investigate the transport of a passive tracer in a two dimensional stratified random medium with flow parallel and perpendicular to the strata assuming a gaussian random flow with a gaussian correlation function it is not only possible to derive exact expressions for the temporal behaviour of the dispersion coefficients characterizing the tracer transport but also to investigate the self averaging properties of these quantities we give explicit results for the dispersion coefficient and its mean square fluctuations as a function of time as it turns out the sample to sample fluctuations which are encoded in the latter quantity remain finite even in the asymptotic limit of infinite times which implies that the given two dimensional model is not self averaging

on bayesian analysis and computation for functions with monotonicity and curvature restrictions our goal is inference for shape restricted functions our functional form consists of finite linear combinations of basis functions prior elicitation is difficult due to the irregular shape of the parameter space we show how to elicit priors that are flexible theoretically consistent and proper we demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non uniform prior that addresses this issue we introduce simulation methods that meet challenges posed by the shape of the parameter space we analyze data from a consumer demand experiment

non parametric unconditional quantile estimation for efficiency analysis with an application to federal reserve check processing operations abstract this paper examines the technical efficiency of us federal reserve check processing offices over 1980 2003 we extend results from park et al park b simar l weiner c 2000 fdh efficiency scores from a stochastic point of view econometric theory 16 855 877 and daouia and simar daouia a simar l 2007 nonparametric efficiency analysis a multivariate conditional quantile approach journal of econometrics 140 375 400 to develop an unconditional hyperbolic quantile estimator of efficiency our new estimator is fully non parametric and robust with respect to outliers when used to estimate distance to quantiles lying close to the full frontier it is strongly consistent and converges at rate root n thus avoiding the curse of dimensionality that plagues data envelopment analysis dea estimators our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices

nonlinear hypotheses inequality restrictions and non nested hypotheses exact simultaneous tests in linear regressions in the context of the classical linear model the problem of comparing two arbitrary hypotheses on the regression coefficients is considered problems involving nonlinear hypotheses inequality restrictions or non nested hypotheses are included as special cases exact bounds on the null distribution of likelihood ratio statistics are derived the bounds are based on the central fisher distribution and are very easy to use in an important special case a bounds test similar to the durbin watson test is proposed multiple testing problems are also studied the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows one to combine any number of tests this result extends to nonlinear hypotheses a well known result given by scheffe for linear hypotheses a method of building bounds induced tests is also suggested

fast algorithms for bipartite network flow we discuss network flow in a bipartite graph g with node sets s and t we show that karzanov s algorithm runs in time o s 2 t on g and that the mpm algorithm can be modified to run in the same bound for the common case that the degree of each node in t is bounded by a constant we show that a modified version of the mpm algorithm runs in time o s 3 s t on g the importance of these results comes from the common occurrence of problems that can be modeled and solved using network flow on bipartite graphs where s ll t in many applications involving bounded degree on the nodes in t t theta s 2 and our results reduce the best bounds on bipartite flow from o s 6 to o s 3 we use our results on bipartite flow to obtain the fastest known bounds on several combinatorial problems and mention several additional problems involving bipartite flow where s is much smaller than t

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

short cuts to dynamic factor demand modelling abstract by means of so called virtual or shadow prices short run factor demands short run marginal costs etc can be derived from any long run cost function the traditional approach short run restricted conditional variable cost functions is criticized and it is also shown that technological change scale effects etc can be added to any cost function by means of disembodied factor augmenting efficiency indexes easing the interpretations of the effects but without loss of flexibility it is shown that the trend and scale parameters of the long run translog cost function can be directly translated into trend and scale parameters of such efficiency indexes the techniques are illustrated on the well known berndt wood data set using a diewert long run generalized leontief gl cost function and assuming that capital and labour are quasi fixed

on the bias in flexible functional forms and an essentially unbiased form the fourier flexible form abstract the fourier flexible form and its derived expenditure system are introduced subject to smoothness conditions on the consumer s true indirect utility function the consumer s true expenditure system must be of the fourier form over the region of interest in an empirical investigation arbitrarily accurate finite parameter approximations of the consumer s true expenditure system are obtained by dropping all high order terms of the fourier expenditure system past an appropriate truncation point the resulting finite parametersystem is tractable in empirical studies the reader who is primarily interested in applications need only read the second and fifth sections the remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in translog specifications

