cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

an optimized spectral difference scheme for caa problems in the implementation of spectral difference sd method the conserved variables at the flux points are calculated from the solution points using extrapolation or interpolation schemes the errors incurred in using extrapolation and interpolation would result in instability on the other hand the difference between the left and right conserved variables at the edge interface will introduce dissipation to the sd method when applying a riemann solver to compute the flux at the element interface in this paper an optimization of the extrapolation and interpolation schemes for the fourth order sd method on quadrilateral element is carried out in the wavenumber space through minimizing their dispersion error over a selected band of wavenumbers the optimized coefficients of the extrapolation and interpolation are presented and the dispersion error of the original and optimized schemes is plotted and compared an improvement of the dispersion error over the resolvable wavenumber range of sd method is obtained the stability of the optimized fourth order sd scheme is analyzed it is found that the stability of the 4th order scheme with chebyshev gauss lobatto flux points which is originally weakly unstable has been improved through the optimization the weak instability is eliminated completely if an additional second order filter is applied on selected flux points one and two dimensional linear wave propagation analyses are carried out for the optimized scheme it is found that in the resolvable wavenumber range the new sd scheme is less dispersive and less dissipative than the original scheme and the new scheme is less anisotropic for 2d wave propagation the optimized sd solver is validated with four computational aeroacoustics caa workshop benchmark problems the numerical results with optimized schemes agree much better with the analytical data than those with the original schemes

regression on manifolds estimation of the exterior derivative collinearity and near collinearity of predictors cause difficulties when doing regression in these cases variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the regression coefficients and interpretation of the coefficients is ambiguous because gradients are not defined using a differential geometric interpretation in which the regression coefficients are interpreted as estimates of the exterior derivative of a function we develop a new method to do regression in the presence of collinearities our regularization scheme can improve estimation error and it can be easily modified to include lasso type regularization these estimators also have simple extensions to the large p small n context

gmm with many moment conditions this paper provides a first order asymptotic theory for generalized method of moments gmm estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak examples in which these asymptotics are relevant include instrumental variable iv estimation with many possibly weak or uninformed instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments under certain regularity conditions the gmm estimators are shown to converge in probability but not necessarily to the true parameter and conditions for consistent gmm estimation are given a general framework for the gmm limit distribution theory is developed based on epiconvergence methods some illustrations are provided including consistent gmm estimation of a panel model with time varying individual effects consistent limited information maximum likelihood estimation as a continuously updated gmm estimator and consistent iv structural estimation using large numbers of weak or irrelevant instruments some simulations are reported

consistency results for stationary autoregressive processes with constrained coefficients we consider stationary autoregressive processes with coefficients restricted to an ellipsoid these are included in the family of autoregressive processes with absolutely summable coefficients we provide consistency results under different norms for the estimation of such processes using constrained and penalized estimators as an application we show a weak form of universal consistency simulations show that directly including the constraint in the estimation can lead to results that are more robust

on the validity of the pairs bootstrap for lasso estimators we study the validity of the pairs bootstrap for lasso estimators in linear regression models with random covariates and heteroscedastic error terms we show that the naive pairs bootstrap does not consistently estimate the distribution of the lasso estimator in particular we identify two dierent sources for the failure of the bootstrap first in the bootstrap samples the lasso estimator fails to correctly mimic the population moment condition satisfied by the regression parameter second the bootstrap lasso estimation criterion does not reproduce the sign of the zero coecients with sucient accuracy to overcome these problems we introduce a modified pairs bootstrap procedure that consistently estimates the distribution of the lasso estimator finally we consider also the adaptive lasso estimator also in this case we show that the modified pairs bootstrap consistently estimates the distribution of the adaptive lasso estimator monte carlo simulations confirm a desirable accuracy of the modified pairs bootstrap procedure these results show that when properly defined the pairs bootstrap may provide a valid approach for estimating the distribution of lasso estimators

on a principal varying coefficient model we propose a novel varying coefficient model vcm called principal varying coefficient model pvcm by characterizing the varying coefficients through linear combinations of a few principal functions compared with the conventional vcm pvcm reduces the actual number of nonparametric functions and thus has better estimation efficiency compared with the semivarying coefficient model svcm pvcm is more flexible but with the same estimation efficiency when the number of principal functions in pvcm and the number of varying coefficients in svcm are the same model estimation and identification are investigated and the better estimation efficiency is justified theoretically incorporating the estimation with the l 1 penalty variables in the linear combinations can be selected automatically and hence the estimation efficiency can be further improved numerical experiments suggest that the model together with the estimation method is useful even when the number of covariates is large supplementary mat

multiobjective optimum design in mixed integer and discrete design variable problems a min max variant of the global criterion approach is proposed to obtain solutions to multiobjective optimum design problems involving a mix of continuous discrete and integer design variables this modified global criterion approach is used in conjunction with a branch and bound algorithm where the latter was configured especially to accommodate a mix of integer and discrete design variables the use of a weighting strategy with the proposed method allows the generation of a set of pareto optimal solutions for both convex and nonconvex problems

