passivity preserving model reduction via interpolation of spectral zeros abstract an algorithm is developed for passivity preserving model reduction of linear time invariant systems implementation schemes are described for both medium scale dense and large scale sparse applications the algorithm is based upon interpolation at selected spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros these interpolation conditions are satisfied through the computation of a basis for a selected invariant subspace of a certain block matrix which has the spectral zeros as its spectrum explicit interpolation is avoided and passivity of the reduced model is established instead through satisfaction of the necessary conditions of the positive real lemma it is also shown that this procedure indirectly solves the associated controllability and observability riccati equations and how to select the interpolation points to give maximal or minimal solutions of these equations from these a balancing transformation may be constructed to give a reduced model that is balanced as well as passive and stable

structure preserving reduced order modeling for gradient systems abstract minimization of energy in gradient systems leads to formation of oscillatory and turing patterns in reaction diffusion systems these patterns should be accurately computed using fine space and time meshes over long time horizons to reach the spatially inhomogeneous steady state in this paper a reduced order model rom is developed which preserves the gradient dissipative structure the coupled system of reaction diffusion equations are discretized in space by the symmetric interior penalty discontinuous galerkin sipg method the resulting system of ordinary differential equations odes are integrated in time by the average vector field avf method which preserves the energy dissipation of the gradient systems the roms are constructed by the proper orthogonal decomposition pod with galerkin projection the nonlinear reaction terms are computed efficiently by discrete empirical interpolation method deim preservation of the discrete energy of the foms and roms with pod deim ensures the long term stability of the steady state solutions numerical simulations are performed for the gradient dissipative systems with two specific equations real ginzburg landau equation and swift hohenberg equation numerical results demonstrate that the pod deim reduced order solutions preserve well the energy dissipation over time and at the steady state

goodness of fit and related inference processes for quantile regression abstract we introduce a goodness of fit process for quantile regression analogous to the conventional r2 statistic of least squares regression several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated the asymptotic behavior of the inference processes is shown to be closely related to earlier p sample goodness of fit theory involving bessel processes the approach is illustrated with some hypothetical examples an application to recent empirical models of international economic growth and some monte carlo evidence

estimating and testing a quantile regression model with interactive effects this paper proposes a quantile regression estimator for a panel data model with interactive effects potentially correlated with the independent variables we provide conditions under which the slope parameter estimator is asymptotically gaussian monte carlo studies are carried out to investigate the finite sample performance of the proposed method in comparison with other candidate meth ods we discuss an approach to testing the model specification against a competing fixed effects specification the paper presents an empirical application of the method to study the effect of class size and class composition on educational attainment the findings show that i a change in the gender composition of a class impacts differently low and high performing students ii while smaller classes are beneficial for low performers larger classes are beneficial for high performers iii reductions in class size do not seem to impact mean and median student performance iv the fixed effects specification is rejected in favor of the interactive effects specification

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

tests of linear hypotheses and l 1 estimation statistics of a linear hypothesis in the standard linear model these test statistics which correspond to wald likelihood ratio and lagrange multiplier tests are shown to have the same limiting chi square behavior under mild regularity conditions on design and the distribution of errors the asymptotic theory of the tests is derived for a large class of error distributions thus in huber s 10 terminology we investigate the behavior of the likelihood ratio test under non standard conditions the asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly gaussian errors but may yield large efficiency gains in non gaussian situations the lagrange multiplier test seems particularly attractive from a computational standpoint we derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis extension of these results to hypotheses of the form r 8 r is a straightforward exercise when the density of the error distribution is strictly positive at the median all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null when the variance of the error distribution is bounded analogous results are well known for classical forms of the wald likelihood ratio and lagrange multipler tests based on least squares methods see for example silvey 18 and the discussion in section 4 below

