edge preserving and noise reducing reconstruction for magnetic particle imaging magnetic particle imaging mpi is an emerging medical imaging modality which is based on the non linear response of magnetic nanoparticles to an applied magnetic field it is an important feature of mpi that even fast dynamic processes can be captured for 3d volumes the high temporal resolution in turn leads to large amounts of data which have to be handled efficiently but as the system matrix of mpi is non sparse the image reconstruction gets computationally demanding therefore currently only basic image reconstruction methods such as tikhonov regularization are used however tikhonov regularization is known to oversmooth edges in the reconstructed image and to have only a limited noise reducing effect in this work we develop an efficient edge preserving and noise reducing reconstruction method for mpi as regularization model we propose to use the nonnegative fused lasso model and we devise a discretization that is adapted to the acquisition geometry of the preclinical mpi scanner considered in this work we develop a customized solver based on a generalized forward backward scheme which is particularly suitable for the dense and not well structured system matrices in mpi already a non optimized prototype implementation processes a 3d volume within a few seconds so that processing several frames per second seems amenable we demonstrate the improvement in reconstruction quality over the state of the art method in an experimental medical setup for an in vitro angioplasty of a stenosis

statistical inference for infinite dimensional parameters via asymptotically pivotal estimating functions summary suppose that a consistent estimator for an infinite dimensional parameter can be readily obtained via a set of estimating functions which has a good local linear approximation around the true value of the parameter however it may be difficult to estimate the variance function of this estimator well we show that if the set of estimating functions evaluated at the true parameter value is asymptotically pivotal then the fiducial distri bution of the parameter can be used to approximate the distribution of this consistent estimator we present three examples to illustrate that the corresponding inference for the parameter can be made via a simple simulation technique without involving complex high dimensional nonparametric density estimates

instrumental variable quantile regression a robust inference approach abstract in this paper we develop robust inference procedures for an instrumental variables model defined by y d u where d u is strictly increasing in u and u is a uniform variable that may depend on d but is independent of a set of instrumental variables z the proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely the use of the proposed procedures is illustrated through two empirical examples

estimation and inference in semiparametric quantile factor models we propose an estimation methodology for a semiparametric quantile factor panel model we provide tools for inference that are robust to the existence of moments and to the form of weak cross sectional dependence in the idiosyncratic error term we apply our method to crsp daily data

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

on the distribution of a studentized quantile la variance asymptotique du quantile d echantillon depend de la valeur de la densite de population et du quantile de la population on considere l estimateur de siddiqui bloch gastwinth

convex envelopes for edge concave functions deterministic global optimization algorithms frequently rely on the convex underestimation of nonconvex functions in this paper we describe the structure of the polyhedral convex envelopes of edge concave functions over polyhedral domains using geometric arguments an algorithm for computing the facets of the convex envelope over hyperrectangles in 3 is described sufficient conditions are described under which the convex envelope of a sum of edge concave functions may be shown to be equivalent to the sum of the convex envelopes of these functions

discriminative feature representation to improve projection data inconsistency for low dose ct imaging in low dose computed tomography ldct imaging the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images to deal with this problem we propose here a new sinogram restoration approach the sinogram discriminative feature representation s dfr method different from other sinogram restoration methods the proposed method works through a 3 d representation based feature decomposition of the projected attenuation component and the noise component using a well designed composite dictionary containing atoms with discriminative features this method can be easily implemented with good robustness in parameter setting its comparison to other competing methods through experiments on simulated and real data demonstrated that the s dfr method offers a sound alternative in ldct

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

total variation stokes strategy for sparse view x ray ct image reconstruction previous studies have shown that by minimizing the total variation tv of the to be estimated image with some data and or other constraints a piecewise smooth x ray computed tomography image can be reconstructed from sparse view projection data however due to the piecewise constant assumption for the tv model the reconstructed images are frequently reported to suffer from the blocky or patchy artifacts to eliminate this drawback we present a total variation stokes projection onto convex sets tvs pocs reconstruction method in this paper the tvs model is derived by introducing isophote directions for the purpose of recovering possible missing information in the sparse view data situation thus the desired consistencies along both the normal and the tangent directions are preserved in the resulting images compared to the previous tv based image reconstruction algorithms the preserved consistencies by the tvs pocs method are expected to generate noticeable gains in terms of eliminating the patchy artifacts and preserving subtle structures to evaluate the presented tvs pocs method both qualitative and quantitative studies were performed using digital phantom physical phantom and clinical data experiments the results reveal that the presented method can yield images with several noticeable gains measured by the universal quality index and the full width at half maximum merit as compared to its corresponding tv based algorithms in addition the results further indicate that the tvs pocs method approaches to the gold standard result of the filtered back projection reconstruction in the full view data case as theoretically expected while most previous iterative methods may fail in the full view case because of their artificial textures in the results