efficient calculation of optimum design sensitivity two methods for obtaining the sensitivity of an optimized design to changes in problem parameters are presented the first order method uses gradient information to estimate the required sensitivity the second order method uses second derivatives of the design objective and constraint functions to provide a quadratic approximation to the new design which results from changing the specified parameter it is shown that the sensitivity of the optimized design may be discontinuous with respect to the new parameter this discontinuity is accounted for in the present methods these methods are compared to a previous approach based on the kuhn tucker necessary conditions for optimality it is shown that the present methods provide the appropriate sensitivity information in an efficient manner the methods are demonstrated by a structural synthesis example

consistency of trace norm minimization regularization by the sum of singular values also referred to as the trace norm is a popular technique for estimating low rank rectangular matrices in this paper we extend some of the consistency results of the lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss we also provide an adaptive version that is rank consistent even when the necessary condition for the non adaptive version is not fulfilled

estimating the frequency distribution of crossovers during meiosis from recombination data estimation of tetrad crossover frequency distributions from genetic recombination data is a classic problem dating back to weinstein 1936 genetics 21 155 199 but a number of important issues such as how to specify the maximum number of crossovers how to construct confidence intervals for crossover probabilities and how to obtain correct p values for hypothesis tests have never been adequately addressed in this article we obtain some properties of the maximum likelihood estimate mle for crossover probabilities that imply guidelines for choosing the maximum number of crossovers we give these results for both normal meiosis and meiosis with nondisjunction we also develop an accelerated em algorithm to find the mle more efficiently we propose bootstrap based methods to find confidence intervals and p values and conduct simulation studies to check the validity of the bootstrap approach

localization of multi constrained optima and avoidance of local optima in structural optimization problems abstract this paper describes two new methods of structural optimization the first method is seen primarily in conjunction with optimality criteria algorithms it proposes a new procedure for the solution of multi constrained optimization problems based on the calculation of partial optima the partial optima refer to solutions of the optimization problem only for part of the constraints in the simplest case only for a single constraint and can be easily determined by already known procedures the second method is a new mathematical programming method designed to combine a high convergence speed together with a high reliability with respect to the avoidance of local minima

path consistent model selection in additive risk model via lasso as a flexible alternative to the cox model the additive risk model assumes that the hazard function is the sum of the baseline hazard and a regression function of covariates for right censored survival data when variable selection is needed along with model estimation we propose a path consistent model selector using a modified lasso approach under the additive risk model assumption we show that the proposed estimator possesses the oracle variable selection and estimation property applications of the proposed approach to three right censored survival data sets show that the proposed modified lasso yields parsimonious models with satisfactory estimation and prediction results

inference and testing on the boundary in extended constant conditional correlation garch models we consider inference and testing in extended constant conditional correlation garch models in the case where the true parameter vector is a boundary point of the parameter space this is of particular importance when testing for volatility spillovers in the model the large sample properties of the qmle are derived together with the limiting distributions of the related lr wald and lm statistics due to the boundary problem these large sample properties become nonstandard the size and power properties of the tests are investigated in a simulation study as an empirical illustration we test for no volatility spillovers between foreign exchange rates

the best test of exponentiality against singly truncated normal alternatives abstract we show that the likelihood ratio test of exponentiality against singly truncated normal alternatives is the uniformly most powerful unbiased test and can be expressed in terms of the sampling coefficient of variation this test is closely related to greenwood s statistic for testing departures from the uniform distribution we provide a way to approximate the critical points of the test using saddlepoint methods that gives a high degree of accuracy

optimum design sensitivity based on approximation concepts and dual methods an optimum design sensitivity analysis capability is reported which exploits the approximation concepts dual method formulation of the minimum weight structural sizing problem an efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables estimates on the useful range of parameter perturbations over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs are also obtained numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported

minimum weight design of trusses by an optimality criteria method this work presents an optimality criteria method which accurately and efficiently solves the structural optimization problem of trusses subject to deflection and stress constraints the method is based upon the newton raphson method and a first order approximation both for deflection and stress constraints using the method of virtual work it solves the problem rigorously and no serious difficulties have yet been encountered in spite of the drawbacks inherent in the newton raphson method worked examples show its superiority to other methods and its ability to cope with trusses with many members and subject to multiple constraints

on min norm and min max methods of multi objective optimization this paper examines pareto optimality of solutions to multi objective problems scalarized in the min norm compromise programming generalized goal programming or unrestricted min max formulations issues addressed include among others uniqueness in solution or objective space penalization for over achievement of goals min max reformulation of goal programming inferiority in tchebycheff norm minimization strength and weakness of weighted bound optimization quasi satisficing decision making just attaining or even over passing the goals trading off by modifying weights or goals non convex pareto frontier new general necessary and sufficient conditions for both pareto optimality and weak pareto optimality are presented various formulations are compared in theoretical performance with respect to the goal point location ideas for advanced goal programming and interactive decision making are introduced

