small sample properties of dimensionality statistics for fitting var models to aggregate economic data a monte carlo study abstract the analysis of aggregate economic phenomena by var s as suggested by sims often results in a small sample relative to the number of estimated parameters since the model is identified by a dimensionality criterion the small sample properties of available criteria are important this paper presents a study of small sample properties for six criteria with monte carlo methods it is found that no criterion performs well and that underfitting of models may be quite common

semi nonparametric estimation of binary response models with an application to natural resource valuation abstract a semi nonparametric binary response model is estimated to obtain the willingness to pay for the environmental quality improvement when the willingness to pay is restricted to be nonnegative the model estimation is straightforward by using conventional maximum likelihood software because the semi nonparametric model is the generalization of the parametric model the generality can be assessed by a likelihood ratio test by using an existing referendum survey data set it is shown that the semi nonparametric estimation provides a significant improvement over the parametric estimation the willingness to pay is sensitive to the distribution assumption

model selection in the presence of nonstationarity abstract this paper studies model selection methods in the presence of nonstationarity we focus on the bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice first we derive each of these criteria in the presence of nonstationarity in particular we study the bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity one important feature of the bayesian model selection criterion bmsc is that bmsc gives different weights to the stationary and nonstationary components of a model while the other criteria do not this feature of bmsc is a desirable property for a model selection rule in the presence of possible nonstationarity second we compare these criteria with regard to parsimony and power we have found that bmsc shows the highest parsimony aic is the second and c p and r 2 having the same level of parsimony are the third with regard to power the order is not clearly established however for the size adjusted power bmsc becomes dominant as the sample size increases without size adjustment the order in the power is exactly the opposite to that in parsimony also we find that bmsc is a consistent selection rule while the other criteria are not third we consider four different cases of practical interest for which bmsc with some of the other criteria is applicable we discuss how our bmsc can be used in these cases of practical interest results of an extensive monte carlo simulation for models in these four cases show that overall the bmsc outperforms other criteria

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

the conditional autoregressive wishart model for multivariate stock market volatility abstract we propose a conditional autoregressive wishart caw model for the analysis of realized covariance matrices of asset returns our model assumes an autoregressive moving average structure for the scale matrix of the wishart distribution it accounts for positive definiteness of covariance matrices without imposing parametric restrictions and can be estimated by maximum likelihood we also propose extensions of the caw model obtained by including a mixed data sampling midas component and heterogeneous autoregressive har dynamics for long run fluctuations the caw models are applied to realized variances and covariances for five new york stock exchange stocks

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

the neumann problem in a 2 d exterior domain with cuts and singularities at the tips abstract the neumann problem for the harmonic functions in an exterior connected plane region with cuts is studied the problem is considered with different conditions at infinity which lead to different theorems on uniqueness and solvability the existence of a classical solution is proved by potential theory the problem is reduced to a fredholm equation of the second kind which is uniquely solvable explicit formulas for singularities of a gradient of the solution at the tips of the cuts are obtained the results of the paper can be used to model the flow of an ideal fluid over several obstacles including wings

globally flexible functional forms the neural distance function the output distance function is a key concept in economics however its empirical estimation often violates properties dictated by neoclassical production theory in this paper we introduce the neural distance function ndf which constitutes a global approximation to any arbitrary production technology with multiple outputs given by a neural network nn specification the ndf imposes all theoretical properties such as monotonicity curvature and homogeneity for all economically admissible values of outputs and inputs fitted to a large data set for all us commercial banks 1989 2000 the ndf explains a very high proportion of the variance of output while keeping the number of parameters to a minimum and satisfying the relevant theoretical properties all measures such as total factor productivity tfp and technical efficiency te are computed routinely next the ndf is compared with the translog popular specification and is found to provide very satisfactory results as it possesses the properties thought as desirable in neoclassical production theory in a way not matched by its competing specification