bayesian quantile regression based nonlinear mixed effects joint models for time to event and longitudinal data with multiple features this article explores bayesian joint models for a quantile of longitudinal response mismeasured covariate and event time outcome with an attempt to i characterize the entire conditional distribution of the response variable based on quantile regression that may be more robust to outliers and misspecification of error distribution ii tailor accuracy from measurement error evaluate non ignorable missing observations and adjust departures from normality in covariate and iii overcome shortages of confidence in specifying a time to event model when statistical inference is carried out for a longitudinal data set with non central location non linearity non normality measurement error and missing values as well as event time with being interval censored it is important to account for the simultaneous treatment of these data features in order to obtain more reliable and robust inferential results toward this end we develop bayesian joint modeling approach to simultaneously estimating all parameters in the three models quantile regression based nonlinear mixed effects model for response using asymmetric laplace distribution linear mixed effects model with skew t distribution for mismeasured covariate in the presence of informative missingness and accelerated failure time model with unspecified nonparametric distribution for event time we apply the proposed modeling approach to analyzing an aids clinical data set and conduct simulation studies to assess the performance of the proposed joint models and method copyright 2016 john wiley sons ltd

quantiles for counts this article studies the estimation of conditional quantiles of counts given the discreteness of the data some smoothness must be artificially imposed on the problem we show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques the performance and implementation of the estimators are illustrated by simulations and an application

cluster robust bootstrap inference in quantile regression models abstractin this article i develop a wild bootstrap procedure for cluster robust inference in linear quantile regression models i show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process the proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much smaller than the sample size an application to project star data is provided supplementary materials for this article are available online

a branch and cut algorithm for nonconvex quadratically constrained quadratic programming we present a branch and cut algorithm that yields in finite time a globally e optimal solution with respect to feasibility and optimality of the nonconvex quadratically constrained quadratic programming problem the idea is to estimate all quadratic terms by successive linearizations within a branching tree using reformulation linearization techniques rlt to do so four classes of linearizations cuts depending on one to three parameters are detailed for each class we show how to select the best member with respect to a precise criterion the cuts introduced at any node of the tree are valid in the whole tree and not only within the subtree rooted at that node in order to enhance the computational speed the structure created at any node of the tree is flexible enough to be used at other nodes computational results are reported that include standard test problems taken from the literature some of these problems are solved for the first time with a proof of global optimality

quantile regression with measurement error regression quantiles can be substantially biased when the covariates are measured with error in this paper we propose a new method that produces consistent linear quantile estimation in the presence of covariate measurement error the method corrects the measurement error induced bias by constructing joint estimating equations that simultaneously hold for all the quantile levels an iterative em type estimation algorithm to obtain the solutions to such joint estimation equations is provided the finite sample performance of the proposed method is investigated in a simulation study and compared to the standard regression calibration approach finally we apply our methodology to part of the national collaborative perinatal project growth data a longitudinal study with an unusual measurement error structure

regression rank scores and regression quantiles we show that regression quantiles which could be computed as solutions of a linear programming problem and the solutions of the corresponding dual problem which we call the regression rank scores generalize the duality of order statistics and of ranks from the location to the linear model noting this fact we study the regression quantile and regression rank score processes in the heteroscedastic linear regression model obtaining some new estimators and interesting comparisons with existing estimators