permutation tests for least absolute deviation regression a permutation test based on proportionate reduction in sums of absolute deviations when passing from reduced to full parameter models is developed for testing hypotheses about least absolute deviation lad estimates of conditional medians in linear regression models sampling simulations demonstrated that the permutation test on full model lad estimates had greater relative power 1 06 1 43 than normal theory tests on least squares estimates for asymmetric chi square error distributions and symmetric double exponential error distributions for models with one n 35 and n 63 and three n 63 independent variables relative power was 77 84 for normal error distributions power simulations demonstrated the low sensitivity of lad estimates and permutation tests to outlier contamination and heteroscedasticity that was a linear function of x and increased sensitivity to heteroscedasticity that was a function of x2 for simple regression models three permutation procedures for testing partial models in multiple regression were compared permuting residuals from the reduced model permuting residuals from the full model and permuting the dependent variable permuting residuals from the reduced model maintained nominal error rates best under the null hypothesis for all error distributions and for correlated and uncorrelated independent variables power under the alternative hypotheses for this partial testing procedure was similar to full lad regression model tests four example applications of lad regression are provided

preserving lagrangian structure in nonlinear model reduction with application to structural dynamics this work proposes a model reduction methodology that preserves lagrangian structure and achieves computational efficiency in the presence of high order nonlinearities and arbitrary parameter dependence as such the resulting reduced order model retains key properties such as energy conservation and symplectic time evolution maps we focus on parameterized simple mechanical systems subjected to rayleigh damping and external forces and consider an application to nonlinear structural dynamics to preserve structure the method first approximates the system s lagrangian ingredients the riemannian metric the potential energy function the dissipation function and the external force and subsequently derives reduced order equations of motion by applying the forced euler lagrange equation with these quantities from the algebraic perspective key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness matri

a new look at proper orthogonal decomposition we investigate some basic properties of the proper orthogonal decomposition pod method as it is applied to data compression and model reduction of finite dimensional nonlinear systems first we provide an analysis of the errors involved in solving a nonlinear ode initial value problem using a pod reduced order model then we study the effects of small perturbations in the ensemble of data from which the pod reduced order model is constructed on the reduced order model we explain why in some applications this sensitivity is a concern while in others it is not we also provide an analysis of computational complexity of solving an ode initial value problem and study the computational savings obtained by using a pod reduced order model we provide several examples to illustrate our theoretical results

reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation we present a new approach to treating nonlinear operators in reduced basis approximations of parametrized evolution equations our approach is based on empirical interpolation of nonlinear differential operators and their frechet derivatives efficient offline online decomposition is obtained for discrete operators that allow an efficient evaluation for a certain set of interpolation functionals an a posteriori error estimate for the resulting reduced basis method is derived and analyzed numerically we introduce a new algorithm the podei greedy algorithm which constructs the reduced basis spaces for the empirical interpolation and for the numerical scheme in a synchronized way the approach is applied to nonlinear parabolic and hyperbolic equations based on explicit or implicit finite volume discretizations we show that the resulting reduced scheme is able to capture the evolution of both smooth and discontinuous solutions in case of symmetries of the problem the approach realizes an automatic and intuitive space compression or even space dimensionality reduction we perform empirical investigations of the error convergence and run times in all cases we obtain a good run time acceleration

aerodynamic data reconstruction and inverse design using proper orthogonal decomposition the application of proper orthogonal decomposition for incomplete gappy data for compressible external aerodynamic problems has been demonstrated successfully in this paper for the first time using this approach it is possible to construct entire aerodynamic flowfields from the knowledge of computed aerodynamic flow data or measured flow data specified on the aerodynamic surface thereby demonstrating a means to effectively combine experimental and computational data the sensitivity of flow reconstruction results to available measurements and to experimental error is analyzed another new extension of this approach allows one to cast the problem of inverse airfoil design as a gappy data problem the gappy methodology demonstrates a great simplification for the inverse airfoil design problem and is found to work well on a range of examples including both subsonic and transonic cases

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

an analysis of weighted eigenspace methods in the presence of sensor errors among all direction finding methods eigenspace based spectral methods are of interest because they are known to yield asymptotically unbiased and efficient estimates these algorithms require knowledge of the array geometry and its elements characteristics in real systems only approximate knowledge of the required array characterization is available there is valid concern that deviation of nominal sensor gain and phase values can result in degradation of doa estimates we analyze the effects of sensor gain and phase perturbation on weighted eigenspace methods wems we quantify the sensitivity of wems by first and second order statistical analyses simulation results are included to validate our analytical results

