approach to equilibrium of particles diffusing on curved surfaces abstract we present a simple numerical analysis of the diffusion on a curved surface given by the equation r 0 in a finite domain d r 3 the first non vanishing eigenvalue of the beltrami laplace operator with the reflecting boundary conditions is determined in our simulations for the p d g s s1 and i wp nodal periodic surfaces where d is their respective cubic unit cell we observe that the first eigenvalue for the surfaces of simple topology p d g i wp is smaller than for the surfaces of complex topology s s1

systematic approach to bicontinuous cubic phases in ternary amphiphilic systems the fourier approach and theories of space groups and color symmetries are used to systematically generate and compare bicontinuous cubic structures in the framework of a ginzburg landau model for ternary amphiphilic systems both single and double structures are investigated they correspond to systems with one or two monolayers in a unit cell respectively we show how and why single structures can be made to approach triply periodic minimal surfaces very closely and give improved nodal approximations for g d i wp and p surfaces we demonstrate that the relative stability of the single structures can be calculated from the geometrical properties of their interfaces only the single gyroid g turns out to be the most stable bicontinuous cubic phase since it has the smallest porosity the representations are used to calculate distributions of the gaussian curvature and 2 h nuclear magnetic resonance band shapes for c p c d s c y and f rd surfaces s1063 651x 99 01005 3

testing nonnested euler conditions with quadrature based methods of approximation abstract singleton 1985 proposed a test of the validity of an euler equation specification which incorporates information on a nonnested set of euler equations from an alternative economic model the information about the alternative model is introduced into the testing framework by constructing a sequence of local alternatives to the euler equations of the maintained model which are in the direction of the euler equations of the alternative model singleton s test is easy to apply but is designed to have power against an alternative that in many cases does not have a straightforward economic interpretation in this paper we reexamine the construction of local alternatives to euler equations we compare singleton s approach with a method based on perturbing the data generation process dgp of the maintained model in the direction of the dgp of the alternative model the second approach leads to tests which are always of interest but require the complete specification of the dgp in this paper we derive a test for discriminating between two nonnested sets of euler conditions which have been estimated us ing generalized method of moments gmm the test is based on the encompassing principle of cox 1961 and mizon and richard 1986 and uses tauchen s 1986 quadrature based nethods for approximating the expectation of nonlinear functions of stationary random variables singleton s empirical examples are also reconsidered

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

a variational level set approach for surface area minimization of triply periodic surfaces in this paper we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions phases that the surface separates using a variational level set method formulation we present a theoretical characterization of and a numerical algorithm for computing these surfaces we use our theoretical and computational formulation to study the optimality of the schwartz primitive p schwartz diamond d and schoen gyroid g surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases are not equal due to the computational cost of the fully three dimensional shape optimization problem we implement our numerical simulations using a parallel level set method software package

heteroscedastic nonlinear regression several parameter estimation methods for dealing with heteroscedasticity in nonlinear regression are described these include variations on ordinary weighted iteratively reweighted extended and generalized least squares some of these variations are new and one of them in particular modified extended iteratively reweighted least squares meirls allows parameters of an assumed heteroscedastic variance model to be estimated with an adjustment for bias due to estimation of the regression parameters the context of the discussion is primarily that of pharmacokinetic type data although an example is given involving chemical reaction data using simulated data from 21 heteroscedastic pharmacokinetic type models some of the methods are compared in terms of mean absolute error and 95 confidence interval coverage from these comparisons meirls and the variations on generalized least squares emerge as the methods of choice

identification in a generalization of bivariate probit models with dummy endogenous regressors abstract this paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables the joint distribution of the latent error terms is specified through a parametric copula structure that satisfies a particular dependence ordering while the marginal distributions are allowed to be arbitrary but known this class of models is broad and includes bivariate probit models as a special case the paper demonstrates that having an exclusion restriction is necessary and sufficient for global identification in a model without common exogenous covariates where the excluded variable is allowed to be binary having an exclusion restriction is sufficient in models with common exogenous covariates that are present in both equations the paper then extends the identification analyses to a model where the marginal distributions of the error terms are unknown

bayesian inference in a sample selection model this paper develops methods of bayesian inference in a sample selection model the main feature of this model is that the outcome variable is only partially observed we first present a gibbs sampling algorithm for a model in which the selection and outcome errors are normally distributed the algorithm is then extended to analyze models that are characterized by nonnormality specifically we use a dirichlet process prior and model the distribution of the unobservables as a mixture of normal distributions with a random number of components the posterior distribution in this model can simultaneously detect the presence of selection effects and departures from normality our methods are illustrated using some simulated data and an abstract from the rand health insurance experiment