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

parametric modeling of quantile regression coefficient functions estimating the conditional quantiles of outcome variables of interest is frequent in many research areas and quantile regression is foremost among the utilized methods the coefficients of a quantile regression model depend on the order of the quantile being estimated for example the coefficients for the median are generally different from those of the 10th centile in this article we describe an approach to modeling the regression coefficients as parametric functions of the order of the quantile this approach may have advantages in terms of parsimony efficiency and may expand the potential of statistical modeling goodness of fit measures and testing procedures are discussed and the results of a simulation study are presented we apply the method to analyze the data that motivated this work the described method is implemented in the qrcm r package

generalized bilinear programming part i models applications and linear programming relaxation abstract the evolution of the bilinear programming problem is reviewed and a new more general model is discussed the model involves two decision vectors and reduces to a linear program when one of the decision vectors is fixed the class of problems under consideration contains traditional bilinear programs general quadratic programs and bilinearly constrained and quadratically constrained extensions of these problems we describe how several important applications from the literature including the multiple modular design problem can be modeled as generalized bilinear programs finally we derive a linear programming relaxation that can be used as a subproblem in algorithmic solution schemes based on outer approximation and branch and bound

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

quantile regression under misspecification with an application to the u s wage structure quantile regression qr fits a linear model for conditional quantiles just as ordinary least squares ols fits a linear model for conditional means an attractive feature of ols is that it gives the minimum mean squared error linear approximation to the conditional expectation function even when the linear model is misspecified empirical research using quantile regression with discrete covariates suggests that qr may have a similar property but the exact nature of the linear approximation has remained elusive in this paper we show that qr minimizes a weighted mean squared error loss function for specification error the weighting function is an average density of the dependent variable near the true conditional quantile the weighted least squares interpretation of qr is used to derive an omitted variables bias formula and a partial quantile regression concept similar to the relationship between partial regression and ols we also present asymptotic theory for the qr process under misspecification of the conditional quantile function the approximation properties of qr are illustrated using wage data from the u s census these results point to major changes in inequality from 1990 to 2000

on convex envelopes for bivariate functions over polytopes in this paper we discuss convex envelopes for bivariate functions satisfying suitable assumptions over polytopes we first propose a technique to compute the value and a supporting hyperplane of the convex envelope over a general two dimensional polytope through the solution of a three dimensional convex subproblem with continuously differentiable constraint functions then for quadratic functions as well as for some polynomial and rational ones again satisfying suitable assumptions we show how the same computations can be carried out through the solution of a single semidefinite problem

approximate least trimmed sum of squares fitting and applications in image analysis the least trimmed sum of squares lts regression estimation criterion is a robust statistical method for model fitting in the presence of outliers compared with the classical least squares estimator which uses the entire data set for regression and is consequently sensitive to outliers lts identifies the outliers and fits to the remaining data points for improved accuracy exactly solving an lts problem is np hard but as we show here lts can be formulated as a concave minimization problem since it is usually tractable to globally solve a convex minimization or concave maximization problem in polynomial time inspired by we instead solve lts approximate complementary problem which is convex minimization we show that this complementary problem can be efficiently solved as a second order cone program we thus propose an iterative procedure to approximately solve the original lts problem our extensive experiments demonstrate that the proposed method is robust efficient and scalable in dealing with problems where data are contaminated with outliers we show several applications of our method in image analysis

nonparametric confidence bands for a quantile comparison function this article develops statistical methods useful for comparing the marginals f and g of a bivariate distribution such comparisons are appropriate in the analysis of matched pair data involving a treatment and a control or two treatments the quantile comparison functionq g 1 f proposed by lehmann as a generalized measure of treatment effect in fully randomized experiments is shown to be applicable and also useful in the analysis of matched pair data nonparametric simultaneous confidence bands for q are constructed using asymptotic and permutation methods the copula of the bivariate distribution plays a significant role in the methodology application of the results is illustrated on a dataset from an industrial experiment

a simple slp algorithm for solving a class of nonlinear programs successive linear programming slp algorithms solve nonlinear optimization problems via a sequence of linear programs we present an approach for a special class of nonlinear programming problems which arise in multiperiod coal blending the class of nonlinear programming problems and the solution approach considered in this paper are quite different from previous work the algorithm is very simple easy to apply and can be applied to as large a problem as the linear programming code can handle the quality of solution produced by the proposed algorithm is discussed and the results of some test problems in the real world environment are provided