asymptotic normality and consistency of semi nonparametric regression estimators using an upwards f test truncation rule abstract the consistency and asymptotic normality of semi nonparametric regression estimators are shown when the truncation parameter is selected by an upwards f test moreover the same statements are also shown to apply to a large class of linear estimators the article concludes with a discussion of f test critical value settings and includes results from a simulation study which demonstrates that confidence interval coverage can be increased by varying the critical values in a nonstandard way

an alternative quasi likelihood approach bayesian analysis and data based inference for model specification abstract this paper studies an alternative quasi likelihood approach under possible model misspecification we derive a filtered likelihood from a given quasi likelihood ql called a limited information quasi likelihood li ql that contains relevant but limited information on the data generation process our li ql approach in one hand extends robustness of the ql approach to inference problems for which the existing approach does not apply our study in this paper on the other hand builds a bridge between the classical and bayesian approaches for statistical inference under possible model misspecification we can establish a large sample correspondence between the classical ql approach and our li ql based bayesian approach an interesting finding is that the asymptotic distribution of an li ql based posterior and that of the corresponding quasi maximum likelihood estimator share the same sandwich type second moment based on the li ql we can develop inference methods that are useful for practical applications under possible model misspecification in particular we can develop the bayesian counterparts of classical ql methods that carry all the nice features of the latter studied in white 1982 in addition we can develop a bayesian method for analyzing model specification based on an li ql

asymptotic optimality of generalized cl cross validation and generalized cross validation in regression with heteroskedastic errors abstract the problem considered here is that of using a data driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter in contrast to other papers on this subject we consider models with heteroskedastic errors the results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators nearest neighbor estimators and local regression estimators among others generalized c l gc l cross validation cv and generalized cross validation gcv procedures are analyzed the gc l and cv criteria are shown to be asymptotically optimal under general conditions a feasible version of gc l however is available only in some applications the gcv criterion is found to be asymptotically optimal only under a condition that is satisfied in some applications but not in others for example it is satisfied in the nearest neighbor estimation context but not in the series estimation local regression estimation or model selection contexts thus the cv criterion is the only feasible criterion of the three that is asymptotically optimal under general conditions the proofs rely heavily on results of li 1987

on deviations between neoclassical and gft based true cost of living indexes derived from the same demand function system abstract given that a generalized fechner thurstone gft direct utility function and a neoclassical direct utility function yield exactly the same system of demand functions then for which combinations of a regions of the domain of neoclassical parameters and b price and total expenditure regimes do the alternative true cost of living indexes tcli s and their sensitivities to changes in casual factors differ significantly practical neoclassical alternatives to the gft based non parametric tcli s are limited to parametric tcli s based on the class of implicit utility models discussed by barnett this paper describes the design and results of a simulation experiment which generated alternative tcli s under different parameter specifications focus of appraisal is on specifications which produced realistic demand elasticities and large deviations between tcli s

an effective semiparametric estimation approach for the sufficient dimension reduction model abstractin the exploratory data analysis the sufficient dimension reduction model has been widely used to characterize the conditional distribution of interest different from the existing approaches our main achievement is to simultaneously estimate two essential elements basis and structural dimension of the central subspace and the bandwidth of a kernel distribution estimator through a single estimation criterion with an appropriate order of kernel function the proposed estimation procedure can be effectively carried out by starting with a dimension of zero until the first local minimum is reached meanwhile the optimal bandwidth selector is ensured to be a valid tuning parameter for the central subspace estimator an important advantage of this estimation technique is its flexibility to allow a response to be discrete and some of covariates to be discrete or categorical providing that a certain continuity condition holds under very mild assumptions we further derive the uniform consistency of

symmetry constraints for feedforward network models of gradient systems this paper concerns the use of a priori information on the symmetry of cross differentials available for problems that seek to approximate the gradient of a differentiable function we derive the appropriate network constraints to incorporate the symmetry information show that the constraints do not reduce the universal approximation capabilities of feedforward networks and demonstrate how the constraints can improve generalization

