testing the restrictions implied by the rational expectations hypothesis abstract the nature and form of the restrictions implied by the rational expectations hypothesis are examined in a variety of models with expectations and the properties of appropriate test statistics are analyzed with monte carlo evidence specifically we consider the implications of lagged variables simultaneous equations and future period expectations upon the number and functional form of the rational expectations restrictions two asymptotically equivalent test statistics a likelihood ratio and a wald test are available for implementing a test of these restrictions monte carlo evidence is offered to provide a comparison between the properties of the alternative test statistics in small samples

global optimization and simulated annealing in this paper we are concerned with global optimization which can be defined as the problem of finding points on a bounded subset of n in which some real valued functionf assumes its optimal maximal or minimal value we present a stochastic approach which is based on the simulated annealing algorithm the approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems the mathematical formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima furthermore we discuss an implementation of the algorithm and compare its performance with other well known algorithms the performance evaluation is carried out for a standard set of test functions from the literature

transformations to reduce boundary bias in kernel density estimation we consider kernel estimation of a univariate density whose support is a compact interval if the density is non zero at either boundary then the usual kernel estimator can be seriously biased reflection at a boundary removes some bias but unless the first derivative of the density is 0 at the boundary the estimator with reflection can still be much more severely biased at the boundary than in the interior we propose to transform the data to a density that has its first derivative equal to 0 at both boundaries the density of the transformed data is estimated and an estimate of the density of the original data is obtained by a change of variables the transformation is selected from a parametric family which is allowed to be quite general in our theoretical study we propose algorithms where the transformation is either a quartic polynomial a b cumulative density function cdf or a linear combination of a polynomial and a b cdf the last two types of transformation are designed to accommodate possible poles at the boundaries the first two algorithms are tested on simulated data and compared with an adjusted kernel method of rice we find that our proposal performs similarly to rice s for densities with one sided derivatives at the boundaries unlike rice s method our proposal is guaranteed to produce non negative estimates this can be a distinct advantage when the density is 0 at either boundary our algorithm for densities with poles outperforms the rice adjustment when the density has a pole at a boundary

jump tails extreme dependencies and the distribution of stock returns we provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices our estimates are based on in fill asymptotics for directly identifying the jumps together with extreme value theory evt approximations and methods of moments for assessing the tail decay parameters and tail dependencies on implementing the procedures with a panel of intraday prices for a large cross section of individual stocks and the s p 500 market portfolio we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy tailed and close to symmetric and show how the jump tail dependencies deduced from the high frequency data together with the day to day variation in the diffusive volatility account for the extreme joint dependencies observed at the daily level

identification information and instruments in linear econometric models with rational expectations abstract this paper establishes a convenient set of criteria for the identification of linear simultaneous econometric models with rational expectations we consider the model with one period ahead expectations conditional upon current exogenous or predetermined variables or their forecasts if current values are unavailable a collection of instrument counting rules are developed which turn out to be identical with those for the standard textbook model provided that we treat the expectational variables in the light of endogenous variates this suggests that rationally formed expectational variables are best treated as a second set of endogenous variables a general inverse relationship holds between information and identification the less agents know about current values of exogenous variables the greater are the possibilities for statistical identification of the system describing their behavior

fixed k asymptotic inference about tail properties we consider inference about tail properties of a distribution from an iid sample based on extreme value theory all of the numerous previous suggestions rely on asymptotics where eventually an in

large factorial designs for product engineering and marketing research applications we propose an algorithm that incorporates both combinatorial and heuristic optimization methods for generating d efficient factorial designs this includes an approach that can automatically construct more than 115 000 orthogonal arrays including at least one array for every known specification with fewer than 144 runs the algorithm tries various initialization and iteration methods chooses the most promising method and then applies more computational effort with the chosen method the algorithm can make orthogonal and nearly orthogonal arrays and it can accommodate restrictions interactions and large designs usage requires minimal expertise and input applications in the area of optimal product design choice modeling and marketing research are discussed

probabilistic measures of adequacy of a numerical search for a global maximum abstract measures of the probability of all unobserved species are applied to the problem of assessing the adequacy of a search for a global maximum using random starting points the measures as used here estimate the probability that an iterative algorithm using a randomly selected starting point will find a solution not observed in previous random starting points the probability of an unobserved global maximum is less than or equal to this probability we used these measures to evaluate the adequacy of our search procedure for the maximum likelihood estimates of the parameters of a mixture of two normals these measures indicated that for most problems generated there was little chance that there were unobserved domains of convergence occasional problems however had appreciable estimated probabilities in such problems examination of the data suggested regions where a more focused search for unobserved domains of convergence was warranted