forecasting for quantile self exciting threshold autoregressive time series models self exciting threshold autoregressive time series models have been used extensively and the conditional mean obtained from these models can be used to predict the future value of a random variable in this paper we consider quantile forecasts of a time series based on the quantile self exciting threshold autoregressive time series models proposed by cai and stander 2008 and present a new forecasting method for them simulation studies and application to real time series show that the method works very well

algorithm enabled low dose micro ct imaging micro computed tomography micro ct is an important tool in biomedical research and preclinical applications that can provide visual inspection of and quantitative information about imaged small animals and biological samples such as vasculature specimens currently micro ct imaging uses projection data acquired at a large number 300 1000 of views which can limit system throughput and potentially degrade image quality due to radiation induced deformation or damage to the small animal or specimen in this work we have investigated low dose micro ct and its application to specimen imaging from substantially reduced projection data by using a recently developed algorithm referred to as the adaptive steepest descent projection onto convex sets asd pocs algorithm which reconstructs an image through minimizing the image total variation and enforcing data constraints to validate and evaluate the performance of the asd pocs algorithm we carried out quantitative evaluation studies in a number of tasks of practical interest in imaging of specimens of real animal organs the results show that the asd pocs algorithm can yield images with quality comparable to that obtained with existing algorithms while using one sixth to one quarter of the 361 view data currently used in typical micro ct specimen imaging

conditional empirical likelihood estimation and inference for quantile regression models abstract this paper considers two empirical likelihood based estimation inference and specification testing methods for quantile regression models first we apply the method of conditional empirical likelihood cel by kitamura et al 2004 empirical likelihood based inference in conditional moment restriction models econometrica 72 1667 1714 and zhang and gijbels 2003 sieve empirical likelihood and extensions of the generalized least squares scandinavian journal of statistics 30 1 24 to quantile regression models second to avoid practical problems of the cel method induced by the discontinuity in parameters of cel we propose a smoothed counterpart of cel called smoothed conditional empirical likelihood scel we derive asymptotic properties of the cel and scel estimators parameter hypothesis tests and model specification tests important features are i the cel and scel estimators are asymptotically efficient and do not require preliminary weight estimation ii by inverting the cel and scel ratio parameter hypothesis tests asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators and iii in contrast to cel the scel method can be implemented by some standard newton type optimization simulation results demonstrate that the scel method in particular compares favorably with existing alternatives

lack of fit tests for quantile regression models the paper novelly transforms lack of fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates accordingly by applying some successful two sample test statistics in the literature two tests are constructed to check the lack of fit for low and high dimensional quantile regression models the low dimensional test works well when the number of covariates is moderate whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size the null distribution of the high dimensional test has an explicit form and the p values or critical values can then be calculated directly the finite sample performance of the tests proposed is examined by simulation studies and their usefulness is further illustrated by two real examples

specification analysis of linear quantile models this paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels these tests may be applied to assess the validity of post estimation inferences regarding the effect of conditioning variables on the distribution of outcomes we show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure monte carlo evidence and an application to the empirical analysis of age earnings curves are included

specification tests of parametric dynamic conditional quantiles this article proposes omnibus specification tests of parametric dynamic quantile models in contrast to the existing procedures we allow for a flexible specification where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data generating process since the null limit distribution of tests is not pivotal we propose a subsampling approximation of the asymptotic critical values a monte carlo study shows that the asymptotic results provide good approximations for small sample sizes finally an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk

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

quantile regression inference with adaptive control of size abstractregression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors this article develops a new estimate of the asymptotic var

jointly constrained biconvex programming this paper presents a branch and bound algorithm for minimizing the sum of a convex function in x a convex function in y and a bilinear term in x and y over a closed set such an objective function is called biconvex with biconcave functions similarly defined the feasible region of this model permits joint constraints in x and y to be expressed the bilinear programming problem becomes a special case of the problem addressed in this paper we prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point the algorithm is proven to converge to a global solution of the nonconvex program we discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs for which the algorithm has been implemented

the maximization of a function over the efficient set via a penalty function approach abstract in this paper we present several equivalent mathematical programming formulations of the problem of maximizing a function over the efficient set in the case of a polytopal feasible region and linear functions penalty function formulations and their properties are given an examination is made of computational aspects epsilon efficiency the appropriateness of the original problem formulation and of nonlinear extensions