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

on the pareto optimum sensitivity analysis in multicriteria optimization to analyse the trade off relations among the set of criteria in multicriteria optimization pareto optimum sensitivity analysis is systematically studied in this paper original contributions cover two parts theoretical demonstrations are firstly made to validate the gradient projection method in pareto optimum sensitivity analysis it is shown that the projected gradient direction evaluated at a given pareto optimum in the design variable space rigorously corresponds to the tangent direction of the pareto curve surface at that point in the objective space this statement holds even for the change of the set of active constraints in the perturbed problem secondly a new active constraint updating strategy is proposed which permits the identification of the active constraint set change to determine the influence of this change upon the differentiability of the pareto curve and finally to compute directional derivatives in non differentiable cases this work will highlight some basic issues in multicriteria optimization some numerical problems are solved to illustrate these novelties

minimax multiobjective optimization in structural design summary the use of multiobjective optimization techniques which may be regarded as a systematic sensitivity analysis for the selection and modification of system parameters is presented a minimax multiobjective optimization model for structural optimization is proposed three typical multiobjective optimization techniques goal programming compromise programming and the surrogate worth trade off method are used to solve such a problem the application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

on the asymptotics of constrained m estimation limit theorems for an m estimate constrained to lie in a closed subset of r d are given under two different sets of regularity conditions a consistent sequence of global optimizers converges under chernoff regularity of the parameter set a n consistent sequence of local optimizers converges under clarke regularity of the parameter set in either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value limit theorems for the optimal value are also obtained agreeing with chernoff s result in the case of maximum likelihood with global optimizers

a massive data framework for m estimators with cubic rate the divide and conquer method is a common strategy for handling massive data in this article we study the divide and conquer method for cubic rate estimators under the massive data framework we develop a general theory for establishing the asymptotic distribution of the aggregated m estimators using a weighted average with weights depending on the subgroup sample sizes under certain condition on the growing rate of the number of subgroups the resulting aggregated estimators are shown to have faster convergence rate and asymptotic normal distribution which are more tractable in both computation and inference than the original m estimators based on pooled data our theory applies to a wide class of m estimators with cube root convergence rate including the location estimator maximum score estimator and value search estimator empirical performance via simulations and a real data application also validate our theoretical findings

maximum a posteriori estimators as a limit of bayes estimators maximum a posteriori and bayes estimators are two common methods of point estimation in bayesian statistics it is commonly accepted that maximum a posteriori estimators are a limiting case of bayes estimators with 0 1 loss in this paper we provide a counterexample which shows that in general this claim is false we then correct the claim that by providing a level set condition for posterior densities such that the result holds since both estimators are defined in terms of optimization problems the tools of variational analysis find a natural application to bayesian point estimation

statistics with set valued functions applications to inverse approximate optimization much of statistics relies upon four key elements a law of large numbers a calculus to operationalize stochastic convergence a central limit theorem and a framework for constructing local approximations these elements are well understood for objects in a vector space e g points or functions however much statistical theory does not directly translate to sets because they do not form a vector space building on probability theory for random sets this paper uses variational analysis to develop operational tools for statistics with set valued functions these tools are first applied to nonparametric estimation kernel regression of set valued functions the second application is to the problem of inverse approximate optimization in which approximate solutions corrupted by noise to an optimization problem are observed and then used to estimate the amount of suboptimality of the solutions and the parameters of the optimization problem that generated the solutions we show that previous approaches to this problem are statistically inconsistent when the data is corrupted by noise whereas our approach is consistent under mild conditions

multicriterion evolutionary structural optimization using the weighting and the global criterion methods the design of structures using evolutionary structural optimisation eso has previously been based on a single criterion this paper aims at incorporating multiple criteria into the eso process this is done using a weighting method and a global criterion method in the present work two criteria are optimised simultaneously namely the maximisation of the first mode of natural frequency and the minimisation of the mean compliance of the structure which is inversely proportional to stiffness several examples are provided showing that the solutions produced by the weighting method form the pareto solution space the solutions of the global criterion method also form part of the pareto solution space it appears to have a notable similarity to a solution of 50 stiffness 50 frequency ratio of criteria weighting the results point towards a means of resolving pareto solution spaces when there are more than two optimality criteria

a rank corrected procedure for matrix completion with fixed basis coefficients for the problems of low rank matrix completion the efficiency of the widely used nuclear norm technique may be challenged under many circumstances especially when certain basis coefficients are fixed for example the low rank correlation matrix completion in various fields such as the financial market and the low rank density matrix completion from the quantum state tomography to seek a solution of high recovery quality beyond the reach of the nuclear norm in this paper we propose a rank corrected procedure using a nuclear semi norm to generate a new estimator for this new estimator we establish a non asymptotic recovery error bound more importantly we quantify the reduction of the recovery error bound for this rank corrected procedure compared with the one obtained for the nuclear norm penalized least squares estimator this reduction can be substantial around 50 we also provide necessary and sufficient conditions for rank consistency in the sense of bach j mach learn res 9 1019 1048 2008 very interestingly these conditions are highly related to the concept of constraint nondegeneracy in matrix optimization as a byproduct our results provide a theoretical foundation for the majorized penalty method of gao and sun a majorized penalty approach for calibrating rank constrained correlation matrix problems http www math nus edu sg matsundf majorpen may5 pdf 2010 and gao 2010 for structured low rank matrix optimization problems extensive numerical experiments demonstrate that our proposed rank corrected procedure can simultaneously achieve a high recovery accuracy and capture the low rank structure