immune based algorithms for dynamic optimization the main problem with biologically inspired algorithms like evolutionary algorithms or particle swarm optimization when applied to dynamic optimization is to force their readiness for continuous search for new optima occurring in changing locations immune based algorithm being an instance of an algorithm that adapt by innovation seem to be a perfect candidate for continuous exploration of a search space in this paper we describe various implementations of the immune principles and we compare these instantiations on complex environments

on the membrane locking of h p finite elements in a cylindrical shell problem we study the performance of high order h p finite clement schemes in approximating the nearly inexlensional deformation state of a thin cylindrical shell roof with both ends free severe locking is demonstrated for both quadratic and cubic elements and even for higher order if the grid is not aligned with the axis of the cylinder carefully designed selective reduced integration is shown to improve the accuracy of the finite element approximation at low and moderately high orders however so far this technique seems to work well only on aligned grids

estimating the extremal index summary the extremal index is an important parameter measuring the degree of clustering of process the extremal index a parameter in the interval 0 1 is the reciprocal of the mean cluster size apart from being of interest in its own right it is a crucial parameter for determining the limiting distribution of extreme values from the process in this paper we review current work on statistical estimation of the extremal index and consider an optimality criterion based on a bias variance trade off theoretical results are developed for a simple doubly stochastic process and it is argued that the main formula obtained is valid for a much wider class of processes the practical implications are examined through simulations and a real data example

estimation of extreme depth based quantile regions consider the extreme quantile region induced by the halfspace depth function hd of the form q fx 2 rd hd x p g such that pq p for a given very small p 0 this region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the convex hull of the data using extreme value theory we construct a natural semiparametric estimator of this quantile region and prove a refined consistency result a simulation study clearly demonstrates the good performance of our estimator we use the procedure for risk management by applying it to stock market returns

formulating wald tests of nonlinear restrictions on montre a partir de l evidence de monte carlo que les differences dans la forme fonctionnelle des restrictions non lineaires sont importantes dans les petites tailles d echantillons

extreme matrices or how an exponential map links classical and free extreme laws using our proposed approach to describe extreme matrices we find an explicit exponentiation formula linking the classical extreme laws of frechet gumbel and weibull given by the fisher tippet gnedenko classification and free extreme laws of free frechet free gumbel and free weibull of ben arous and voiculescu we also develop an extreme random matrix formalism in which refined questions about extreme matrices can be answered in particular we demonstrate explicit calculations for several more or less known random matrix ensembles providing examples of all three free extreme laws finally we present an exact mapping showing the equivalence of free extreme laws to the peak over threshold method in classical probability

a test for global maximum abstract we give simple necessary and sufficient conditions for consistency and asymptotic optimality of a root to the likelihood equation based on the results a large sample test is proposed for detecting whether a given root is consistent and asymptotically efficient a property often possessed by the global maximizer of the likelihood function a number of examples and the connection between the proposed test and the test of white for model misspecification are discussed monte carlo studies show that the test performs quite well when the sample size is large but may suffer the problem of overrejection with relatively small samples

generalized simulated annealing for function optimization a generalized simulated annealing method has been developed and applied to the optimization of functions possibly constrained having many local extrema the method is illustrated in some difftcult pedagogical examples and used to solve a problem analyzed by bates technometrics 25 pp 373 376 1983 for which we identify an improved optimum the sensitivity of the solution to changes in the constraints and in other specifications of the problem is analyzed and discussed

interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters this paper presents interactive decision making methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters on the basis of the level sets of the fuzzy numbers the concept of multiobjective programming and local m pareto optimality is introduced through the interaction with the decision maker dm the fuzzy goals of the dm for each of the objective functions in multiobjective programming are quantified by eliciting the corresponding membership functions after determining the membership functions in order to generate a candidate for the local satisficing solution which is also local m pareto optimal if the dm specifies the degree of the level sets and the reference membership values the augmented minimax problem is solved and the dm is supplied with the corresponding local m pareto optimal solution together with the trade off rates among the values of the membership functions and the degree then by considering the current values of the membership functions and as well as the trade off rates the dm responds by updating his her reference membership values and or the degree in this way the local satisficing solution for the dm can be derived efficiently from among an m pareto optimal solution set based on the proposed methods for multiobjective linear linear fractional and nonlinear programming problems with fuzzy parameters interactive computer programs are developed and an illustrative numerical example for nonlinear case is demonstrated

