simplified estimation and testing in unbalanced repeated measures designs in this paper we propose a simple estimator for unbalanced repeated measures design models where each unit is observed at least once in each cell of the experimental design the estimator does not require a model of the error covariance structure thus circularity of the error covariance matrix and estimation of correlation parameters and variances are not necessary together with a weak assumption about the reason for the varying number of observations the proposed estimator and its variance estimator are unbiased as an alternative to confidence intervals based on the normality assumption a bias corrected and accelerated bootstrap technique is considered we also propose the naive percentile bootstrap for wald type tests where the standard wald test may break down when the number of observations is small relative to the number of parameters to be estimated in a simulation study we illustrate the properties of the estimator and the bootstrap techniques to calculate confidence intervals and conduct hypothesis tests in small and large samples under normality and non normality of the errors the results imply that the simple estimator is only slightly less efficient than an estimator that correctly assumes a block structure of the error correlation matrix a special case of which is an equi correlation matrix application of the estimator and the bootstrap technique is illustrated using data from a task switch experiment based on an experimental within design with 32 cells and 33 participants

approximation theorems for random permanents and associated stochastic processes the limit theorems for certain stochastic processes generated by permanents of random matrices of independent columns with exchangeable components are established the results are based on the martingale decomposition of a random permanent function similar to the one known for u statistics and on relating the components of this decomposition to some multiple stochastic integrals

panel unit root tests in the presence of a multifactor error structure this paper extends the cross sectionally augmented panel unit root test proposed by pesaran 2007 to the case of a multifactor error structure the basic idea is to exploit information regarding the unobserved factors that are shared by other time series in addition to the variable under consideration importantly our test procedure only requires speci cation of the maximum number of factors in contrast to other panel unit root tests based on principal components that require in addition the estimation of the number of factors as well as the factors themselves small sample properties of the proposed test are investigated by monte carlo experiments which suggest that it controls well for size in almost all cases especially in the presence of serial correlation in the error term contrary to alternative test statistics empirical applications to fisher s in ation parity and real equity prices across

partial relaxation approach an eigenvalue based doa estimator framework in this paper the partial relaxation approach is introduced and applied to the direction of arrival estimation problem using spectral search unlike existing spectral based methods such as conventional beamformer capon beamformer or music that can be considered as single source approximation of multi source estimation criteria the proposed approach accounts for the existence of multiple sources at each considered direction the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed which results in closed form estimates for the interference parameters thanks to this relaxation the conventional multi source optimization problem reduces to a simple spectral search following this principle we propose estimators based on the deterministic maximum likelihood weighted subspace fitting and covariance fitting methods to calculate the null spectra efficiently an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods simulation results show that irrespective of any specific structure of the sensor array the performance of the proposed estimators is superior to the conventional methods especially in the case of low signal to noise ratio and low number of snapshots while maintaining a computational cost that is comparable to music

connections between the real positive semidefinite and distance matrix completion problems abstract though the real symmetric positive semidefinite psd matrices and the euclidean distance matrices are closely related exact relationships between the corresponding completion problems are not apparent we establish strong partial relationships of two types this permits the transfer of some insights from one problem to the other and allows computational tools for the psd problem to be used for the distance problem

what are schur complements anyway abstract given a matrix m a b c d the schur complements of a in m are the matrices of the form s d cab where a is a generalized inverse of a we survey several recent characterizations of schur complements and discuss where they arose and how they are related

definiteness and semidefiniteness of quadratic forms revisited abstract it is shown how the schur complement theory can be used for the derivation of criteria for the definiteness or semidefiniteness of the restriction of a quadratic form to the null space of a matrix

bootstrap critical values for tests based on generalized method of moments estimators monte carlo experiments have shown that tests based on generalized method ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used this paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions particular attention is given to the case of dependent data it is shown that with such data the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data the results of monte carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first order asymptotic theory are used the bootstrap also provides an indication of the accuracy of critical values obtained from first order asymptotic theory

dykstra s algorithm for constrained least squares rectangular matrix problems abstract in a recent paper the authors applied dykstra s alternating projection algorithm to solve constrained least squares n n matrix problems we extend these results in two different directions first we make use of the singular value decomposition to solve now constrained least squares rectangular m n matrix problems that arise in several applications second we propose a new and improved implementation of the projection algorithm onto the e positive definite set of matrices this implementation does not require the computation of all eigenvalues and eigenvectors of a matrix per iteration and still guarantees convergence finally encouraging preliminary numerical results are discussed

an iteration method to solve multiple constrained least squares problems abstract in this paper we propose an iteration method to solve the multiple constrained least squares matrix problem we first transform the multiple constrained least squares matrix problems into the multiple constrained matrix optimal approximation problem and then we use the idea of dykstra s algorithm to derive the basic iterative pattern we observe that we only need to solve multiple single constrained least squares matrix problems at each iteration step of the proposed algorithm we give a numerical example to illustrate the effectiveness of the proposed method to solve the original problems also we give an example to illustrate that the method proposed by escalante and li to solve the single constrained least squares matrix problem is not correct

quantum stochastic calculus operation valued stochastic processes and continual measurements in quantum mechanics the physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process ovsp in this article it is shown how the formalism of quantum stochastic calculus of hudson and parthasarathy allows in a simple way for constructing a large class of ovsp s that in particular contains the quantum counting processes of davies and srinivas and continual gaussian measurements this result is obtained by means of a stochastic dilation of the ovsp s at the level of the enlarged system probabilities turn out to be expressed in terms of projection valued measures associated with certain time dependent commuting self adjoint operators