renormalization group analysis of superdiffusion in random velocity fields field theoretic renormalization group theory is applied to the analysis of the asymptotic behaviour of diffusion in random velocity fields each nonvanishing component of which is independent of the coordinate along the direction of that component below the critical dimension dc 3 the corresponding field theory is shown to have a nontrivial infrared stable fixed point of the renormalization group which controls the long time large distance behaviour of the model the anomalous dimension nu has been found exactly in the epsilon 3 d expansion and the leading logarithmic corrections to the normal diffusion at d 3 have been determined for all d 1 or d or d where d is the number of components of the drift field

unbiased determination of production technologies abstract to determine whether an industry exhibits constant returns to scale whether the production function is homothetic or whether inputs are separable a common approach is to specify a cost function estimate its parameters using data such as prices and quantities of inputs and then test the parametric restrictions corresponding to constant returns a homothetic technology or separability statistically such inferences are valid if the true cost function is a member of the parametric class considered otherwise the inference is biased that is the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test the use of fixed parameter flexible functional forms such as the translog the generalized leontief or the box cox will not alleviate this problem the fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound depending on the number of parameters on the error as measured by the sobolev norm of approximation to an arbitrary cost function thus it is possible to construct statistical tests for constant returns a homothetic technology or separability which are asymptotically size by letting the number of parameters of the fourier flexible form depend on sample size that is the true rejection probability converges to the nominal size of the test as sample size tends to infinity the rate of convergence depends on the smoothness of the true cost function the more times is differentiable the true cost function the faster the convergence the method is illustrated using the data on aggregate u s manufacturing of berndt and wood 1975 1979 and berndt and khaled 1979

explicitly infinite dimensional bayesian analysis of production technologies abstract the firm s cost function is viewed as a point in a function space and data is viewed as following some probability law that has as its parameters various functionals evaluated at the firm s cost function the fourier flexible form is used to represent a cost function as an infinite dimensional vector whose elements are the parameters of the fourier form this representation is used to assign a prior distribution to the function space a procedure for numerical computation of the posterior distribution of an elasticity of substitution is set forth the ideas are illustrated with an example

effective transport in random shear flows we obtain an effective transport description for the superdiffusive motion of random walkers in stratified flow by projection of the process on the direction of stratification the effective dimensionally reduced motion is shown to describe a correlated random walk characterized by the lagrangian velocity correlation we analyze the projected motion through exact analytical solutions for the distribution density for an arbitrary correlated gaussian noise and derive an evolution equation for the one point and conditional two point displacement densities the latter gives an explicit effective equation for superdiffusive transport in stratified random flow and demonstrates that the displacement density has a gaussian scaling form for all times

superdiffusion in random velocity fields abstract stochastic transport in a medium containing random but spatially correlated velocity fields is discussed this type of disorder generally leads to superdiffusive behavior in which the mean square displacement of a random walk x2 t grows faster than linearly with time for a two dimentional layered medium with y dependent random velocities in the x direction ux y x2 x t2 with v 3 4 and with strong sample to sample fluctuations the probability distribution of displacements averaged over environments takes a non gaussian scaling form at large time p x t 3 4 x t 3 4 where u exp u for u 1 with 4 3 for an isotropic two dimensional medium with ux y having the same statistical properties we find v 2 3 and 1 1 3 for the layered medium the moments of the time for a random walker to first reach a distance x in the longitudinal direction increases as t n 1 n x 4 3 possibly modified by logarithmic corrections however the probability that the walk has not reached a distance x in a time t decreases asymptotically as e t with x2 indicating that more than a single time scale is needed to account for first passage properties

on a high dimensional model representation method based on copulas abstract this article provides an alternative to high dimensional model representation using a copula approximation of an unknown functional form we apply our methodology in the context of an extensive monte carlo study and to a sample of large us commercial banks in the monte carlo experiment the approximations errors of the copula approach are small and behave randomly in our empirical application we find that the copula approximation performs much better in terms of bayes factors for model comparison compared to high dimensional model representation which in turn provides better results when compared with standard flexible functional forms like the translog the minflex laurent and the generalized leontief or a multilayer perceptron moreover the choice of approximation has significant implications for productivity and its components returns to scale technical inefficiency technical change and efficiency change

efficient algorithms for the hitchcock transportation problem we consider the hitchcock transportation problem on n supply points and k demand points when n is much greater than k the problem can be solved in o k n 2 log n n 2 log 2 n time if an efficient minimum cost flow algorithm is directly applied applying a geometric method named splitter finding and a randomization technique we can improve the time complexity when the ratio c of the maximum supply to the minimum supply is sufficiently small the expected running time of our randomized algorithm is o frac kn log cn log n k 4 log 2 k if n k 4 log 2 k and o k 5 log 2 n log cn if n le k 4 log 2 k if n omega k 4 epsilon epsilon 0 and c mbox poly n the problem is solved in o kn time which is optimal