mixed interpolated elements for reissner mindlin plates dcpartement de mathtmatiyue l nit ersitt 1 aral quthec canado summary we present in this paper a procedure to establish reissner mindlin plate bending elements the procedure is based on the idea to combine known resuits on the approximation of stokes problems with known results on the approximation of elliptic problems the proposed elements satisfy the mathematical conditions of stability and convergence and some of them promise to provide efficient elements for practical solutions

inverse methods and data assimilation in nonlinear ocean models abstract an overview is given of the current status of inverse methods and data assimilation for nonlinear ocean models the inverse theory for time dependent dynamical models is formulated and the most promising solution methods like simulated annealing the representer method and sequential methods based on monte carlo simulations are discussed with special focus on applications with nonlinear dynamics a rather general model independent presentation has been used to make the methodology more accessible for different scientific areas dealing with dynamical models and data

minimax risk bounds in extreme value theory asymptotic minimax risk bounds for estimators of a positive extreme value index under zero one loss are investigated in the classical i i d setup to this end we prove the weak convergence of suitable local experiments with pareto distributions as center of localization to a white noise model which was previously studied in the context of nonparametric local density estimation and regression from this result we derive upper and lower bounds on the asymptotic minimax risk in the local and in certain global models as well finally the implications for fixed length confidence intervals are discussed in particular asymptotic confidence intervals with almost minimal length are constructed while the popular hill estimator is shown to yield a little longer confidence intervals

optimization of non linear gravity models through generalized simulated annealing abstract in this paper we apply the generalized simulated annealing gsa approach to the inversion of gravity data for 2 d and 3 d density distributions we consider a modeling process where the input is the vector of model parameters m that can be density contrast mass or some coordinates and the output is described by the transformation h m d where d is the vector of data parameters we generally have access in practical problems if the vector d describes the observed actual output of the system the problem is to choose or estimate the parameters m est in order to minimize in some sense in our case in the least squares sense the difference between the observed vector d and the prescribed output of the system h m est the tests with synthetic data show the promising application of gsa in gravity inversion the results obtained suggest us that the gsa approach enables to find quickest optimization machines than the two conventional approaches boltzmann and cauchy machines

integer valued minimax robust designs for estimation and extrapolation in heteroscedastic approximately linear models abstract we present our findings on a new approach to robust regression design this approach differs from previous investigations into this area in three respects the use of a finite design space the use of simulated annealing to carry out the numerical minimization problems and in our search for integer valued rather than continuous designs we present designs for the situation in which the response is thought to be approximately polynomial we also discuss the cases of approximate first and second order multiple regression in each case we allow for possible heteroscedasticity and also obtain minimax regression weights the results are extended to cover extrapolation of the regression response to regions outside of the design space a case study involving dose response experimentation is undertaken the optimal robust designs which protect against bias as well as variance can be roughly described as being obtained from the classical variance minimizing designs by replacing replicates with clust

selection of the k largest order statistics for the domain of attraction of the gumbel distribution abstract statistical modeling of the largest k observations or the exceedances over a high threshold based on extreme value theory has produced powerful methods for drawing inferences about the tail behavior of a distribution however a method for selecting k has not been established we suggest using a forward selection procedure based on a suitable goodness of fit statistic to search for the optimal k when the sample is of finite size and from a distribution in the domain of attraction of the gumbel distribution two criteria are examined generalized least squares and the shapiro wilk goodness of fit simulation studies indicate that the latter is preferable in terms of variation extension of the selection procedure to distributions in the domains of attraction of the frechet and weibull distributions is also discussed the use of the proposed method is illustrated through two examples based on real data

numerical methods for estimating parameters in nonlinear models with errors in the variables a numerically stable implementation of the gauss newton method for computing least squares estimates of parameters and variables in explicit nonlinear models with errors in the variables is proposed the algorithm uses only orthogonal transformations and exploits the special structure of the problem moreover a partially regularized marquardt like version is described that works with a reasonable overhead of arithmetic operations and storage compared to the error free case

testing the assumptions behind importance sampling importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals its reliable use requires the sampler to possess a variance for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral however this assumption is seldom checked in this paper we use extreme value theory to empirically assess the appropriateness of this assumption our main application is the stochastic volatility model where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model

stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints the aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent in addition the related dual problems for which the set of feasible parameters and the solvability set are studied these fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers the existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of a pareto optimality an illustrative example is given to clarify the obtained results