estimating regression models of finite but unknown order abstract this paper considers some problems associated with estimation and inference in the normal linear regression model y t j 1 m0 j x tj e t var e t 2 when m 0 is unknown the regressors are taken to be stochastic and assumed to satisfy v grenander s 1954 conditions almost surely it is further supposed that estimation and inference are undertaken in the usual way conditional on a value of m 0 chosen to minimize the estimation criterion function ec m t 2 m mg t with respect to m where 2m is the maximum likelihood estimate of 2 it is shown that subject to weak side conditions if g t a s 0 and tg t a s then this estimate is weakly consistent it follows that estimates conditional on the chosen value of m 0 are asymptotically efficient and inference undertaken in the usual way is justified in large samples when g t converges to a positive constant with probability one then in large samples m 0 will never be chosen too small but the probability of choosing m 0 too large remains positive the results of the paper are stronger than similar ones r shibata 1976 r j bhansali and d y downham 1977 in that a known upper bound on m 0 is not assumed the strengthening is made possible by the assumptions of strictly exogenous regressors and normally distributed disturbances the main results are used to show that if the model selection criteria of h akaike 1974 t amemiya 1980 c l mallows 1973 or e parzen 1979 are used to choose m 0 in 1 then in the limit the probability of choosing m 0 too large is at least 0 2883 the approach taken by g schwarz 1978 leads to a consistent estimator of m 0 however these results are illustrated in a small sampling experiment

consistent estimation of minimal sujbset dimension for a general paramnetric model we consider the problem of consistently estimating that permissible subset of the parameter space that contains the true parameter point and has smallest dimension the subset selection is done by means of a model selection criterion of

estimating substitution elasticities with the fourier cost function some monte carlo results abstract the fourier flexible form possesses desirable asymptotic properties that are not shared by other flexible forms such as the translog generalized leontief and generalized box cox one of them is that an elasticity of substitution can be estimated with negligible bias in sufficiently large samples regardless of what the true form actually is save that it be smooth enough this article reports the results of an experiment designed to determine whether or not this property obtains in samples of the sizes customarily encountered in practice a three input homothetic version of the generalized box cox cost function was used to generate technologies that were oriented in a two dimensional design space according to a central composite rotatable design the two factors of the design were the box cox parameter and a measure of the dispersion of the substitution matrix the fourier cost function was used to estimate the substitution elasticities at each design point and the bias at each point was estimated using the monte carlo method a response surface over the entire design space was fitted to these estimates an examination of the surface reveals that the bias is small over the entire design space roughly speaking the estimates of elasticities of substitution are unbiased to three significant digits using the fourier flexible form no matter what the true technology our conclusion is that the small bias property of the fourier form does obtain in samples of reasonable size this claim must be tampered by the usual caveats associated with inductive inference

measures of conditional linear dependence and feedback between time series abstract measures of linear dependence and feedback for two multiple time series conditional on a third are defined the measure of conditional linear dependence is the sum of linear feedback from the first to the second conditional on the third linear feedback from the second to the first conditional on the third and instantaneous linear feedback between the first and second series conditional on the third the measures are non negative and may be expressed in terms of measures of unconditional feedback between various combinations of the three series the measures of conditional linear feedback can be additively decomposed by frequency estimates of these measures are straightforward to compute and their distribution can be routinely approximated by bootstrap methods an empirical example involving real output money and interest rates is presented

nonparametric function estimation subject to monotonicity convexity and other shape constraints this paper uses free knot and fixed knot regression splines in a bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log concave likelihood functions the shape constraints we consider include monotonicity convexity and functions with a single minimum a computationally efficient mcmc sampling algorithm is developed that converges faster than previous methods for non gaussian models simulation results indicate the monotonically constrained function estimates have good small sample properties relative to i unconstrained function estimates and ii function estimates obtained from other constrained estimation methods when such methods exist also asymptotic results show the methodology provides consistent estimates for a large class of smooth functions two detailed illustrations exemplify the ideas