energy balance and mass conservation in reduced order models of fluid flows abstract in this paper we investigate theoretically and computationally the conservation properties of reduced order models roms for fluid flows specifically we investigate whether the roms satisfy the same or similar energy balance and mass conservation as those satisfied by the navier stokes equations all of our theoretical findings are illustrated and tested in numerical simulations of a 2d flow past a circular cylinder at a reynolds number r e 100 first we investigate the rom energy balance we show that using the snapshot average for the centering trajectory which is a popular treatment of nonhomogeneous boundary conditions in roms yields an incorrect energy balance then we propose a new approach in which we replace the snapshot average with the stokes extension theoretically the stokes extension produces an accurate energy balance numerically the stokes extension yields more accurate results than the standard snapshot average especially for longer time intervals our second contribution centers around rom mass conservation we consider roms created using two types of finite elements the standard taylor hood th element which satisfies the mass conservation weakly and the scott vogelius sv element which satisfies the mass conservation pointwise theoretically the error estimates for the sv rom are sharper than those for the th rom numerically the sv rom yields significantly more accurate results especially for coarser meshes and longer time intervals

structure preserving model reduction of port hamiltonian systems by moment matching at infinity model reduction of port hamiltonian systems by means of the krylov methods is considered aiming at port hamiltonian structure preservation it is shown how to employ the arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the markov parameters but also the port hamiltonian structure for the reduced order model furthermore it is shown how the lanczos method can be applied in a structure preserving manner to a subclass of port hamiltonian systems which is characterized by an algebraic condition in fact for the same subclass of port hamiltonian systems the arnoldi method and the lanczos method turn out to be equivalent in the sense of producing reduced order port hamiltonian models with the same transfer function

non linearly stable reduced order models for incompressible flow with energy conserving finite volume methods abstract a novel reduced order model rom formulation for incompressible flows is presented with the key property that it exhibits non linearly stability independent of the mesh of the full order model the time step the viscosity and the number of modes the two essential elements to non linear stability are 1 first discretise the full order model and then project the discretised equations and 2 use spatial and temporal discretisation schemes for the full order model that are globally energy conserving in the limit of vanishing viscosity for this purpose as full order model a staggered grid finite volume method in conjunction with an implicit runge kutta method is employed in addition a constrained singular value decomposition is employed which enforces global momentum conservation the resulting velocity only rom is thus globally conserving mass momentum and kinetic energy for non homogeneous boundary conditions a one time poisson equation is solved that accounts for the boundary contribution the stability of the proposed rom is demonstrated in several test cases furthermore it is shown that explicit runge kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation

bias and variance of direction of arrival estimates from music min norm and fine we derive variance and bias expressions of direction of arrival doa estimates for min norm and fine these expressions for arbitrarily configured arrays are valid and accurate over wide ranges of snr and number of snapshots using these expressions we illustrate that both min norm and fine have smaller estimate bias and further fine has comparable estimate variance compared to music

tractable bayesian variable selection beyond normality abstractbayesian variable selection often assumes normality but the effects of model misspecification are not sufficiently understood there are sound reasons behind this assumption particularly for large p ease of interpretation analytical and computational convenience more flexible frameworks exist including semi or non parametric models often at the cost of some tractability we propose a simple extension that allows for skewness and thicker than normal tails but preserves tractability it leads to easy interpretation and a log concave likelihood that facilitates optimization and integration we characterize asymptotically parameter estimation and bayes factor rates under certain model misspecification under suitable conditions misspecified bayes factors induce sparsity at the same rates than under the correct model however the rates to detect signal change by an exponential factor often reducing sensitivity these deficiencies can be ameliorated by inferring the error distribution a simp

families of moment matching based structure preserving approximations for linear port hamiltonian systems in this paper we propose a solution to the problem of moment matching with preservation of the port hamiltonian structure in the framework of time domain moment matching we characterize several families of parameterized port hamiltonian models that match the moments of a given port hamiltonian system at a set of finite interpolation points we also discuss the problem of markov parameters matching for linear systems as a moment matching problem for descriptor representations associated with the given system at zero interpolation points solving this problem yields families of parameterized reduced order models that achieve markov parameter matching finally we apply these results to the port hamiltonian case resulting in families of parameterized reduced order port hamiltonian approximations