morphological changes during the order disorder transition in the two and three dimensional systems of scalar nonconserved order parameters the order disorder transition is studied in a system of a scalar nonconserved order parameter we use this well studied system to show that the application of the methods of topology and geometry reveals that our knowledge of the kinetic pathways by which the order disorder transition proceeds is far from being complete we show that in two dimensional 2d and 3d systems there are three dynamical regimes in the evolution of the system early intermediate and late in the intermediate regime two length scales govern the behavior of the system whereas in the early and intermediate regime there is only one length scale the size distribution of the domain area indicates the pathway by which the domains change their size there are only two types of domains in a 2d system circular and elongated with well defined characteristics scaling of the area with the contour length which in the late regime do not depend on time after rescaling by the average area and contour in the system the elongated domains continuously change into circular domains reducing in this way the overall dissipation in the system in order to reach a lifshitz cahn allen lca late stage regime the number of elongated domains must be strongly reduced in the intermediate regime the number of elongated domains is large and simple lca scaling does not hold in a 3d symmetric system we always have a bicontinuous structure that evolves by cutting small connections the late stage regime seems to be associated with the appearance of the preferred nonzero mean curvature the early intermediate regime crossover is associated with the saturation of the order parameter inside the domains while the intermediate late stage regime crossover is related to the global breaking of the order parameter symmetry marked by the appearance of the nonzero mean curvature but still zero average magnetization the times for the occurrence of these crossovers do not depend on the size of the system

a maximum likelihood estimation method for random coefficient regression models summary a method for estimating the distribution of the parameters of a random coefficient regression model is proposed this distribution accounting for interindividual variability is assumed to lie in a wide class of probability distributions rather than in a given parametric class estimation is based on observations from a sample of individuals and likelihood is the estimation criterion experimental designs may be different among individuals allowing the method to apply to routinely collected data the problem has strong connections with the theory of optimum design of experiments conditions are given under which the problem has a unique solution which then corresponds to a discrete distribution a simple pharmacokinetic model involving two parameters is used as an example these parameters have a bimodal distribution as statistical specification moreover only one observation is available per individual thus the method applies even when the model is not identifiable

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

semiparametric maximum likelihood for measurement error model regression this paper presents an em algorithm for semiparametric likelihood analysis of linear generalized linear and nonlinear regression models with measurement errors in explanatory variables a structural model is used in which probability distributions are specified for a the response and b the measurement error a distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood for various types of extra information about the measurement error distribution the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of a and b if the true x were available simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption the approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution

triply periodic minimal surface using a modified allencahn equation we present a fast and efficient model for triply periodic minimal surface by using a modified allencahn equation the proposed numerical method with second order accuracy of time and space exhibits excellent stability various numerical experiments are performed to show the accuracy and robustness of the proposed method in this paper we propose a fast and efficient model for triply periodic minimal surface the proposed model is based on the allencahn equation with a lagrange multiplier term the allencahn equation has the motion of mean curvature and the lagrange multiplier term corresponding to the constant volume constraint also relates to the average of mean curvature by combining two terms the mean curvature will be constant everywhere on the surface at the equilibrium condition the proposed numerical method with the second order accuracy of time and space exhibits excellent stability in addition the resulting discrete system is solved by a fast numerical method such as a multigrid method various numerical experiments are performed to demonstrate the accuracy and robustness of the proposed method

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

inference in nonparametric instrumental variables with partial identification this paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework we construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction the same test statistic can be employed under identification in which case the hypothesis is whether the true model satisfies the posited property an almost sure consistent bootstrap procedure is provided for obtaining critical values possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set as an illustration we obtain confidence intervals for the level and slope of brazilian fuel engel curves a monte carlo study examines finite sample performance

estimating stochastic differential equations efficiently by minimum chi squared summary we propose a minimum chi squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state we prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi squared criterion increases and as the number of past observations entering each moment function increases the minimised criterion is asymptotically chi squared and can be used to test system adequacy when a fitted system is rejected inspecting studentised moments suggests how the fitted system might be modified to improve the fit the method and diagnostic tests are applied to daily observations on the u s dollar to deutschmark exchange rate from 1977 to 1992

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

era s a new approach to small sample theory this article proposes a new approach to small sample theory that achieves a meaningful integration of earlier directions of research in this field the approach centers on the constructive technique of approximating distributions developed recently by the author in 10 this technique utilizes extended rational approximants era s which build on the strengths of alternative less flexible approximation methods such as those based on asymptotic expansions and which simultaneously blend information from diverse analytic numerical and experimental sources the first part of the article explores the general theory of approximation of continuous probability distributions by means of era s existence characterization error bound and uniqueness theorems for these approximants are given and a new proof is provided for the convergence result obtained earlier in 10 some further aspects of finding era s by modifications to multiple point pade approximants are presented and the new approach is applied to the noncircular serial correlation coefficient the results of this application demonstrate how era s provide systematic improvements over edgeworth and saddlepoint techniques these results taken with those of the earlier article 10 suggest that the approach offers considerable potential for empirical application in terms of its reliability convenience and generality

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

nonparametric errors in variables models with measurement errors on both sides of the equation abstract measurement errors are often correlated as in surveys where respondent s biases or tendencies to err affect multiple reported variables we extend schennach 2007 to identify moments of the conditional distribution of a true y given a true x when both are measured with error the measurement errors in y and x are correlated and the true unknown model of y given x has nonseparable model errors after showing nonparametric identification we provide a sieve generalized method of moments based estimator of the model and apply it to nonparametric engel curve estimation in our application measurement errors on the expenditures of a good y are by construction correlated with measurement errors in total expenditures x this problem which is present in many consumption data sets has been ignored in most demand applications we find that accounting for this problem casts doubt on hildenbrand s 1994 increasing dispersion assumption