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

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

efficiency of weighted average derivative estimators and index models weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis this paper gives efficiency results for average derivative estimators including formulating estimators that have high efficiency our analysis is carried out in three steps first we derive the efficiency bound for weighted average derivatives of conditional location functionals such as the conditional mean and median second we derive the efficiency bound for semiparametric index models where the location measure depends only on indices or linear combinations of the regressors third we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients we characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric in more general cases we discuss how to combine estimators with different weight functions to achieve efficiency we derive a general condition for approximate efficiency of pooled minimum chi square estimators for index model coefficients based on weighted average derivatives finally we discuss ways of selecting the type and number of weighting functions to achieve high efficiency

exponential series estimator of multivariate densities abstract we present an exponential series estimator ese of multivariate densities which has an appealing information theoretic interpretation for a d dimensional random variable x with density p 0 the ese takes the form p x exp i 1 0 m 1 i d 0 m d i i x where i are some real valued linearly independent functions defined on the support of p 0 we derive the convergence rate of the ese in terms of the kullback leibler information criterion the integrated squared error and some other metrics we also derive its almost sure uniform convergence rate we then establish the asymptotic normality of p we undertake two sets of monte carlo experiments the first experiment examines the ese performance using mixtures of multivariate normal densities the second estimates copula density functions the results demonstrate the efficacy of the ese an empirical application on the joint distributions of stock returns is presented

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

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

a fast approach for dimensionality reduction with image data an important objective in image analysis is dimensionality reduction the most often used data exploratory technique with this objective is principal component analysis which performs a singular value decomposition on a data matrix of vectorized images when considering an array data or tensor instead of a matrix the high order generalization of pca for computing principal components offers multiple ways to decompose tensors orthogonally as an alternative we propose a new method based on the projection of the images as matrices and show that it leads to a better reconstruction of images than previous approaches

semi nonparametric estimation of the call option price surface under strike and time to expiry no arbitrage constraints abstract we suggest a semi nonparametric estimator for the call option price surface the estimator is a bivariate tensor product b spline to enforce no arbitrage constraints across strikes and expiry dates we establish sufficient no arbitrage conditions on the control net of the b spline surface the conditions are linear and therefore allow for an implementation of the estimator by means of standard quadratic programming techniques the consistency of the estimator is proved by means of simulations we explore the statistical efficiency benefits that are associated with estimating option price surfaces and state price densities under the full set of no arbitrage constraints we estimate a call option price surface families of first order strike derivatives and state price densities for s p 500 option data

comparison of alternative functional forms in production abstract in this paper a bayesian approach to choosing between two non nested multivariate regression systems is developed the bayesian approach involves the calculation of the posterior probabilities of alternative hypotheses and formation of a posterior odds ratio specific results are obtained for the comparison of a multivariate regression and seemingly unrelated regression model these odds ratio results are applied to the choice between translog and fourier flexible form cost share equation systems when calculated for aggregate u s manufacturing cost data the odds ratios favor the fourier flexible form over the translog form even in small samples the fourier series expansion appears to be an effective approximation technique

ring theoretical properties of affine cellular algebras abstract as a generalisation of graham and lehrer s cellular algebras affine cellular algebras have been introduced in 12 in order to treat affine hecke algebras of type a and affine versions of diagram algebras like affine temperley lieb algebras in a unifying fashion affine cellular algebras include kleshchev s graded quasihereditary algebras khovanov lauda rouquier algebras and various other classes of algebras in this paper we will study ring theoretical properties of affine cellular algebras we show that any affine cellular algebra a satisfies a polynomial identity furthermore we show that a can be embedded into its asymptotic algebra if the occurring commutative affine k algebras b j are reduced and the determinants of the swich matrices are non zero divisors as a consequence we show that the gelfand kirillov dimension of a is less than or equal to the largest krull dimension of the algebras b j and that equality holds in case all affine cell ideals are idempotent or if the krull dimension of the algebras b j is less than or equal to 1 special emphasis is given to the question when an affine cell ideal is idempotent generated by an idempotent or finitely generated