a common tabu search algorithm for the global optimization of engineering problems abstract a novel common tabu algorithm for global optimizations of engineering problems is presented the robustness and efficiency of the presented method are evaluated by using standard mathematical functions and by solving a practical engineering problem the numerical results show that the proposed method is i superior to the conventional tabu search algorithm in robustness and ii superior to the simulated annealing algorithm in efficiency

estimation of the minimum of a function using order statistics abstract suppose a is a bounded set in d and f a real function defined on a suppose m min f x x a exists using a random sample x 1 x 2 x n from a uniform distribution over a we construct a confidence interval for m using asymptotic theory our results contain some statistical results valid in general extreme value theory estimation of the main parameter of extreme value distributions

decomposition of the fuzzy parametric space in multiobjective nonlinear programming problems this paper deals with a method for decomposing the fuzzy parametric space in multiobjective nonlinear programming problems using the generalized tchebycheff norm this approach is simpler than the corresponding one using the nonnegative weighted sum of objectives also several results are introduced which relate two fuzzy programs with each other one with fuzzy parameters in the constraints and the other with fuzzy parameters in both objective functions and constraints these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the decomposition of parametric space in multiobjective convex programs using the generalized tchebycheff norm are reformulated to study under the concept of pareto optimality such results make the study of the first type of problems rather simple three illustrated examples are presented in the paper which clarify the developed theory

on tail categorization of probability laws abstract a classification scheme for probability laws by tail behavior is proposed it circumvents the smoothness conditions usually imposed on the probability laws by current classification schemes and yields a complete characterization of the probability distributions belonging to each category that is a distribution function f has a long medium or short tail depending on whether f ln x is slowly varying regularly varying or rapidly varying a clear and concise connection with the limiting behavior of extreme spacings is also established and the connection with the existence of moments and moment generating functions is noted closure properties of the classification scheme under reliability operations are also considered

a test for extreme value domain of attraction abstract a simple statistic is proposed to test the hypothesis that a sample comes from a distribution in the domain of attraction of the gumbel distribution it is based on the top k order statistics and is a generalization of the shapiro wilk goodness of fit statistic the critical region of the test and its power against the alternative that the sample comes from a distribution in another domain of attraction are studied theoretically and by simulation the power turns out to be superior to that of other tests previously proposed

on some basic notions of fuzzy parametric nonsmooth multiobjective nonlinear fractional programming problems different basic notions like the solvability set the stability set of the first and of the second kind for the smooth fuzzy parametric multiobjective nlp programs have been discussed in several papers in this paper these notions have been defined and qualitatively analyzed for a general class of nonsmooth multiobjective nonlinear fractional programming problems with fuzzy parameters under the concept of pareto optimality the stability sets of the third and of the fourth kinds have also been defined and analyzed for this problem a determination of the stability sets of the third and of the fourth kinds will be given

single and multiobjective structural optimization in discrete continuous variables using simulated annealing a multivariable optimization technique based on the monte carlo method used in statistical mechanics studies of condensed systems is adapted for solving single and multiobjective structural optimization problems this procedure known as simulated annealing draws an analogy between energy minimization in physical systems and objective function minimization in structural systems the search for a minimum is simulated by a relaxation of the statistical mechanical system where a probabilistic acceptance criterion is used to accept or reject candidate designs to model the multiple objective functions in the problem formulation a cooperative game theoretic approach is used numerical results obtained using three different annealing strategies for the single and multiobjective design of structures with discrete continuous variables are presented the influence of cooling schedule parameters on the optimum solutions obtained is discussed simulation results indicate that in several instances the optimum solutions obtained using simulated annealing outperform the optimum solutions obtained using some gradient based and discrete optimization techniques the results also indicate that simulated annealing has substantial potential for additional applications in optimization especially for problems with mixed discrete continuous variables

the derivative of x x and its uses the determinant of matrices of the form x x is used as the d optimal design criterion for parameter estimation in nonlinear regression and as the estimation criterion for multiresponse parameter estimation it is helpful to be able to calculate the gradient of this determinant so that sophisticated optimization methods can be used a method is given to efficiently compute the determinant using modern computational linear algebra and at the same time to provide the necessary information to compute the gradient the method is extended to cases in which a part of the x matrix is fixed examples from multiresponse parameter estimation and from experimental design are given