penalized weighted least squares approach to sinogram noise reduction and image reconstruction for low dose x ray computed tomography reconstructing low dose x ray computed tomography ct images is a noise problem this work investigated a penalized weighted least squares pwls approach to address this problem in two dimensions where the wls considers first and second order noise moments and the penalty models signal spatial correlations three different implementations were studied for the pwls minimization one utilizes a markov random field mrf gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the pwls cost function by iterative gauss seidel algorithm another employs karhunen loeve kl transform to de correlate data signals among nearby views and minimizes the pwls adaptively to each kl component by analytical calculation where the spatial correlation among nearby bins is modeled by the same gibbs functional the third one models the spatial correlations among image pixels in image domain also by a mrf gibbs functional and minimizes the pwls by iterative successive over relaxation algorithm in these three implementations a quadratic functional regularization was chosen for the mrf model phantom experiments showed a comparable performance of these three pwls based methods in terms of suppressing noise induced streak artifacts and preserving resolution in the reconstructed images computer simulations concurred with the phantom experiments in terms of noise resolution tradeoff and detectability in low contrast environment the kl pwls implementation may have the advantage in terms of computation for high resolution dynamic low dose ct imaging

the inverse optimal value problem this paper considers the following inverse optimization problem given a linear program a desired optimal objective value and a set of feasible cost vectors determine a cost vector such that the corresponding optimal objective value of the linear program is closest to the desired value the above problem referred here as the inverse optimal value problem is significantly different from standard inverse optimization problems that involve determining a cost vector for a linear program such that a pre specified solution vector is optimal in this paper we show that the inverse optimal value problem is np hard in general we identify conditions under which the problem reduces to a concave maximization or a concave minimization problem we provide sufficient conditions under which the associated concave minimization problem and correspondingly the inverse optimal value problem is polynomially solvable for the case when the set of feasible cost vectors is polyhedral we describe an algorithm for the inverse optimal value problem based on solving linear and bilinear programming problems some preliminary computational experience is reported

linear programming based converses for finite blocklength lossy joint source channel coding a linear programming lp based framework is presented for obtaining converses for finite blocklength lossy joint source channel coding problems the framework applies for any loss criterion generalizes certain previously known converses and also extends to multi terminal settings the finite blocklength problem is posed equivalently as a nonconvex optimization problem and using a lift and project like method a close but tractable lp relaxation of this problem is derived lower bounds on the original problem are obtained by the construction of feasible points for the dual of the lp relaxation a particular application of this approach leads to new converses which recover and improve on the converses of kostina and verdu for finite blocklength lossy joint source channel coding and lossy source coding for finite blocklength channel coding the lp relaxation recovers the converse of polyanskiy poor and verdu and leads to a new improvement on the converse of wolfowitz showing thereby that our lp relaxation is asymptotically tight with increasing blocklengths for channel coding lossless source coding and joint source channel coding with the excess distortion probability as the loss criterion using a duality based argument a new converse is derived for finite blocklength joint source channel coding for a class of source channel pairs employing this converse the lp relaxation is also shown to be tight for all blocklengths for the minimization of the expected average symbolwise hamming distortion of a q ary uniform source over a q ary symmetric memoryless channel for any q in mathbb n the optimization formulation and the lift and project method are extended to networked settings and demonstrated by obtaining an improvement on a converse of zhou et al for the successive refinement problem for successively refinable source distortion measure triplets

a linear programming approach to solving bilinear programmes this paper discusses the maximization of a bilinear function over two independent polytopes the maximization problem is converted into a max min problem using duality this problem is then solved via a sequence of dual linear programmes whose constraint vectors are successively determined bytth order optima of a master linear programme

efficient and safe global constraints for handling numerical constraint systems numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques local consistencies and interval methods this paper first recalls the principles of tt quad a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints then it introduces a generalization of tt quad to polynomial constraint systems it also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system different linearization techniques are investigated to limit the number of generated constraints tt quadsolver a new branch and prune algorithm that combines tt quad local consistencies and interval methods is introduced tt quadsolver has been evaluated on a variety of benchmarks from kinematics mechanics and robotics on these benchmarks it outperforms classical interval methods as well as constraint satisfaction problem solvers and it compares well with state of the art optimization solvers