the rank of demand systems theory and nonparametric estimation w m gorman s 1981 concept of engel curve rank is extended to apply to any demand system rank is shown to have implications for specification separability and aggregation of demands a simple nonparametric test of rank using engel curve data is described and applied to u s and u k consumer survey data the test employs a new general method for testing the rank of estimated matrices the results are used to assess theoretical and empirical aggregation error in representative consumer models and to explain a representative consumer paradox copyright 1991 by the econometric society

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

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

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

affine cellularity of affine yokonuma hecke algebras abstract we establish an explicit algebra isomorphism between the affine yokonuma hecke algebra y r n q and a direct sum of matrix algebras with coefficients in tensor products of affine hecke algebras of type a as an application of this result we show that y r n q is affine cellular in the sense of koenig and xi and further prove that it has finite global dimension when the parameter q is not a root of the poincare polynomial as another application we also recover the modular representation theory of y r n q previously obtained in 7

asymptotic normality of series estimators for nonparametric and semiparametric regression models this paper establishes the asymptotic normality of series estimators for nonparametric regression models gallant s fourier flexible form estimators trigonometric series estimators and polynomial series estimators are prime examples of the estimators covered by the results the results apply to a wide variety of estimates in the regression model under consideration including derivatives and integrals of the regression function the errors in the model may be homoskedastic or heteroskedastic the paper also considers series estimators for additive interactive regression semiparametric regression and semiparametric index regression models and shows them to be consistent and asymptotically normal copyright 1991 by the econometric society

on the asymptotic normality of fourier flexible form estimates abstract rates of increase in the number of parameters of a fourier factor demand system that imply asymptotically normal elasticity estimates are characterized this is the multivariate analog of work by andrews 1991 our proof strategy is new and consists of relating the minimum eigenvalue of the sample sum of squares and cross products matrix to the minimum eigenvalue of the population matrix via a uniform strong law with rate that is established using results from the empirical processes literature in its customary form the minimum eigenvalue of the fourier sum of squares and cross products matrix considered as a function of the number of parameters decreases faster than any polynomial the consequence is that the rate at which parameters may increase is slower than any fractional power of the sample size in this case we get the same rate as andrews when our results are applied to multivariate regressions with a minimum eigenvalue that is bounded or declines at a polynomial rate the rate on the parameters is a fractional power of the sample size in this case our method of proof gives faster rates than andrews andrews results cover the heteroskedastic case ours do not

global approximation to arbitrary cost functions a bayesian approach with application to us banking this paper proposes and estimates a globally flexible functional form for the cost function which we call neural cost function ncf the proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates the functional form can be estimated easily using markov chain monte carlo mcmc techniques or standard iterative sure we use a large panel of u s banks to illustrate our approach the results are consistent with previous knowledge about the sector and in accordance with mathematical production theory

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

affine cellularity of bln algebras abstract we show that the bln algebra which was introduced by mcgerty is affine cellular in the sense of koenig and xi in fact we establish a stronger property namely that the affine cell ideals are generated by idempotents this particularly implies that the global dimension of the bln algebra is finite for affine type a we obtain that the affine q schur algebra u d n n when d n is affine cellular and has finite global dimension