estimating demand with distance functions parameterization in the primal and dual abstract our purpose is to investigate the ability of different parametric forms to correctly estimate consumer demands based on distance functions using monte carlo methods our approach combines economic theory econometrics and quadratic approximation we begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property homogeneity is typical of shephard distance functions and expenditure functions whereas translation is characteristic of benefit shortage or directional distance functions the functional forms which satisfy these conditions and include both first and second order terms are the translog and quadratic forms respectively we then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic we assess functional form performance by focusing on empirical violations of the regularity conditions our analysis corroborates results from earlier monte carlo studies on the production side suggesting that the quadratic form more closely approximates the true technology or in our context consumer preferences than the translog

persistence of randomly coupled fluctuating interfaces we study the persistence properties in a simple model of two coupled interfaces characterized by heights h 1 and h 2 respectively each growing over a d dimensional substrate the first interface evolves independently of the second and can correspond to any generic growing interface e g of the edwards wilkinson or of the kardar parisi zhang variety the evolution of h 2 however is coupled to h 1 via a quenched random velocity field in the limit d ensuremath rightarrow 0 our model reduces to the matheron de marsily model in two dimensions for d 1 our model describes a rouse polymer chain in two dimensions advected by a transverse velocity field we show analytically that after a long waiting time t 0 ensuremath rightarrow ensuremath infty the stochastic process h 2 at a fixed point in space but as a function of time becomes a fractional brownian motion with a hurst exponent h 2 1 ensuremath ensuremath beta 1 2 where ensuremath beta 1 is the growth exponent characterizing the first interface the associated persistence exponent is shown to be ensuremath theta s 2 1 ensuremath h 2 ensuremath beta 1 2 these analytical results are verified by numerical simulations

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

a maximum b matching problem arising from median location models with applications to the roommates problem we consider maximumb matching problems where the nodes of the graph represent points in a metric space and the weight of an edge is the distance between the respective pair of points we show that if the space is either the rectilinear plane or the metric space induced by a tree network then theb matching problem is the dual of the single median location problem with respect to the given set of points this result does not hold for the euclidean plane however we show that in this case theb matching problem is the dual of a median location problem with respect to the given set of points in some extended metric space we then extend this latter result to any geodesic metric in the plane the above results imply that the respective fractionalb matching problems have integer optimal solutions we use these duality results to prove the nonemptiness of the core of a cooperative game defined on the roommate problem corresponding to the above matching model 1998 the mathematical programming society inc published by elsevier science b v

introduction to internally consistent modeling aggregation inference and policy abstract this special issue of the journal of econometrics honors william a barnett s exceptional contributions to unifying economic theory with rigorous statistical inference to interpret economic data and inform public policy it is devoted to papers that advance microeconometrics macroeconometrics and financial econometrics to build models to interpret evidence

hamilton paths in grid graphs a grid graph is a node induced finite subgraph of the infinite grid it is rectangular if its set of nodes is the product of two intervals given a rectangular grid graph and two of its nodes we give necessary and sufficient conditions for the graph to have a hamilton path between these two nodes in contrast the hamilton path and circuit problem for general grid graphs is shown to be np complete this provides a new relatively simple proof of the result that the euclidean traveling salesman problem is np complete

fractional demand systems abstract this paper provides a complete characterization of fractional demand systems which are utility derived demand equations having quantities or budget shares proportional to af bg where f and g depend on income and a and b vary across goods and depend on prices it is proved that all such demand systems reduce to seven basic forms only four of which homothetic pigl piglog and translog have been previously described in the literature uses and virtues of fractional demand systems in terms of estimation aggregation possible global properties and uses for testing the adequacy of other common functional forms are described an empirical example comparing the general fractional form of the translog system to its more usual piglog form is provided

wald criteria for jointly testing equality and inequality restrictions on montre comment le test de wald s applique a des ensembles de restrictions d egalite et d inegalite et on presente la distribution pour de grands echantillons du test sous l hypothese nulle