stability and passivity preserving petrov galerkin approximation of linear infinite dimensional systems this contribution presents two approximation methods for linear infinite dimensional systems that ensure the preservation of stability and passivity the first approach allows one to approximate internal source free infinite dimensional systems such that the resulting approximation is a port controlled hamiltonian system with dissipation the second method deals with the class of systems that are not required to have conjugated outputs but only a dissipative system operator it yields approximations with a dissipative system matrix for which bounds of their stability margin are provided both approaches are based on a state space formulation of the infinite dimensional system this makes it possible to use the petrov galerkin approximation whose free parameters are partly used for achieving the structure preservation since still free parameters remain further application specific objectives such as e g moment matching can be achieved both approaches are applied to the approximation of an euler bernoulli beam

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

model reduction for compressible flows using pod and galerkin projection abstract we present a framework for applying the method of proper orthogonal decomposition pod and galerkin projection to compressible fluids for incompressible flows only the kinematic variables are important and the techniques are well known in a compressible flow both the kinematic and thermodynamic variables are dynamically important and must be included in the configuration space we introduce an energy based inner product which may be used to obtain pod modes for this configuration space we then obtain an approximate version of the navier stokes equations valid for cold flows at moderate mach number and project these equations onto a pod basis the resulting equations of motion are quadratic and are much simpler than projections of the full compressible navier stokes equations

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

nonlinear model reduction via a locally weighted pod method summary in this article we propose a new approach for model reduction of parameterized partial differential equations pdes by a locally weighted proper orthogonal decomposition lwpod method the presented approach is particularly suited for large scale nonlinear systems characterized by parameter variations instead of using a global basis to construct a global reduced model lwpod approximates the original system by multiple local reduced bases each local reduced basis is generated by the singular value decomposition of a weighted snapshot matrix compared with global model reduction methods such as the classical proper orthogonal decomposition lwpod can yield more accurate solutions with a fixed subspace dimension as another contribution we combine lwpod with the chord iteration to solve elliptic pdes in a computationally efficient fashion the potential of the method for achieving large speedups while maintaining good accuracy is demonstrated for both elliptic and parabolic pdes in a few numerical examples copyright 2016 john wiley sons ltd

entropy stable reduced order modeling of nonlinear conservation laws abstract reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model we introduce projection based hyper reduced models of nonlinear conservation laws which are globally conservative and inherit a semi discrete entropy inequality independently of the choice of basis and choice of parameters

structure preserving galerkin pod reduced order modeling of hamiltonian systems abstract the proper orthogonal decomposition reduced order model pod rom has been widely used as a computationally efficient surrogate model in large scale numerical simulations of complex systems however when it is applied to a hamiltonian system a naive application of the pod method can destroy the hamiltonian structure in the reduced order model in this paper we develop a new reduced order modeling approach for hamiltonian systems which modifies the galerkin projection based pod rom so that the appropriate hamiltonian structure is preserved since the pod truncation can degrade the approximation of the hamiltonian function we propose to use a pod basis from shifted snapshots to improve the approximation to the hamiltonian function we further derive a rigorous a priori error estimate for the structure preserving rom and demonstrate its effectiveness in several numerical examples this approach can be readily extended to dissipative hamiltonian systems port hamiltonian systems etc

nonlinear model reduction via discrete empirical interpolation a dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition pod method for constructing reduced order models for time dependent and or parametrized nonlinear partial differential equations pdes in the presence of a general nonlinearity the standard pod galerkin technique reduces dimension in the sense that far fewer variables are present but the complexity of evaluating the nonlinear term remains that of the original problem the original empirical interpolation method eim is a modification of pod that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by pod we propose a discrete empirical interpolation method deim a variant that is suitable for reducing the dimension of systems of ordinary differential equations odes of a certain type as presented here it is applicable to odes arising from finite difference discretization of time dependent pdes and or parametrically dependent steady state problems however the approach extends to arbitrary systems of nonlinear odes with minor modification our contribution is a greatly simplified description of the eim in a finite dimensional setting that possesses an error bound on the quality of approximation an application of deim to a finite difference discretization of the one dimensional fitzhugh nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long time integration that fully captures nonlinear limit cycle behavior we also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results