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

subvector inference when the true parameter vector may be near or at the boundary abstract extremum estimators are not asymptotically normally distributed when the estimator satisfies the restrictions on the parameter space such as the non negativity of a variance parameter and the true parameter vector is near or at the boundary this possible lack of asymptotic normality makes it difficult to construct tests for testing subvector hypotheses that control asymptotic size in a uniform sense and have good local asymptotic power irrespective of whether the true parameter vector is at near or far from the boundary we propose a novel estimator that is asymptotically normally distributed even when the true parameter vector is near or at the boundary and the objective function is not defined outside the parameter space the proposed estimator allows the implementation of a new test based on the conditional likelihood ratio statistic that is easy to implement controls asymptotic size and has good local asymptotic power properties furthermore we show that the test enjoys certain asymptotic optimality properties when the parameter of interest is scalar in an application of the random coefficients logit model berry levinsohn and pakes 1995 to the european car market we find that for most parameters the new test leads to tighter confidence intervals than the two sided t test commonly used in practice

a recursive quadratic programming method with active set strategy for optimal design recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics there are two recursive quadratic programming methods that have been published in the literature one is by han and the other is by pshenichny published in 1977 and 1970 respectively the algorithm of pshenichny had been undiscovered until now and is examined here for the first time it is found that the proof of global convergence by han requires computing sensitivity coefficients derivatives of all constraint functions of the problem at every iteration this is prohibitively expensive for large scale applications in optimal design in contrast pshenichny has proved global convergence of his algorithm using only an active set strategy this is clearly preferable for large scale applications the method of pshenichny has been coded into a fortran program applications of this method to four example problems are presented the method is found to be very reliable however the method is found to be very sensitive to local minima i e it converges to a local minimum nearest to the starting design thus for optimal design problems which usually possess multiple local minima it is suggested that pshenichny s method be used as part of a hybrid method

normal constraint method with guarantee of even representation of complete pareto frontier multiobjective optimization is rapidly becoming an invaluable tool in engineering design a particular class of solutions to the multiobjective optimization problem is said to belong to the pareto frontier a pareto solution the set of which comprises the pareto frontier is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other accordingly the pareto frontier plays an important role in engineering design it characterizes the tradeoffs between conflicting design objectives some optimization methods can be used to automatically generate a set of pareto solutions from which a final design is subjectively chosen by the designer for this approach to be successful the generated pareto set must be truly representative of the complete optimal design space pareto frontier in other words the set must not overrepresent one region of the design space or neglect others some commonly used methods comply with this requirement whereas others do not this paper offers a new phase in the development of the normal constraint method which is a simple approach for generating pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives the even distribution of the generated pareto solutions can facilitate the process of developing an analytical expression for the pareto frontier in n dimension an even distribution of pareto solutions also facilitates the task of choosing the most desirable final design from among the set of pareto solutions the normal constraint method bears some similarities to the normal boundary intersection and constraint methods importantly the developments presented in this paper define its critical distinction namely the ability to generate a set of evenly distributed pareto solutions over the complete pareto frontier examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method as well as with the original normal constraint method

on testing marginal versus conditional independence we consider testing marginal independence versus conditional independence in a trivariate gaussian setting the two models are non nested and their intersection is a union of two marginal independences we consider two sequences of such models one from each type of independence that are closest to each other in the kullback leibler sense as they approach the intersection they become indistinguishable if the signal strength as measured by the product of two correlation parameters decreases faster than the standard parametric rate under local alternatives at such rate we show that the asymptotic distribution of the likelihood ratio depends on where and how the local alternatives approach the intersection to deal with this non uniformity we study a class of envelope distributions by taking pointwise suprema over asymptotic cumulative distribution functions we show that these envelope distributions are well behaved and lead to model selection procedures with rate free uniform error guarantees and near optimal power to control the error even when the two models are indistinguishable rather than insist on a dichotomous choice the proposed procedure will choose either or both models

inferring optimal peer assignment from experimental data this article studies the problem of optimally dividing individuals into peer groups to maximize social gains from heterogeneous peer effects the specific setting analyzed here concerns efficient ways of allocating roommates in college dormitories using confidential data on a sample of dartmouth college freshmen who were randomly assigned to be roommates the article derives efficient roommate pairing rules based on demographic and academic background which maximize different aggregate outcomes segregation by precollege academic standing and by race are seen to minimize mean enrolment into sororities and maximize mean enrolment into fraternities segregation has no effect on mean and median freshman year grade point average gpa but increases the higher and decreases the lower percentiles of the gpa distribution for both men and women efficiency loss due to legal constraints on allocations e g race blindness is shown to be significant and also larger for women for whom peer effects are more nonl