smoothing bias in the measurement of marginal effects abstract this paper examines the tendency of kernel regression estimators to underestimate marginal effects or derivatives by developing the connection between smoothing and errors in variables structure we explain how smoothing itself leads to attenuation bias in derivatives or bias toward zero when the true model is linear and the regressors normal the attenuation bias is uniform and can be accurately explained by standard errors in variables bias formulae these formulations also indicate the seriousness of the attenuation bias with different numbers of regressors and different sample sizes for the situation where the true model is nonlinear we examine the related errors in variables structure and indicate what features affect the size of attenuation bias in derivatives finally we explain the connections between our analysis and the standard bias expansion for kernel regression estimators including brief consideration of technical devices such as higher order kernels

the global properties of the two minflex laurent flexible functional forms abstract the minflex laurent flexible functional form is a special case of a second order laurent series expansion the minflex laurent when constructed in square roots is called the minflex laurent ml generalized leontief the minflex laurent ml translog model is the minflex laurent in logarithms we find that the regular region of the ml translog is most often even larger than that of the ml generalized leontief model except when substitutability is very low we previously have shown that the regular region of the ml generalized leontief is substantially larger than that of the usual translog and generalized leontief models

multipoint concentration statistics for transport in stratified random velocity fields we determine the full multipoint concentration statistics for superdiffusive transport in a steady stratified random velocity field using a lagrangian approach we derive explicit analytical expressions for the multipoint moments of concentration and specifically for the concentration variance which is a measure for concentration uncertainty the multipoint concentration moments are fully characterized by the lagrangian mean velocity and by the one and two particle velocity correlations while the relative variance at the center of mass of the mean concentration is constant it increases exponentially with time and distance from the center of mass this implies that small concentration values are particularly uncertain which can pose a serious practical concern as these are typically the earliest and latest to arrive at a point

the three dimensional global properties of the minflex laurent generalized leontief and translog flexible functional forms abstract we use the caves and christensen procedure to produce the regular regions of three flexible functional forms generalized leontief translog and barnett s new minflexlaurent model we display the regular regions in six cases with three goods using both three dimensional color graphics and two dimensional sections we find that minflex laurent generally has the largest regular region in addition the regular regions of that model are the most stable in shape across the six cases and always expand as real income increases consequently that model is especially well suited for use with income trended time series data

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

two algorithmic results for the traveling salesman problem for any norm in a euclidean space and for any number 0 we present a polynomial time algorithm which computes a hamiltonian circuit with the given vertices in the space whose length approximates with relative error less than the largest length of a hamiltonian circuit with these vertices we also present an algorithm which for a given graph with n vertices computes the number of hamiltonian circuits in this graph with 2n olog n time complexity and a polynomial in n space complexity as a by product of our approach we prove that the permanent of a matrix can be computed in polynomial time provided the rank of the matrix is fixed

the minflex laurent translog flexible functional form abstract barnett s minflex laurent generalized leontief model was produced from a special case of a second order laurent series expansion in the square roots in this paper we produce a minflex laurent translog flexible functional form by the analogous expansion in the logarithms we prove that the model s regular region always grows monotonically as real income increases as a result the model is especially well suited for use with income trended time series data we also prove that the model satisfies diewert s definition of a flexible functional form and is no more deeply parameterized than is necessary to satisfy the flexibility criterion

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

a normalized quadratic semiflexible functional form estimation of flexible functional forms for large consumer or producer demand systems is often precluded due to computational difficulties or due to a lack of degrees of freedom we propose the concept of a semiflexible form which is a special case of a flexible form but which requires fewer free parameters our proposed method of estimation allows the researcher to choose the degree of flexibility consistent with feasibility of estimation while at the same time maintaining the concavity in prices property required by economic theory in our empirical illustration we estimate a normalized quadratic semiflexible form using canadian per capita time series data for ten consumer expenditure categories

the geometric maximum traveling salesman problem we consider the traveling salesman problem when the cities are points in n x211d d for some fixed d and distances are computed according to geometric distances determined by some norm we show that for any polyhedral norm the problem of finding a tour of maximum length can be solved in polynomial time if arithmetic operations are assumed to take unit time our algorithms run in time o nf 2 log n where f is the number of facets of the polyhedron determining the polyhedral norm thus for example we have o n2 log n algorithms for the cases of points in the plane under the rectilinear and sup norms this is in contrast to the fact that finding a minimum length tour in each case is np hard our approach can be extended to the more general case of quasi norms with a not necessarily symmetric unit ball where we get a complexity of o n2f 2 log n for the special case of two dimensional metrics with f 4 which includes the rectilinear and sup norms we present a simple algorithm with o n running time the algorithm does not use any indirect addressing so its running time remains valid even in comparison based models in which sorting requires n log n time the basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms complementing the results on simplicity for polyhedral norms we prove that for the case of euclidean distances in n x211d d for d 3 the maximum tsp is np hard this sheds new light on the well studied difficulties of euclidean distances