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

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

robustness checks and robustness tests in applied economics a common exercise in empirical studies is a robustness check where the researcher examines how certain core regression coe cient estimates behave when the regression speci cation is modi ed by adding or removing regressors if the coe cients are plausible and robust this is commonly interpreted as evidence of structural validity here we study when and how one can infer structural validity from coe cient robustness and plausibility as we show there are numerous pitfalls as commonly implemented robustness checks give neither necessary nor su cient evidence for structural validity indeed if not conducted properly robustness checks can be completely uninformative or entirely misleading we discuss how critical and non critical core variables can be properly speci ed and how noncore variables for the comparison regression can be chosen to ensure that robustness checks are indeed structurally informative we provide a straightforward new hausman 1978 type test of robustness for the critical core coe cients additional diagnostics that can help explain why robustness test rejection occurs and a new estimator the feasible optimally combined gls fogless estimator that makes relatively e cient use of the robustness check regressions a new procedure for matlab testrob embodies these methods

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

large sample properties of posterior densities bayesian information criterion and the likelihood principle in nonstationary time series models asymptotic normality of the posterior is a well understood result for dynamic as well as nondynamic models based on sets of abstract conditions whose actual applicability is hardly known especially for the case of nonstationarity in this paper we provide a set of conditions by which we can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity this result reinforces and generalizes the point of sims and uhlig 1991 that inference based on the likelihood principle explained by berger and wolpert 1988 will be unchanged regardless of whether the data are generated by a stationary process or by a unit root process on the other hand our conditions allow us to generalize the bayesian information criterion known as the schwarz criterion to the case of possible nonstationarity in addition we have shown that consistency of the maximum likelihood estimator not the asymptotic normality of the estimator with some minor additional assumptions is sufficient for asymptotic posterior normality

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

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

binary choice models with discrete regressors identification and misspecification this paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support i focus mainly on the models under the conditional median restriction as in manski 1985 i find sharp bounds on the components of the parameter of interest and outline several applications the formulas for bounds obtained using a recursive procedure help analyze cases where one regressor s support becomes increasingly dense furthermore i investigate asymptotic properties of estimators of the identification set i describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified

constrained nonlinear programming for volatility estimation with garch models this paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity garch volatility estimation models in financial econometrics these models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature whereas they actually fall into the domain of nonconvex nonlinear programming our results demonstrate that constrained nonlinear programming is a worthwhile exercise for garch models especially for the bivariate and trivariate cases as they offer a significant improvement in the quality of the solution of the optimization problem over the diagonal vech and the bekk representations of the multivariate garch model

affine cellular algebras abstract graham and lehrer have defined cellular algebras and developed a theory that allows in particular to classify simple representations of finite dimensional cellular algebras many classes of finite dimensional algebras including various hecke algebras and diagram algebras have been shown to be cellular and the theory due to graham and lehrer successfully has been applied to these algebras we will extend the framework of cellular algebras to algebras that need not be finite dimensional over a field affine hecke algebras of type a and infinite dimensional diagram algebras like the affine temperley lieb algebras are shown to be examples of our definition the isomorphism classes of simple representations of affine cellular algebras are shown to be parameterised by the complement of finitely many subvarieties in a finite disjoint union of affine varieties in this way representation theory of non commutative algebras is linked with commutative algebra moreover conditions on the cell chain are identified that force the algebra to have finite global cohomological dimension and its derived category to admit a stratification these conditions are shown to be satisfied for the affine hecke algebra of type a if the quantum parameter is not a root of the poincare polynomial

semiparametric estimation of monotone and concace utility functions for polychotomous choice models this paper introduces a semiparametric estimation method for polychotomous choice models the method does not require a parametric structure for the systematic subutility of observable exogenous variables the distribution of the random terms is assumed to be known up to a finite dimensional parameter vector in contrast previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified the systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory the estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent a computational technique to calculate the estimators is developed copyright 1991 by the econometric society

risk and rationality uncovering heterogeneity in probability distortion it has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types we present a parsimonious characterization of risk taking behavior by estimating a finite mixture model for three different experimental data sets two swiss and one chinese over a large number of real gains and losses we find two major types of individuals in all three data sets the choices of roughly 80 of the subjects exhibit significant deviations from linear probability weighting of varying strength consistent with prospect theory twenty percent of the subjects weight probabilities near linearly and behave essentially as expected value maximizers moreover individuals are cleanly assigned to one type with probabilities close to unity the reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling

nonlinearity in high frequency stock returns evidence from the athens stock exchange abstract this study investigates empirically the presence of nonlinearities in the athens composite share price index high frequency returns a preliminary analysis indicates that volatility exhibits a periodic intraday inverse j shaped pattern associated with the opening and closing of the market periodicity is then removed employing a flexible fourier form subsequently an arma figarch model over several frequencies yields that return volatility is long memory and self similar nonlinear analysis with the use of the embedding dimension suggests that the filtered return process does not exhibit deterministic or higher order stochastic nonlinearity rather it is reminiscent of a random process we conclude that the acspi data are nonlinear however nonlinearity is attributed to persistent arch effects

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

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

constistent specification testing via nonparametric series regression this paper proposes two consistent one sided specification tests for parametric regression models one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values the other based on the difference in sums of squared residuals between the parametric and nonparametric models we estimate the nonparametric model by series regression the new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate n 1 2 under misspecification while avoiding weighting sample splitting and non nested testing procedures used elsewhere in the literature asymptotically our tests can be viewed as a test of the joint hypothesis that the true parameters of a series regression model are zero where the dependent variable is the residual from the parametric model and the series terms are functions of the explanatory variables chosen so as to support nonparametric estimation of a conditional expectation we specifically consider fourier series and regression splines and present a monte carlo study of the finite sample performance of the new tests in comparison to consistent tests of bierens 1990 eubank and spiegelman 1990 jayasuriya 1990 wooldridge 1992 and yatchew 1992 the results show the new tests have good power performing quite well in some situations we suggest a joint bonferroni procedure that combines a new test with those of bierens and wooldridge to capture the best features of the three approaches

a nonparametric test of weak separability and consumer preferences abstract two stochastic nonparametric procedures are developed to evaluate the significance of violations of weak separability when the data have measurement error we show that the necessary and sufficient weak separability conditions of varian varian h 1983 nonparametric tests of consumer behavior review of economic studies 50 99 110 must also satisfy the afriat inequalities the tests detect weak separability with high probability for weakly separable data in addition the procedures correctly reject weak separability for both nonseparable and random utility simulated data sets the tests also fail to reject weak separability for a monetary and consumption data set which suggests that measurement error may be the source of the observed violations

estimating cross section common stochastic trends in nonstationary panel data this paper studies large dimension factor models with nonstationary dynamic factors also referred to as cross section common stochastic trends we consider the problem of estimating the dimension of the common stochastic trends and the stochastic trends themselves we derive the rates of convergence and the limiting distributions for the estimated common trends and for the estimated loading coefficients generalized dynamic factor models with nonstationary factors are also considered cointegration among the factors is permitted the method is applied to the study of employment fluctuations across 60 industries for the u s we examine the hypothesis that these fluctuations can be explained by a small number of aggregate factors we also test whether some observable macroeconomic variables are the underlying factors

affine cellularity of affine hecke algebras of rank two we show that affine hecke algebras of rank two with generic parameters are affine cellular in the sense of koenig xi

wave diffraction by a half plane with an obstacle perpendicular to the boundary abstract we prove the unique existence of solutions for different types of boundary value problems of wave diffraction by a half plane with a screen or a crack perpendicular to the boundary representations of the solutions are also obtained upon the consideration of some associated operators this is done in a bessel potential spaces framework and for complex non real wave numbers the investigation is mostly based on the construction of explicit operator relations the potential method and a factorization technique for a certain class of oscillating fourier symbols which naturally arise from the problems

estimation of some partially specified nonlinear models abstract this paper presents a procedure for analyzing a partially specified nonlinear regression model in which the nuisance parameter is an unrestricted function of a subset of regressors the procedure does not require parameteric modeling of the nuisance parameter but assumes that the model can be transformed into a partially specified linear equation by inverting some nonlinear functions the model parameters are estimated by applying robinson s 1988a procedure and the estimator is show to be n consistent and asymptotically normal one attraction of the estimator is that is to computationally simple requiring no more than least squares regressions a simulation study indicates that the estimator has practical values