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

asymptotic theory for solutions in statistical estimation and stochastic programming new techniques of local sensitivity analysis for nonsmooth generalized equations are applied to the study of sequences of statistical estimates and empirical approximations to solutions of stochastic programs consistency is shown to follow from a certain local invertibility property and asymptotic distributions are derived from a generalized implicit function theorem that characterizes asymptotic behavior in situations where estimates are subjected to constraints and estimation functionals are nonsmooth

sparse estimation of conditional graphical models with application to gene networks in many applications the graph structure in a network arises from two sources intrinsic connections and connections due to external effects we introduce a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects technically this is formulated as a conditional graphical model in which the external effects are modeled as predictors and the graph is determined by the conditional precision matrix we introduce two sparse estimators of this matrix using the reproduced kernel hilbert space combined with lasso and adaptive lasso we establish the sparsity variable selection consistency oracle property and the asymptotic distributions of the proposed estimators we also develop their convergence rate when the dimension of the conditional precision matrix goes to infinity the methods are compared with sparse estimators for unconditional graphical models and with the constrained maximum likelihood estimate that assumes a know

asymptotic inference for the constrained quantile regression process abstract i investigate the asymptotic distribution of linear quantile regression coefficient estimates when the parameter lies on the boundary of the parameter space in order to allow for inferences made across many conditional quantiles i provide a uniform characterization of constrained quantile regression estimates as a stochastic process over an interval of quantile levels to do this i pose the process of estimates as solutions to a parameterized family of constrained optimization problems parameterized by quantile level a uniform characterization of the dual solution to these problems the so called regression rankscore process is also derived which can be used for score type inference in quantile regression the asymptotic behavior of quasi likelihood ratio wald and regression rankscore processes for inference when the null hypothesis asserts that the parameters lie on a boundary follows from the features of the constrained solutions

optimal selection of weighting matrices in integrated design of structures controls a methodology is developed for the optimal selection of state and input weighting matrices q and r respectively of the linear quadratic regulator lqr method in the integrated design of structures controls an optimal control problem is set up in such a way that design variables are the diagonal entries of q and r the objective function is the trace of the solution matrix to the algebraic riccati equation of the lqr method p matrix and constraints are imposed on the closed loop eigenvalues to satisfy minimum stability conditions for the control system the procedure finds the optimal diagonal q and i that enables the actively controlled system to meet the prespecified stability and performance bounds furthermore the resulting q and r yield the minimum possible performance index and hence the control effort is substantially reduced the proposed method is integrated with a substructure decomposition scheme which results in substantial savings on the numerical computations with very little loss in the accuracy of the original system response it is found that for trusslike space structures the proposed optimization scheme is mostly affected by the changes in the diagonal terms of r and the changes in the velocity diagonal terms of q of the controlled system the method is expected to be very useful for large scale systems and is illustrated with the help of two example problems

restricted likelihood ratio lack of fit tests using mixed spline models penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non linearity in the smooth function estimates this motivates the study of lack of fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values for this one sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies and finite sample approximations to the asymptotic distribution are provided test statistics are studied for simple as well as multiple regression models

performance of some sqp algorithms on structural design problems this paper describes the basic ideas of sequential quadratic programming sqp algorithms for design optimization there are two fundamental differences between the various algorithms i the difinition of the qp subproblem solved at each iteration and ii the descent function used during step size determination the performances of the algorithms can change dramatically depending on how the two steps are executed numerical implementation details of various computational steps are discussed three programs based on sqp algorithms are used to solve 17 structural design problems having 7 to 96 design variables and 10 to 1051 performance constraints besides design variable bounds based on the performance of these programs efficient procedures to execute various steps of the sqp methods are determined it is concluded that the potential constraint strategy where only a subset of the constraints is used to define the qp subproblem is essential for large scale engineering design applications with this strategy the sqp methods are quite robust and have great potential for routine application in engineering design

on the asymptotics of constrained local m estimators we discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and more generally m estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set s we give a counterexample showing that regularity of s in the sense of clarke is not sufficient for asymptotic equivalence of n consistent locally optimal m estimators we argue further that stronger properties such as so called near convexity or prox regularity of s are required in order to ensure that any two n consistent locally optimal m estimators have the same asymptotics

pareto optima of isostatic trusses abstract multicriterion optimization of elastic stress limited isostatic trusses is considered and a numerical method for determining the pareto optimal set of the problem is developed the weight of the structure and some chosen nodal displacements are taken as design criteria and member areas are used as design variables the corresponding bicriterion problem with weight and one displacement in the objective function is solved exactly and this result is used as a basis of the proposed method by introducing certain parameters each joined with one displacement criterion the pareto optimal solutions of the general problem may be obtained with any accuracy two examples are given to illustrate the method

probabilistic causality and detecting collections of interdependence patterns summary interdependent effects are usually distinguished from statistical interaction by using the sufficient causes framework this almost always involves expressing probability distributions as deterministic logic functions where certain conditions invariably produce or prevent an outcome using an idea from the philosophy literature that a cause is defined as an event which increases the probability of an outcome a probabilistic sufficient causes framework is developed here it expresses distributions with probabilistic logic functions and is used to define interdependence without determinism the connections between probabilistic logic and the inequalities which define convex polytopes in the space of the distribution parameters are given interdependence is defined for the response behaviour of individuals defined by latent variables and is not directly observable it is shown that the formulation of the models as geometric objects enables the use of algebraic tools to compute observable constraints for detecting interdependence novel constraints are derived for detecting causal interdependence patterns and the corresponding statistical tests are described