guillotine subdivisions approximate polygonal subdivisions a simple polynomial time approximation scheme for geometric tsp k mst and related problems we show that any polygonal subdivision in the plane can be converted into an m guillotine subdivision whose length is at most 1 c over m times that of the original subdivision for a small constant c m guillotine subdivisions have a simple recursive structure that allows one to search for the shortest of such subdivisions in polynomial time using dynamic programming in particular a consequence of our main theorem is a simple polynomial time approximation scheme for geometric instances of several network optimization problems including the steiner minimum spanning tree the traveling salesperson problem tsp and the k mst problem

an elasticity can be estimated consistently without a priori knowledge of functional form we consider an open question in applied price theory without a priori knowledge of a firm s cost function or a consumer s indirect utility function is it possible to estimate price and substitution elasticities consistently by observing a demand system as the work of white 30 guilkey lovell and sickles 19 and others has shown ordinary flexible functional forms such as the translog cannot achieve this objective we find that if one is prepared to assume that elasticities of substitution cannot oscillate wildly over the region of interest then consistent estimation is possible using the fourier flexible form provided the number of fitted parameters increases as the number of observations increases this result obtains with any of the commonly used statistical methods as for example multivariate least squares maximum likelihood and three stage least squares it obtains if the number of fitted parameters is chosen adaptively by observing the data or chosen deterministically according to some fixed rule we approach the problem along the classical lines of estimability considerations as used in the study of less than full rank linear statistical models and thereby discover that the problem has a fascinating structure which we explore in detail

polynomial time approximation schemes for euclidean traveling salesman and other geometric problems we present a polynomial time approximation scheme for euclidean tsp in fixed dimensions for every fixed c 1 and given any n nodes in r 2 a randomized version of the scheme finds a 1 1 c approximation to the optimum traveling salesman tour in o n log n o c time when the nodes are in r d the running time increases to o n log n o d c d 1 for every fixed c d the running time is n poly log n that is nearly linear in n the algorithmm can be derandomized but this increases the running time by a factor o n d the previous best approximation algorithm for the problem due to christofides achieves a 3 2 aproximation in polynomial time we also give similar approximation schemes for some other np hard euclidean problems minimum steiner tree k tsp and k mst the running times of the algorithm for k tsp and k mst involve an additional multiplicative factor k the previous best approximation algorithms for all these problems achieved a constant factor approximation we also give efficient approximation schemes for euclidean min cost matching a problem that can be solved exactly in polynomial time all our algorithms also work with almost no modification when distance is measured using any geometric norm such as e p for p 1 or other minkowski norms they also have simple parallel i e nc implementations

testing inequality constraints in linear econometric models abstract this paper develops three asymptotically equivalent tests for examining the validity of imposing linear inequality restrictions on the parameters of linear econometric models first we consider the model y x e where e is n 0 and the hypothesis test h r r versus k rk later we generalize this testing framework to the linear simultaneous equations model we show that the joint asymptotic distribution of these test statistics and the test statistics from the hypothesis test h r r versus k r r is a weighted sum of two sets of independent 2 distributions we also derive a useful duality relation between the multivariate inequality constraints test developed here and the multivariate one sided hypothesis test in small samples these three test statistics satisfy inequalities similar to those derived by berndt and savin 1977 for the case of equality constraints the paper also contains an illustrative application of this testing technique

likelihood based inference for regular functions with fractional polynomial approximations abstract this paper shows that regular fractional polynomials can approximate regular cost production and utility functions and their first two derivatives on closed compact subsets of the strictly positive orthant of euclidean space arbitrarily well these functions therefore can provide reliable approximations to demand functions and other economically relevant characteristics of tastes and technology using canonical cost function data it shows that full bayesian inference for these approximations can be implemented using standard markov chain monte carlo methods

flexible functional forms and global curvature conditions empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions lau and gallant and golub have worked out methods for imposing the appropriate curvature conditions locally but those local techniques frequently fail to yield satisfactory results we develop two methods for imposing curvature conditions globally in the context of cost function estimation the first method adopts lau s technique to a generalization of a functional form first proposed by mcfadden using this generalized mcfadden functional form it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally the second method adopts a technique used by mcfadden and barnett which is based on the fact that a non negative sum of concave functions will be concave our various suggested techniques are illustrated using the u s manufacturing data utilized by berndt and khaled