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

application of statistical information criteria for optimal fuzzy model construction theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy however constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple a simpler model is not only easily understood but also less likely to overfit the training data even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed few principled approaches exist in the literature due to the lack of a well defined optimality criterion in this paper we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria 1 the akaike information criterion aic 1974 2 the bhansali downham information criterion bdic 1977 and 3 the information criterion of schwarz 1978 and rissanen 1978 sric we then describe a principled approach to explore the fitness complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition svd the role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example

stochastic specification and estimation of share equation systems abstract this paper discusses a theoretical justification for the stochastic specification of singular share equation systems commonly used in the analysis of producer and consumer behavior which is based on the use of a random objective function the restrictions on the share equations that are implied by this formulation are derived in addition it is shown that in this context additive error terms in share equation models generally can be expected to be heteroskedastic the issue of invariance of a minimum distance estimator to the equation dropped is also explored

low level interpretability and high level interpretability a unified view of data driven interpretable fuzzy system modelling this paper aims at providing an in depth overview of designing interpretable fuzzy inference models from data within a unified framework the objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real world systems whose first principle models are unknown because system behaviour can be described naturally as a series of linguistic rules data driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose however fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability model accuracy and interpretability are two conflicting objectives so interpretation preservation during adaptation in data driven fuzzy system modelling is a challenging task which has received much attention in fuzzy system modelling community in order to clearly discriminate the different roles of fuzzy sets input variables and other components in achieving an interpretable fuzzy model a taxonomy of fuzzy model interpretability is first proposed in terms of low level interpretability and high level interpretability in this paper the low level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level while the high level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage completeness and consistency of the rules in terms of the criteria on fuzzy rule level some criteria for low level interpretability and high level interpretability are identified respectively different data driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low level interpretability and high level interpretability furthermore some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested

the mixed harmonic problem in an exterior cracked domain with dirichlet condition on cracks the mixed dirichlet neumann problem for the laplace equation in an unboundedconnected plane domain with cuts cracks is studied the neumann condition is given on closed curves making up the boundary of the domain while the dirichlet condition is specified on the cuts the existence of a classical solution is proved by means of potential theory and the boundary integral equation method the integral representation for a solution is obtained in the form of potentials the density in potentials satisfies the uniquely solvable fredholm integral equation of the second kind and index zero singularities of the gradient of the solution at the tips of cuts are investigated

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

revisiting tests for neglected nonlinearity using artificial neural networks tests for regression neglected nonlinearity based on artificial neural networks anns have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold this implies that the asymptotic behavior of general ann based tests for neglected nonlinearity is still an open question here we analyze a convenient ann based quasi likelihood ratio statistic for testing neglected nonlinearity paying careful attention to both components of the null we derive the asymptotic null distribution under each component separately and analyze their interaction somewhat remarkably it turns out that the previously known asymptotic null distribution for the type 1 case still applies but under somewhat stronger conditions than previously recognized we present monte carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new stronger regularity conditions are violated

non linear regression with discrete explanatory variables with an application to the earnings function abstract in this paper it will be shown that regression models with discrete explanatory variables take the form of a polynominal of a linear function of the regressors a two stage estimation procedure and various model specification tests will be developed in close harmony with an empirical application to the earnings function

methods and criteria for model selection model selection is an important part of any statistical analysis and indeed is central to the pursuit of science in general many authors have examined the question of model selection from both frequentist and bayesian perspectives and many tools for selecting the best model have been suggested in the literature this paper considers the various proposals from a bayesian decision theoretic perspective

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