expandable factor analysis bayesian sparse factor models have proven useful for characterizing dependence in multivariate data but scaling computation to large numbers of samples and dimensions is problematic we propose expandable factor analysis for scalable inference in factor models when the number of factors is unknown the method relies on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low rank and sparse loadings matrix the structure of the prior leads to an estimation algorithm that accommodates uncertainty in the number of factors we propose an information criterion to select the hyperparameters of the prior expandable factor analysis has better false discovery rates and true positive rates than its competitors across diverse simulation settings we apply the proposed approach to a gene expression study of ageing in mice demonstrating superior results relative to four competing methods

a wavenumber based extrapolation and interpolation method for use in conjunction with high order finite difference schemes the errors incurred in using extrapolation and interpolation in large scale computations are analyzed and quantified in the wavenumber space if a large extrapolation stencil is used the errors in the low wavenumbers can be significantly reduced however the errors in the high wavenumbers are at the same time greatly increased the opposite is true if the stencil size is reduced based on the wavenumber analysis an optimized extrapolation and interpolation method is proposed the optimization is carried out over a selected band of wavenumbers it is known that extrapolation often leads to numerical instability the instability is the result of large error amplification in the high wavenumber range to reduce the tendency to trigger numerical instability it is proposed that an extra constraint be imposed on the optimized extrapolation method the added constraint aims to reduce error amplification over the high wavenumbers numerical examples are provided to illustrate that accurate and stable numerical results can be obtained in large scale simulation using a high order finite difference scheme and the proposed optimized extrapolation method when the same problems are recomputed using the familiar high order polynomials extrapolation method in the lagrange form in one case the numerical results are plagued by large errors and ultimately instability in another problem it is found that the use of the lagrange polynomials extrapolation method would lead immediately to numerical instability

norm methods and partial weighting in multicriterion optimization of structures methods for generating pareto optimal solutions to a multicriterion optimization problem are considered the norm methods based on the scalarization of the original multicriterion problem by using the l norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested in addition an alternative approach which instead of scalarization reduces the dimension of the multicriterion problem is proposed this is called the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted sum of the criteria is used as the objective function the first of these two approaches norm method is very flexible from a designer s point of view and it can be applied also in non convex cases to the determination of the pareto optimal set whereas the latter partial weighting method is especially suitable for problems where the number of criteria is large throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design

concept selection using s pareto frontiers we introduce the notion of s pareto optimality and show how it can be used to improve concept selection in engineering design specie c design alternatives are classie ed as s pareto optimal when there are no other alternatives from the same or any other general design concept that exhibit improvement in all design objectives further we say that the set of s pareto design alternatives comprises the s pareto frontier under the proposed approach the s pareto frontier plays a paramount role in the concept selection process as it is used to dee ne and classify concept dominance thes pareto frontier based concept selection method can becharacterized as onethat capitalizes on the benee ts of computational optimization during the conceptual phase of design before a general design concept has been chosen an introduction to s pareto optimality and a method for generating s pareto frontiersaredeveloped anapproachforusing s paretofrontierstoperformconceptselectionisalsopresented the methods proposed can effectively aid in the elimination of dominated design concepts keep competitive concepts and ultimately choose a specie cdesign alternative from theselected design concept a truss design problem is used to illustrate the usefulness of the method nomenclature g vector of inequality constraints h vector of equality constraints j aggregate objective function mi number of points along ni ni ith vector dee ning the utopia plane n number of design objectives nx number of design variables t k relaxation slack variable for concept k x p generic point on the utopia plane x vector of design variables increment by which feasible space is reduced vector of design objectives or design metrics i ith anchor point k optimum design objective value for concept k si s anchor point for the ith objective

characterizing additively closed discrete models by a property of their maximum likelihood estimators with an application to generalized hermite distributions this article reports on two parameter count distributions satisfying very general conditions that are closed under addition so that their maximum likelihood estimator mle of the population mean is the sample mean the most important of these in practice the generalized hermite distribution is analyzed and a necessary and sufficient condition is given to ensure that the mle is the solution of likelihood equations score test to contrast the poisson assumption is studied and two examples of applications are given

efficient optimum design of structures program dddu abstract an efficient optimization algorithm is developed for engineering structures subject to multiple constraints this highly non linear and implicit problem is reduced to a combination of a sequence of quasi linear constraints and explicit problems of the statically determined structures the method is based on the kuhn tucker necessary conditions for optimality associated with a simple quadratic programme designed simultaneously to determine the lagrange multipliers and to delete non active constraints a number of examples including trusses and wing structures show that the method is efficient when compared with other competing techniques