experiments in projection and clustering by simulated annealing simulated annealing is a stochastic relaxation algorithm which has been used successfully to optimize functions of many variables this paper analyzes the simulated annealing algorithm when applied to the minimization of functions from two common problems encountered in exploratory pattern analysis projection and clustering the projection is a nonlinear mapping of patterns in high dimension to two dimensions the simulated annealing mapping is compared to gradient descent minimization of the same objective function as well as eigenvector projection the simulated annealing clustering is compared to a k means algorithm empirical results show that simulated annealing can produce results as good as those obtained by conventional methods but are impractical for small data sets because of the high computational cost simulated annealing does in the case of the mapping problem yield a better optimization and better retained structure for large data sets containing tight gaussian clusters

on tests for global maximum of the log likelihood function given the location of a relative maximum of the log likelihood function how to assess whether it is the global maximum this paper investigates an existing statistical tool which based on asymptotic analysis answers this question by posing it as a hypothesis testing problem a general framework for constructing tests for global maximum is given the characteristics of the tests are investigated for two cases correctly specified model and model mismatch a finite sample approximation to the power is given which gives a tool for performance prediction and a measure for comparison between tests the sensitivity of the tests to model mismatch is analyzed in terms of the renyi divergence and the kullback leibler divergence between the true underlying distribution and the assumed parametric class and tests that are insensitive to small deviations from the model are derived thereby overcoming a fundamental weakness of existing tests the tests are illustrated for three applications passive localization or direction finding using an array of sensors estimating the parameters of a gaussian mixture model and estimation of superimposed exponentials in noise problems that are known to suffer from local maxima

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

bayesian likelihood methods for estimating the end point of a distribution summary we consider maximum likelihood methods for estimating the end point of a distribution the likelihood function is modified by a prior distribution that is imposed on the location parameter the prior is explicit and meaningful and has a general form that adapts itself to different settings results on convergence rates and limiting distributions are given in particular it is shown that the limiting distribution is non normal in non regular cases parametric bootstrap techniques are suggested for quantifying the accuracy of the estimator we illustrate performance by applying the method to multiparameter weibull and gamma distributions

on testing the extreme value index via the pot method n alternatives based on the point processes n of the exceedances among y n i over a sequence of thresholds t it turns out that the random number of n exceedances t n over t is the central sequence for the log likelihood n ratio d l n rd l n yielding its local asymptotic normality lan b n b n n 0 this result implies in particular that t n carries asymptotically all the information about the underlying parameter b which is contained in n n we establish sharp bounds for the rate at which t n becomes asymptoti cally sufficient which show however that this is quite a poor rate these results remain true if we add an unknown scale parameter 1 n a model assumption on the upper tail of the underlying d f such as m is for example indispensable if one is interested in extreme quantities of the underlying d f that is such quantities of f which are usually outside the range of the given data y y a typical example is inference about 1 n y1 4 extreme quantiles f p inf t g r f t g p with p being close to 1 this problem is typically tackled by hydrologists for the prediction of large w

spline approximation of thin shell dynamics abstract a spline based method for approximating thin shell dynamics is presented here while the method is developed in the context of the donnell mushtari thin shell equations it can be easily extended to the byrne flugge lur ye equations or other models for shells of revolution as warranted by applications the primary requirements for the method include accuracy flexibility and efficiency in smart material applications to accomplish this the method was designed to be flexible with regard to boundary conditions material nonhomogeneities due to sensors and actuators and inputs from smart material actuators such as piezoceramic patches the accuracy of the method was also of primary concern both to guarantee full resolution of structural dynamics and to facilitate the development of pde based controllers which ultimately require real time implementation several numerical examples provide initial evidence demonstrating the efficacy of the method

on some estimates based on sample behavior near high level excursions let j be a stationary sequence of weakly dependent random variables and letm n k be thek th largest value of j 1 j n the estimation of the parameters of the asymptotic distribution ofm n k is considered using a procedure motivated by a limit theorem pertaining to the point process sum nolimits j delta j n n bar f xi j a number of statistical issues concerning the procedure including how to select the tuning parameters are addressed the second problem that we consider is the estimation of the filter of a moving average process with heavy tails in particular the investigation covers the moving average stable process motivated by ideas in rootzen 1978 our estimator uses information contained in the sample behavior of the process near the largest excursion