distance matrices and regular figures abstract a regular figure which includes all regular polygons is a set of points on a hypersphere whose center coincides with their centroid we characterize all regular figures as those whose points generate a euclidean distance matrix edm with eigenvector e the vector of all ones restricting the classical maps of schoenberg gower and critchley for all edms to the subcone of edms with eigenvector e yields new geometrical information about the generating points and a simple formula for the radius of the hypersphere

distance geometry for kissing spheres abstract a kissing sphere is a sphere that is tangent to a fixed reference ball we develop in this paper a distance geometry for kissing spheres which turns out to be a generalization of the classical euclidean distance geometry

a quantum analogue of hunt s representation theorem for the generator of convolution semigroups on lie groups in quantum mechanics certain operator valued measures are introduced called instruments which are an analogue of the probability measures of classical probability theory as in the classical case it is interesting to study convolution semigroups of instruments on groups and the associated semigroups of probability operators in this paper the case is considered of a finite dimensional hilbert space n level quantum system and of instruments defined on a finite dimensional lie group then the generator of a continuous semigroup of quantum probability operators is characterized in this way a quantum analogue of hunt s representation theorem for the generator of convolution semigroups on lie groups is obtained

distance shrinkage and euclidean embedding via regularized kernel estimation summary although recovering a euclidean distance matrix from noisy observations is a common problem in practice how well this could be done remains largely unknown to fill in this void we study a simple distance matrix estimate based on the so called regularized kernel estimate we show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances this fact allows us to establish risk bounds for the estimate implying that the true distances can be estimated consistently in an average sense as the number of objects increases in addition such a characterization suggests an efficient algorithm to compute the distance matrix estimator as an alternative to the usual second order cone programming which is known not to scale well for large problems numerical experiments and an application in visualizing the diversity of vpu protein sequences from a recent study of human immunodeficiency virus type 1 further demonstrate the practical merits of the method proposed

computing the nearest euclidean distance matrix with low embedding dimensions euclidean distance embedding appears in many high profile applications including wireless sensor network localization where not all pairwise distances among sensors are known or accurate the classical multi dimensional scaling cmds generally works well when the partial or contaminated euclidean distance matrix edm is close to the true edm but otherwise performs poorly a natural step preceding cmds would be to calculate the nearest edm to the known matrix a crucial condition on the desired nearest edm is for it to have a low embedding dimension and this makes the problem nonconvex there exists a large body of publications that deal with this problem some try to solve the problem directly and some are the type of convex relaxations of it in this paper we propose a numerical method that aims to solve this problem directly our method is strongly motivated by the majorized penalty method of gao and sun for low rank positive semi definite matrix optimization problems the basic geometric object in our study is the set of edms having a low embedding dimension we establish a zero duality gap result between the problem and its lagrangian dual problem which also motivates the majorization approach adopted numerical results show that the method works well for the euclidean embedding of network coordinate systems and for a class of problems in large scale sensor network localization and molecular conformation

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

a lagrangian dual approach to the single source localization problem the single source localization problem sslp which is nonconvex by its nature appears in several important multidisciplinary fields such as signal processing and the global positioning system in this paper we cast sslp as a euclidean distance embedding problem and study a lagrangian dual approach it is proved that the lagrangian dual problem must have an optimal solution under the generalized slater condition we provide a sufficient condition for the zero duality gap and establish the equivalence between the lagrangian dual approach and the existing generalized trust region subproblem gtrs approach studied by beck et al exact and approximate solutions of source localization problems ieee trans signal process vol 56 pp 1770 1778 2008 we also reveal new implications of the assumptions made by the gtrs approach moreover the lagrangian dual approach has a straightforward extension to the multiple source localization problem numerical simulations demonstrate that the lagrangian dual approach can produce localization of similar quality as the gtrs and can significantly outperform the well known semidefinite programming solver for the multiple source localization problem on the tested cases

probability operators and convolution semigroups of instruments in quantum probability in quantum measurement theory a central notion is that of instrument which is a certain kind of operator valued measure in this paper instruments on locally compact groups are studied and as in classical probability theory probability operators associated with instruments are introduced then the generator of a norm continuous semigroup of probability operators is characterized

the best euclidian fit to a given distance matrix in prescribed dimensions abstract in this paper we determine the euclidean distance matrix which is closest to a given not necessarily euclidian one we admit a wide class of appropriate matrix norms as measures of closeness majorization results on sums of eigenvalues of symmetric matrices serve as basic tools

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

eigenstructure of distance matrices with an equal distance subset abstract we characterize the distance matrices with an equal distance subset in terms of eigenstructure and determine edms in this class by examination of a lower dimensional matrix

randomly weighted sums for exchangeable fuzzy random variables many statistical estimators are expressible in the form sn nk 1 ankxnk where ank are constants and xnk are fuzzy random variables then the convergence in probability or with probability one for sn is of interest in determining consistency of the estimators in statistical problems the linear form sn involves possibly random weights and possibly dependent fuzzy random variables which are generated from independent identically distributed fuzzy random variables thus we assume the sequence of fuzzy random variables xnk k 1 to be permutation invariant with respect to distributions instead of assuming independence in particular we look at the stochastic convergence of the form 1 an nk 1 anxnk which is slightly different from the initial form sn

approximation by matrices positive semidefinite on a subspace abstract we obtain the best approximation to a matrix by matrices positive semidefinite on a subspace as a by product we present two new characterizations of euclidean distance matrices

finite metric spaces of strictly negative type abstract we prove that if a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by the infinite extender load vector finite metric spaces that have this property include all spaces on two three or four points all trees and all finite subspaces of euclidean spaces we prove that if the distance matrix is both hypermetric and regular then it is of strictly negative type we show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points in connection with an open problem raised by kelly we conjecture that all finite subspaces of hyperbolic spaces are hypermetric and regular and hence of strictly negative type

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one