new efficient estimation and variable selection methods for semiparametric varying coefficient partially linear models the complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications in this work we propose new estimation and variable selection procedures for the semiparametric varying coefficient partially linear model we first study quantile regression estimates for the nonparametric varying coefficient functions and the parametric regression coefficients to achieve nice efficiency properties we further develop a semiparametric composite quantile regression procedure we establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the estimators achieve the best convergence rate moreover we show that the proposed method is much more efficient than the least squares based method for many non normal errors and that it only loses a small amount of efficiency for normal errors in addition it is shown that the loss in efficiency is at most 11 1 for estimating varying coefficient functions and is no greater than 13 6 for estimating parametric components to achieve sparsity with high dimensional covariates we propose adaptive penalization methods for variable selection in the semiparametric varying coefficient partially linear model and prove that the methods possess the oracle property extensive monte carlo simulation studies are conducted to examine the finite sample performance of the proposed procedures finally we apply the new methods to analyze the plasma beta carotene level data

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

fitting nonlinear and constrained generalized estimating equations with optimization software summary in this article we present an estimation approach for solving nonlinear constrained generalized estimating equations that can be implemented using object oriented software for nonlinear programming such as nlminb in splus or fmincon and lsqnonlin in matlab we show how standard estimating equation theory includes this method as a special case so that our estimates when unconstrained will remain consistent and asymptotically normal to illustrate this method we fit a nonlinear dose response model with nonnegative mixed bound constraints to clustered binary data from a developmental toxicity study satisfactory confidence intervals are found using a nonparametric bootstrap method when a common correlation coefficient is assumed for all the dose groups and for some of the dose specific groups

a dual approach to inference for partially identified econometric models abstract this paper considers inference for the set i of parameter values that minimize a criterion function chernozhukov et al 2007 cht develop a general theory of estimation and inference using the level set of a criterion function we establish a dual relationship between the level set estimator and its support function and show that the properly normalized support function provides alternative wald type inference methods these methods can be used to obtain confidence sets for i and points inside it for models with finitely many moment inequalities we show that our wald type statistic is asymptotically equivalent to cht s statistic under regularity conditions

monte carlo likelihood inference for missing data models we describe a monte carlo method to approximate the maximum likelihood estimate mle when there are missing data and the observed data likelihood is not available in closed form this method uses simulated missing data that are independent and identically distributed and independent of the observed data our monte carlo approximation to the mle is a consistent and asymptotically normal estimate of the minimizer of the kullback leibler information as both monte carlo and observed data sample sizes go to infinity simultaneously plug in estimates of the asymptotic variance are provided for constructing confidence regions for we give logit normal generalized linear mixed model examples calculated using an r package

game theory approach for the integrated design of structures and controls the problem of design of actively controlled structures subject to constraints on the damping parameters of the closed loop system is formulated as a multiobjeetive optimization problem the structural weight and the controlled system energy are considered as objective functions for minimization with cross sectional areas of members as design variables a computational procedure is developed for solving the multiobjeetive optimization problem using cooperative game theory the feasibility of the procedure is demonstrated through the design of two truss structures

when uniform weak convergence fails empirical processes for dependence functions via epi and hypographs for copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube the empirical copula process does not converge weakly with respect to the supremum distance this makes it hard to verify asymptotic properties of inference procedures for such copulas to resolve the issue a new metric for locally bounded functions is introduced and the corresponding weak convergence theory is developed convergence with respect to the new metric is related to epi and hypoconvergence and is weaker than uniform convergence still for continuous limits it is equivalent to locally uniform convergence whereas under mild side conditions it implies lp convergence even in cases where uniform convergence fails weak convergence with respect to the new metric is established for empirical copula and tail dependence processes no additional assumptions are needed for tail dependence functions and for copulas the assumptions reduce to existence and continuity of the partial derivatives almost everywhere on the unit cube the results are applied to obtain asymptotic properties of minimum distance estimators goodness of fit tests and resampling procedures

warped functional regression a characteristic feature of functional data is the presence of phase variability in addition to amplitude variability existing functional regression methods do not handle time variability in an explicit and efficient way in this paper we introduce a functional regression method that incorporates time warping as an intrinsic part of the model the method achieves good predictive power in a parsimonious way and allows unified statistical inference about phase and amplitude components the asymptotic distribution of the estimators is derived and their finite sample properties are studied by simulation an application involving ground level ozone trajectories is presented

optimized explicit finite difference schemes for spatial derivatives using maximum norm we propose an optimized scheme using the maximum norm and the simulated annealing the maximum norm offers the largest set of possible solutions for solvers to search the explicit finite difference operator is greatly improved by our optimized scheme we use a tight error limitation to make accuracy improvement to be high and solid our optimized scheme allows greater saving of computational cost and memory demand conventional explicit finite difference methods have difficulties in handling high frequency components due to strong numerical dispersions one can reduce the numerical dispersions by optimizing the constant coefficients of the finite difference operator different from traditional optimized schemes that use the 2 norm and the least squares we propose to construct the objective functions using the maximum norm and solve the objective functions using the simulated annealing algorithm both theoretical analyses and numerical experiments show that our optimized scheme is superior to traditional optimized schemes with regard to the following three aspects first it provides us with much more flexibility when designing the objective functions thus we can use various possible forms and contents to make the objective functions more reasonable second it allows for tighter error limitation which is shown to be necessary to avoid rapid error accumulations for simulations on large scale models with long travel times finally it is powerful to obtain the optimized coefficients that are much closer to the theoretical limits which means greater savings in computational efforts and memory demand