optimal rates of convergence for estimates of the extreme value index hall and welsh established the best attainable rate of convergence for estimates of a positive extreme value index y under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution as a first generalization we obtain a surprisingly sharp bound on the estimation error if y is still assumed to be positive but the rate of convergence of the maximum may be nonalgebraic this result allows a more accurate evaluation of the asymptotic performance of an estimator for y than the hall and welsh theorem for example it is proved that the hill and the pickands estimators achieve the optimal rate but only the hill estimator attains the sharp bound finally an analogous result is derived for a general not necessarily positive extreme value index in this situation it turns out that location invariant estimators show the best performance 1 introduction consider n i i d random variables r v s whose distribution function d f f belongs to the weak domain of attraction of an extreme value d f

free extreme values free probability analogues of the basics of extreme value theory are obtained based on ando s spectral order this includes clas sification of freely max stable laws and their domains of attraction using free extremal convolutions on the distributions these laws coincide with the limit laws in the classical peaks over threshold approach a free extremal projection valued process over a measure space is constructed which is related to the free poisson point process

identification of rational expectations models abstract this paper deals with the problem of the identification of simultaneous rational expectations re models in the case of re models with current expectations of the endogenous variables the necessary and sufficient conditions for the global identification are derived explicitly in terms of the structural parameters and the linear homogenous identifying restrictions it is shown that in the absence of a priori restrictions on the processes generating the exogenous variables and the disturbances re models and general distributed lag models are observationally equivalent in the case of re models with future expectations of the endogenous variables a general solution that highlights the non uniqueness problem and from which other solutions such as forward or backward solutions can be obtained is derived it is shown that untestable and often quite arbitrary restrictions are needed if re models with future expectations are to be identifiable certain order conditions similar to those obtained for the identification of re models with current expectations are also derived for this case

locking effects in the finite element approximation of elasticity problems we consider the finite element approximation of the 2d elasticity problem when the poisson ratiov is close to 0 5 it is well known that the performance of certain commonly used finite elements deteriorates asv 0 a phenomenon calledlocking we analyze this phenomenon and characterize the strength of the locking androbustness of varioush version schemes using triangular and rectangular elements we prove that thep andh p versions are free of locking with respect to the error in the energy norm a generalization of our theory to the 3d problem is also discussed

kernel type estimators for the extreme value index a large part of the theory of extreme value index estimation is developed for positive extreme value indices the best known estimator of a positive extreme value index is probably the hill estimator this estimator belongs to the category of moment estimators but can also be interpreted as a quasi maximum likelihood estimator it has been generalized to a kernel type estimator but this kernel type estimator can similarly to the hill estimator only be used for the estimation of positive extreme value indices in the present paper we introduce kernel type estimators which can be used for estimating the extreme value index over the whole positive and negative range we present a number of results on their distributional behavior and compare their performance with the performance of other estimators such as moment type estimators for the whole range and the quasi maximum likelihood estimator based on the generalized pareto distribution we also discuss an automatic bandwidth selection method and introduce a kernel estimator for a second order parameter controlling the speed of convergence

on some simple estimates of an exponent of regular variation summary we present a class of simple estimates of an exponent of regular variation unlike those proposed recently by de haan and resnick 1980 ours converge at an algebraic rather than a logarithmic rate and unlike those considered by teugels 1980 their form does not depend on the unknown exponent

reduced order model feedback control design numerical implementation in a thin shell model reduced order models employing the lagrange and popular proper orthogonal decomposition pod reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested the system under consideration is a thin cylindrical shell with surface mounted piezoceramic actuators donnell mushtari equations modified to include kelvin voigt damping are used to model the system dynamics basis functions constructed from fourier polynomials tensored with cubic splines are employed in the galerkin expansion of the full order model reduced basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances numerical examples illustrating the features of the reduced basis methods are presented as a first step toward investigating the behavior of the methods when implemented in physical systems the use of reduced order model feedback control gains in the full order model is considered and numerical examples are presented

some guidelines for constructing exact d optimal designs on convex design spaces some problems unique to the construction of n point d optimal designs on convex design spaces are considered multiple point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single point procedures moreover some recommendations for improving single point methods are given finally empirical evidence is found that supports the galil and kiefer option for constructing initial designs and powell s optimization method for design augmentation

global optimization of statistical functions with simulated annealing abstract many statistical methods rely on numerical optimization to estimate a model s parameters unfortunately conventional algorithms sometimes fail even when they do converge there is no assurance that they have found the global rather than a local optimum we test a new optimization algorithm simulated annealing on four econometric problems and compare it to three common conventional algorithms not only can simulated annealing find the global optimum it is also less likely to fail on difficult functions because it is a very robust algorithm the promise of simulated annealing is demonstrated on the four econometric problems