jackknife model averaging for quantile regressions abstract in this paper we consider model averaging for quantile regressions qr when all models under investigation are potentially misspecified and the number of parameters is diverging with the sample size to allow for the dependence between the error terms and regressors in the qr models we propose a jackknife model averaging jma estimator which selects the weights by minimizing a leave one out cross validation criterion function and demonstrate its asymptotic optimality in terms of minimizing the out of sample final prediction error we conduct simulations to demonstrate the finite sample performance of our estimator and compare it with other model selection and averaging methods we apply our jma method to forecast quantiles of excess stock returns and wages

quantile regression with nominated samples an application to a bone mineral density study this paper studies quantile regression analysis with maxima or minima nomination sampling designs these designs are often used to obtain more representative samples from the tails of the underlying distribution using the easy to access rank information during the sampling process we propose new loss functions to incorporate the rank information of nominated samples in the estimation process also we provide an alternative approach that translates estimation problems with nominated samples to corresponding problems under simple random sampling srs strategies are given to choose proper nomination sampling designs for a given population quantile numerical studies show that quantile regression models with maxima or minima nominated samples have higher relative efficiencies compared with their counterparts under srs for analyzing the upper or lower tail quantiles of the distribution of the response variable results are then implemented on a large cohort study in the canadian province of manitoba to analyze quantiles of bone mineral density using available covariates we show that in some cases methods based on nomination sampling designs require about one tenth of the sample used in srs to estimate the lower or upper tail conditional quantiles with comparable mean squared errors this is a dramatic reduction in time and cost compared with the usual srs approach

hierarchical spline models for conditional quantiles and the demand for electricity abstract methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of koenker and bassett spline parameterizations of the conditional quantile functions are used the methods are illustrated by estimating hierarchical models for household electricity demand using data from the chicago metropolitan area the empirical results show that lower quantiles of demand base load vary only slightly across residential households this variability is difficult to explain using household characteristics however upper quantiles of the demand distribution vary considerably and are systematically related to household characteristics and appliance ownership the implications of analyzing mean demand behavior rather than various quantiles of the distribution of demand are also discussed

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

misspecification testing in a class of conditional distributional models we propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates the test is based on the cramer von mises distance between an unrestricted estimate of the joint distribution function of the data and a restricted estimate that imposes the structure implied by the model the procedure is straightforward to implement is consistent against fixed alternatives has nontrivial power against local deviations of order n 1 2 from the null hypothesis and does not require the choice of smoothing parameters in an empirical application we use our test to study the validity of various models for the conditional distribution of wages in the united states

linear double autoregression abstract this paper proposes the linear double autoregression a conditional heteroscedastic model with a conditional mean structure but compatible with the quantile regression the existence of a strictly stationary solution is discussed for which a necessary and sufficient condition is established a doubly weighted quantile regression estimation procedure is introduced where the first set of weights ensures the asymptotic normality of the estimator and the second set improves its efficiency through balancing individual quantile regression estimators across multiple quantile levels bayesian information criteria are proposed for model selection and two goodness of fit tests are constructed to check the adequacy of the fitted conditional mean and conditional scale structures simulation studies indicate that the proposed inference tools perform well in finite samples and an empirical example illustrates the usefulness of the new model

penalized likelihood sinogram restoration for computed tomography we formulate computed tomography ct sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy degraded measurements ct measurement data are degraded by a number of factors including beam hardening and off focal radiation that produce artifacts in reconstructed images unless properly corrected currently such effects are addressed by a sequence of sinogram preprocessing steps including deconvolution corrections for off focal radiation that have the potential to amplify noise noise itself is generally mitigated through apodization of the reconstruction kernel which effectively ignores the measurement statistics although in high noise situations adaptive filtering methods that loosely model data statistics are sometimes applied as an alternative we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function we consider three different strategies for estimating the set of ideal line integrals one based on direct estimation of ideal monochromatic line integrals that have been corrected for single material beam hardening one based on estimation of ideal polychromatic line integrals that can be readily mapped to monochromatic line integrals and one based on estimation of ideal transmitted intensities from which ideal monochromatic line integrals can be readily estimated the first two approaches involve maximization of a penalized poisson likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares pwls objective applied in the transmitted intensity domain we find that at low exposure levels typical of those being considered for screening ct the poisson likelihood based approaches outperform the pwls objective as well as a standard approach based on adaptive filtering followed by deconvolution at higher exposure levels the approaches all perform similarly