a note on path based variable selection in the penalized proportional hazards model summary we propose an efficient and adaptive shrinkage method for variable selection in the cox model the method constructs a piecewise linear regularization path connecting the maximum partial likelihood estimator and the origin then a model is selected along the path we show that the constructed path is adaptive in the sense that with a proper choice of regularization parameter the fitted model works as well as if the true underlying submodel were given in advance a modified algorithm of the least angle regression type efficiently computes the entire regularization path of the new estimator furthermore we show that with a proper choice of shrinkage parameter the method is consistent in variable selection and efficient in estimation simulation shows that the new method tends to outperform the lasso and the smoothly clipped absolute deviation estimators with moderate samples we apply the methodology to data concerning nursing homes

dispersion and dissipation properties of the 1d spectral volume method and application to a p multigrid algorithm in this article the wave propagation properties of the 1d spectral volume method are studied through analysis of the fourier footprint of the schemes a p multigrid algorithm for the spectral volume method is implemented restriction and prolongation operators are discussed and the efficiency of the smoothing operators is analyzed the results are verified for simple 1d advection problems and for a quasi 1d euler flow it is shown that a significant decrease in computational effort is possible with the p multigrid algorithm

two stage importance sampling with mixture proposals for importance sampling is multiple proposals can be combined to address different aspects of a target distribution there are various methods for is with multiple proposals including hesterberg s stratified is estimator owen and zhou s regression estimator and tan s maximum likelihood estimator for the problem of efficiently allocating samples to different proposals it is natural to use a pilot sample to select the mixture proportions before the actual sampling and estimation however most current discussions are in an empirical sense for such a two stage procedure in this article we establish a theoretical framework of applying the two stage procedure for various methods including the asymptotic properties and the choice of the pilot sample size by our simulation studies these two stage estimators can outperform estimators with naive choices of mixture proportions furthermore while owen and zhou s and tan s estimators are designed for estimating normalizing constants we extend their usa

an iterative method for finite dimensional structural optimization problems with repeated eigenvalues a numerical method for solving finite dimensional structural optimization problems with constraints on natural frequency and on buckling is formulated the method treats nondifferentiable repeated eigenvalues that have been shown to systematically arise in structural optimization recent results on differentiability of eigenvalues are used to develop a generalized gradient projection method for structural optimization the algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues the method is used to solve buckling and vibration optimization problems in which repeated eigenvalues occur

multiobjective optimization of large scale structures this paper presents a multiobjective optimization algorithm based on generalized compound scaling techniques the algorithm handles any number of objective functions similar to handling behavior constraints this technique generates a partial pareto set while solving the optimization problem a reliability ba sed decision criterion is used for selecting the best compromise design the example cases considered in this work include various disciplines in airframe structures such as stress displacement and frequency with hundreds of design variables and constraints this paper also discusses the concept of pareto optima l solutions in the context of a multiobjective structural optimization problem and the commonly used methods of generating pareto optimal solutions

optimization of actively controlled structures using goal programming techniques the problem of design of actively controlled structures subject to restrictions on the damping parameters of the closed loop system is formulated and solved as a multiobjective optimization problem the purpose of control is to effectively suppress structural vibrations due to initial excitation the cross sectional areas of the members are treated as design variables the structural weight and the controlled system energy are considered as objective functions for minimization the goal programming approach is used for the solution of the multiobjective optimization problems the procedure is illustrated through numerical simulations using two bar and twelve bar truss structures

estimation and testing in constrained covariance component models a cutting plane algorithm is proposed for estimating variance and covariance components by maximum likelihood or restricted maximum likelihood enforcing the constraints that covariance matrices be positive semidefinite for tests of hypotheses involving these constrained estimates an asymptotic parametric bootstrap is proposed for approximating the distribution of the likelihood ratio test statistic although the bootstrap is generally inconsistent when the true parameter value is on the boundary of the feasible region the double bootstrap can be used to show that the ordinary bootstrap works well in certain problems

a heuristic method for the design of minimum weight trusses using discrete member sizes abstract this paper describes a heuristic method for obtaining an approximate solution to the problem of determining the minimum weight design of a structural truss using only a discrete set of commercially available member gauges the method treats constraints on joint deflection as well as constraints on member stress and gauge a sufficient condition for convergence of the method to a global optimum is derived together with both an a priori and an a posteriori bound on the approximate solution finally the results obtained from applying the method to several test problems are reported

the moderate deviation principle for minimizers of convex processes abstract this paper mainly discusses the asymptotic behaviors on the minimizers of convex processes in view of the convexity argument it is proved that the minimizers of convex processes with parameterized objective functions satisfy the functional moderate deviation principle as some applications the estimators in two basic models threshold regression models and stochastic dynamical systems are studied in particular the exponential convergence principles on the estimators converging to true parameters are proved