estimation of quantiles of the maximum of n observations summary given independent and identically distributed random variables from an unknown distribution f we want to estimate quantiles of fn using asymptotic extreme value theory two parametric approximations to fn are considered ahd approximate maximum likelihood estimates are obtained conditions for consistency and asymptotic normality of these estimates are given and properties of the estimates are obtained through a small simulation study

stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints abstract the purpose of the paper is to investigate the stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints these fuzzy parameters are characterized by fuzzy numbers for such problems concept and notion of the stability set of the first kind in parametric nonlinear programming problems are redefined and analyzed qualitatively under the concept of pareto optimality an algorithm for the determination of any subset of the parametric space which has the same corresponding pareto optimal solution is proposed a numerical example is given to illustrate the method developed in the paper

stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraints this paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraint functions these fuzzy parameters are characterized by fuzzy numbers qualitative and quantitative analysis of the basic notions like the set of feasible parameters the solvability set the stability sets of the first kind and of the second kind will be reformulated under the concept of pareto optimality an illustrative example is given to clarify the obtained results

tabu search method with random moves for globally optimal design optimum engineering design problems are usually formulated as non convex optimization problems of continuous variables because of the absence of convexity structure they can have multiple minima and global optimization becomes difficult traditional methods of optimization such as penalty methods can often be trapped at a local optimum the tabu search method with random moves to solve approximately these problems is introduced its reliability and efficiency are examined with the help of standard test functions by the analysis of the implementations it is seen that this method is easy to use and no derivative information is necessary it outperforms the random search method and composite genetic algorithm in particular it is applied to minimum weight design examples of a three bar truss coil springs a z section and a channel section for the channel section the optimal design using the tabu search method with random moves saved 26 14 per cent over the weight of the sumt method

optimal design in nonlinear multiresponse estimation poisson model for filter feeding summary d optimality criteria have been applied to construct locally optimal designs for a multiresponse nonlinear model simulated annealing was used to perform the needed numerical optimization calculations as this method can locate the global optimum of a function and can efficiently handle constraints in the independent variables the calculated optimal designs greatly reduce variances of model parameter estimates compared to variances from previously used empirical designs the effect of several design variables including the number of design points and the number of responses on the efficiency of the design was investigated and designs for various subsets of parameters were also calculated new directions for the design of future experiments were suggested by this analysis

compound d and d s optimum designs for determining the order of a chemical reaction estimation of the order of a chemical reaction is often at least as important as estimation of the rate of the reaction locally optimum experimental designs are found for the order and the rate separately and together compound d optimum designs provide a method for designing experiments with specified efficiency for rate or order determination a relationship between the compound designs and d optimum designs for both rate and order aids interpretation of the plots of design efficiencies bayesian designs incorporating prior uncertainty are exemplified monte carlo sampling of the prior is used to design an experiment for the esterification of acetic anhydride

the n city travelling salesman problem statistical mechanics and the metropolis algorithm in any n city travelling salesman problem there are n 1 mathord left vphantom 2 right kern nulldelimiterspace 2 possible tours we use the metropolis algorithm to generate a sequence of such tours this sequence may be viewed as the random evolution of a physical system in contact with a heat bath as the temperature is lowered the tours generated approach the optimal tour it appears that for large n one arrives within a few percent of the optimal solution in better than quadratic time

bayesian design and analysis of computer experiments use of derivatives in surface prediction this article is concerned with the problem of predicting a deterministic response function yo over a multidimensional domain t given values of yo and all of its first derivatives at a set of design sites points in t the intended application is to computer experiments in which yo is an output from a computer model of a physical system and each point in t represents a particular configuration of the input parameters it is assumed that the first derivatives are already available e g from a sensitivity analysis or can be produced by the code that implements the model a bayesian approach in which the random function that represents prior uncertainty about yo is taken to be a stationary gaussian stochastic process is used the calculations needed to update the prior given observations of yo and its first derivatives at the design sites are given and are illustrated in a small example the issue of experimental design is also discussed in particular the criterion of maximizing the reduction in entropy

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

maximum likelihood estimation of the lower tail of a probability distribution summary we consider the estimation of the three parameters of the lower tail of a distribution function based on the k smallest out of n observations the likelihood function has a singularity but it is argued that a local maximum when it exists should be taken as the m l e asymptotic results as k oo n oo k n 0 show that such a local maximum does exist and provides consistent estimators whenever the shape parameter is greater than one otherwise there is no local maximum and likelihood inference fails we also discuss interval estimation and propose a test to distinguish between the type i and weibull limit laws

a note on generalized pareto distributions and thek upper extremes denote byd n k the maximum distance between the distribution function of thekth largest order statistic in aniid sample of sizen equally standardized ink and of its corresponding limiting extreme value distribution