a conical algorithm for globally minimizing a concave function over a closed convex set in this paper we are concerned with the problem of finding the global minimum of a concave function over a closed convex possibly unbounded set in rn the intrinsic difficulty of this problem is due to the fact that a local minimum of the objective function may fail to be a global one which makes the conventional methods of local optimization almost useless

a note on the solution of bilinear programming problems by reduction to concave minimization we present a new algorithm for solving the bilinear programming problem by reduction to concave minimization this algorithm is finite does not assume the boundedness of the constraint set and uses an efficient procedure for checking whether a concave function is bounded below on a given halfline some preliminary computational experience with a computer code for implementing the algorithm on a microcomputer is also reported

testing for structural change in regression quantiles abstract most studies in the structural change literature focus solely on the conditional mean while under various circumstances structural change in the conditional distribution or in conditional quantiles is of key importance this paper proposes several tests for structural change in regression quantiles two types of statistics are considered namely a fluctuation type statistic based on the subgradient and a wald type statistic based on comparing parameter estimates obtained from different subsamples the former requires estimating the model under the null hypothesis and the latter involves estimation under the alternative hypothesis the tests proposed can be used to test for structural change occurring in a pre specified quantile or across quantiles which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function both single and multiple structural changes are considered we derive the limiting distributions under the null hypothesis and show they are nuisance parameter free and can be easily simulated a simulation study is conducted to assess the size and power in finite samples

three step censored quantile regression and extramarital affairs this article suggests very simple three step estimators for censored quantile regression models with a separation restriction on the censoring probability the estimators are theoretically attractive i e asymptotically as efficient as the celebrated powell s censored least absolute deviation estimator at the same time they are conceptually simple and have trivial computational expenses they are especially useful in samples of small size or models with many regressors with desirable finite sample properties and small bias the separation restriction costs a small reduction of generality relative to the canonical censored regression quantile model yet its main plausible features remain intact the estimator can also be used to estimate a large class of traditional models including the normal amemiya tobin model and many accelerated failure and proportional hazard models we illustrate the approach with an extramarital affairs example and contrast our findings with those of fair

quasiconvex relaxations based on interval arithmetic abstract interval analysis provides a tool for i forward error analysis ii estimating and controlling rounding and approximation errors automatically and iii proving existence and uniqueness of solutions in this context the terms self validating methods inclusion methods orverification methods are in use in this paper we present a new self validating method for solving global constrained optimization problems this method is based on the construction of quasiconvex lower bound and quasiconcave upper bound functions of a given function the latter defined by an arithmetical expression no further assumptions about the nonlinearities of the given function are necessary these lower and upper bound functions are rigorous by using the tools of interval arithmetic in its easiest form they are constructed by taking appropriate linear and or quadratical estimators which yield quasiconvex quasiconcave bound functions we show how these bound functions can be used to define rigorous quasiconvex relaxations for constrained global optimization problems and nonlinear systems these relaxations can be incorporated in a branch and bound framework yielding a self validating method

quantile regression for dynamic panel data with fixed effects abstract this paper studies a quantile regression dynamic panel model with fixed effects panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors to reduce the dynamic bias we suggest the use of the instrumental variables quantile regression method of chernozhukov and hansen 2006 along with lagged regressors as instruments in addition we describe how to employ the estimated models for prediction monte carlo simulations show evidence that the instrumental variables approach sharply reduces the dynamic bias and the empirical levels for prediction intervals are very close to nominal levels finally we illustrate the procedures with an application to forecasting output growth rates for 18 oecd countries

bayesian quantile regression for longitudinal studies with nonignorable missing data summary we study quantile regression qr for longitudinal measurements with nonignorable intermittent missing data and dropout compared to conventional mean regression quantile regression can characterize the entire conditional distribution of the outcome variable and is more robust to outliers and misspecification of the error distribution we account for the within subject correlation by introducing a l2 penalty in the usual qr check function to shrink the subject specific intercepts and slopes toward the common population values the informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects we assess the performance of the proposed method using simulation studies and illustrate it with data from a pediatric aids clinical trial