symplectic model reduction of hamiltonian systems in this paper a symplectic model reduction technique proper symplectic decomposition psd with symplectic galerkin projection is proposed to save the computational cost for the simplification of large scale hamiltonian systems while preserving the symplectic structure as an analogy to the classical proper orthogonal decomposition pod galerkin approach psd is designed to build a symplectic subspace to fit empirical data while the symplectic galerkin projection constructs a reduced hamiltonian system on the symplectic subspace for practical use we introduce three algorithms for psd which are based upon the cotangent lift complex singular value decomposition and nonlinear programming the proposed technique has been proven to preserve system energy and stability moreover psd can be combined with the discrete empirical interpolation method to reduce the computational cost for nonlinear hamiltonian systems owing to these properties the proposed technique is better suited than the classical po

second order statistical analysis of totally weighted subspace fitting methods we analyze the effects of a limited number of snapshots on a general class of multidimensional signal subspace estimation methods termed totally weighted subspace fitting twsf methods this class is an extension of the weighted subspace fitting technique that includes row weighting and column weighting of the signal subspace matrix we quantify the asymptotic statistical properties of the twsf method by means of a second order statistical analysis the main contribution of this article is that it provides for the first time the estimator bias some simulation results are included to validate our analytical results

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

numerical methods in control we study classical control problems like pole assignment stabilization linear quadratic control and h control from a numerical analysis point of view we present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework we also discuss some new algorithmic approaches

structure preserving model reduction for mechanical systems this paper focuses on methods of constructing of reduced order models of mechanical systems which preserve the lagrangian structure of the original system these methods may be used in combination with standard spatial decomposition methods such as the karhunen loeve expansion balancing and wavelet decompositions the model reduction procedure is implemented for three dimensional finite element models of elasticity and we show that using the standard newmark implicit integrator significant savings are obtained in the computational costs of simulation in particular simulation of the reduced model scales linearly in the number of degrees of freedom and parallelizes well

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

bent line quantile regression with application to an allometric study of land mammals speed and mass summary quantile regression which models the conditional quantiles of the response variable given covariates usually assumes a linear model however this kind of linearity is often unrealistic in real life one situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates to analyze such data we propose a bent line quantile regression model we derive its parameter estimates prove that they are asymptotically valid given the existence of a change point and discuss several methods for testing the existence of a change point in bent line quantile regression together with a power comparison by simulation an example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests

least absolute error estimation in the presence of serial correlation abstract in this paper we consider some aspects of least absolute error estimation applied to a regression model with serially correlated errors in addition to the estimation itself we study an estimator of the asymptotic covariance matrix of the estimator a generalized version of the estimator analogous to gls and the properties of several tests for serial correlation both the theoretical and small sample properties are analyzed the latter through a monte carlo experiment

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

geometric integrators for odes geometric integration is the numerical integration of a differential equation while preserving one or more of its geometric properties exactly i e to within round off error many of these geometric properties are of crucial importance in physical applications preservation of energy momentum angular momentum phase space volume symmetries time reversal symmetry symplectic structure and dissipation are examples in this paper we present a survey of geometric numerical integration methods for ordinary differential equations our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade to this end the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature

robust penalized quantile regression estimation for panel data this paper investigates a class of penalized quantile regression estimators for panel data the penalty serves to shrink a vector of individual specific effects toward a common value the degree of this shrinkage is controlled by a tuning parameter it is shown that the class of estimators is asymptotically unbiased and gaussian when the individual effects are drawn from a class of zero median distribution functions the tuning parameter can thus be selected to minimize estimated asymptotic variance monte carlo evidence reveals that the estimator can significantly reduce the variability of the fixed effect version of the estimator without introducing bias

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

a new result on passivity preserving model reduction abstract the problem of model reduction with preservation of passivity is investigated the approach is based on positive real interpolation and is inspired by the similarity between lowner and pick matrices the former are important in problems of general rational interpolation while the latter in problems of interpolation by positive real functions it follows that interpolation of the original set of data together with an appropriately defined mirror image set of data yields automatically positive real interpolants subsequently we show how this result can be implemented using a krylov projection procedure the ensuing model reduction method preserves stability and passivity and can be implemented efficiently for the large scale systems