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

stability of multiobjective nonlinear programming problems with random variables in the objective functions abstract this paper deals with multiobjective nonlinear programming problems with random variables in the objective functions these random variables are characterized by possibility density functions the existing results concerning the qualitative analysis of basic notions in parametric nonlinear programming problems are reformulated to study the stability sets of the first second third and fourth kind for multiobjective nonlinear programming problems under the concept of possibility efficient

a stopping rule for the computation of generalized method of moments estimators to obtain consistency and asymptotic normality a generalized method of moments gmm estimator typically is defined to be an approximate global minimizer of a gmm criterion function to compute such an estimator however can be problematic because of the difficulty of global optimization in consequence practitioners usually ignore the problem and take the gmm estimator to be the result of a local optimization algorithm this yields an estimator that is not necessarily consistent and asymptotically normal the use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function which makes it difficult to know when to stop the algorithm to alleviate these problems of global and local optimization we propose a stopping rule sr procedure for computing gmm estimators the sr procedure eliminates the need for global search with high probability and it provides an explicit sr for problems of stability that may arise with local optimization problems

estimation of extreme risk regions under multivariate regular variation when considering d possibly dependent random variables one is often interested in extreme risk regions with very small probability p we consider risk regions of the form z rd f z where f is the joint density and a small number estimation of such an extreme risk region is difficult since it contains hardly any or no data using extreme value theory we construct a natural estimator of an extreme risk region and prove a refined form of consistency given a random sample of multivariate regularly varying random vectors in a detailed simulation and comparison study the good performance of the procedure is demonstrated we also apply our estimator to financial data

stability of multiobjective nlp problems with fuzzy parameters in the objectives and constraints functions abstract this paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the objectives and constraints functions these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the qualitative analysis of the notions solvability set stability sets of the first kind and of the second kind in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality an algorithm for obtaining any subset of the parametric space which has the same corresponding pareto optimal solution is also presented an illustrative example is given to clarify the obtained results

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

fuzzy linear programming problems with fuzzy numbers abstract linear programming problems with fuzzy parameters are formulated by fuzzy functions the ambiguity considered here is not randomness but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership parameters on constraint and objective functions are given by fuzzy numbers in this paper our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters this fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential

estimation of jump tails we propose a new and flexible non parametric framework for estimating the jump tails of ito semimartingale processes the approach is based on a relatively simple to implement set of estimating equations associated with the compensator for the jump measure or its intensity that only utilizes the weak assumption of regular variation in the jump tails along with in fill asymptotic arguments for directly estimating the large jumps the procedure assumes that the large sized jumps are identically distributed but otherwise allows for very general dynamic dependencies in jump occurrences and importantly does not restrict the behavior of the small jumps nor the continuous part of the process and the temporal variation in the stochastic volatility on implementing the new estimation procedure with actual high frequency data for the s p 500 aggregate market portfolio we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature

a study of fuzzy parametric on multiobjective nonlinear programming problems without differentiability this paper deals with multiobjective nonlinear programming problems with fuzzy parameters in the objective functions without differentiability these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the stability notions of parametric convex programs are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality without differentiability on the functions considered

applications of the annealing algorithm to combinatorial problems in statistics summary there are several problems in statistics which can be formulated so that the desired solution is the global minimum of some explicitly defined objective function in many cases the number of candidate solutions increases exponentially with the size of the problem making exhaustive search impossible but descent procedures devised to reduce the number of solutions examined can terminate with local minima in this paper we describe the annealing algorithm a widely applicable stochastic search procedure which can escape local optima and we use the evolutionary tree problem to illustrate the method of application

estimating the stable index alpha in order to measure tail thickness a critique stable laws are often fit to outlier prone data and if the index alpha is estimated to be much less than two then the normal law is rejected in favor of an infinite variance stable law this paper derives the theoretical properties of such a procedure when the true distribution is stable the distribution of the m l e of alpha is non regular if alpha 2 when the true distribution is not stable the estimate of alpha is not a robust measure of the rate of decrease of the tail probabilities a more robust procedure is developed and a statistic for describing and comparing the tail shapes of arbitrary samples is proposed