high dimensional semiparametric bigraphical models in multivariate analysis a gaussian bigraphical model is commonly used for modelling matrix valued data in this paper we propose a semiparametric extension of the gaussian bigraphical model called the nonparanormal bigraphical model a projected nonparametric rank based regularization approach is employed to estimate sparse precision matrices and produce graphs under a penalized likelihood framework theoretically our semiparametric procedure achieves the parametric rates of convergence for both matrix estimation and graph recovery empirically our approach outperforms the parametric gaussian model for non gaussian data and is competitive with its parametric counterpart for gaussian data extensions to the categorical bigraphical model and the missing data problem are discussed copyright 2013 oxford university press

sparse matrix graphical models matrix variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information in this article we propose a novel sparse matrix graphical model for these types of statistical problems by penalizing respectively two precision matrices corresponding to the rows and columns our method yields a sparse matrix graphical model that synthetically characterizes the underlying conditional independence structure our model is more parsimonious and is practically more interpretable than the conventional sparse vector variate graphical models asymptotic analysis shows that our penalized likelihood estimates enjoy better convergent rates than that of the vector variate graphical model the finite sample performance of the proposed method is illustrated via extensive simulation studies and several real datasets analysis

estimating structured correlation matrices in smooth gaussian random field models this article considers the estimation of structured correlation matrices in infinitely differentiable gaussian random field models the problem is essentially motivated by the stochastic modeling of smooth deterministic responses in computer experiments in particular the log likelihood function is determined explicitly in closed form and the sieve maximum likelihood estimators are shown to be strongly consistent under mild conditions

the ubiquitous kronecker product abstract the kronecker product has a rich and very pleasing algebra that supports a wide range of fast elegant and practical algorithms several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future first the application areas where kronecker products abound are all thriving these include signal processing image processing semidefinite programming and quantum computing second sparse factorizations and kronecker products are proving to be a very effective way to look at fast linear transforms researchers have taken the kronecker methodology as developed for the fast fourier transform and used it to build exciting alternatives third as computers get more powerful researchers are more willing to entertain problems of high dimension and this leads to kronecker products whenever low dimension techniques are tensored together

analysis of linear transformation models with covariate measurement error and interval censoring among several semiparametric models the cox proportional hazard model is widely used to assess the association between covariates and the time to event when the observed time to event is interval censored often covariates are measured with error to handle this covariate uncertainty in the cox proportional hazard model with the interval censored data flexible approaches have been proposed to fill a gap and broaden the scope of statistical applications to analyze time to event data with different models in this paper a general approach is proposed for fitting the semiparametric linear transformation model to interval censored data when a covariate is measured with error the semiparametric linear transformation model is a broad class of models that includes the proportional hazard model and the proportional odds model as special cases the proposed method relies on a set of estimating equations to estimate the regression parameters and the infinite dimensional parameter for handling interval censoring and covariate measurement error a flexible imputation technique is used finite sample performance of the proposed method is judged via simulation studies finally the suggested method is applied to analyze a real data set from an aids clinical trial

testing for nodal dependence in relational data matrices relational data are often represented as a square matrix the entries of which record the relationships between pairs of objects many statistical methods for the analysis of such data assume some degree of similarity or dependence between objects in terms of the way they relate to each other however formal tests for such dependence have not been developed we provide a test for such dependence using the framework of the matrix normal model a type of multivariate normal distribution parameterized in terms of row and column specific covariance matrices we develop a likelihood ratio test lrt for row and column dependence based on the observation of a single relational data matrix we obtain a reference distribution for the lrt statistic thereby providing an exact test for the presence of row or column correlations in a square relational data matrix additionally we provide extensions of the test to accommodate common features of such data such as undefined diagonal entries a nonzero mean multipl

asymptotic behavior of m estimators of p regression parameters when p 2 n is large ii normal approximation in a general linear model y x beta r with y and r n dimensional x a n times p matrix and beta p dimensional let hat beta be an m estimator of beta satisfying 0 sum x i psi y i x i beta let p rightarrow infty such that p log n 3 2 n rightarrow 0 then max i x i hat beta beta rightarrow p 0 and it is possible to find a uniform normal approximation for the distribution of hat beta under which arbitrary linear combinations a n hat beta beta are asymptotically normal when appropriately normalized and hat beta beta x x hat beta beta is approximately chi 2 p

a new representation for the green s function of multilayer media based on plane wave expansion in this paper a new representation for the space domain green s function of general multilayer media is presented this approach is based on an efficient plane wave expansion of the source incident field using the transmission line model for the multilayer medium the effect of the layered medium on the incident plane waves is determined by a transmission coefficient and the amplitude and phase of each plane wave at the field point are obtained the total field is evaluated by summing the resultant plane waves at the field point the main advantage of the proposed method is that the spatial domain green s function of multilayer media can be obtained easily as a summation of simple exponential functions without the need for sommerfeld integration or complex image approximation the plane wave approximation is independent of the parameters of the medium and is valid over a wide frequency range furthermore the exponential form of the plane wave solution makes it possible to compute the method of moments matrix elements analytically for most important types of basis functions in multilayer problems

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

parsimonious tensor response regression abstractaiming at abundant scientific and engineering data with not only high dimensionality but also complex structure we study the regression problem with a multidimensional array tensor response and a vector predictor applications include among others comparing tensor images across groups after adjusting for additional covariates which is of central interest in neuroimaging analysis we propose parsimonious tensor response regression adopting a generalized sparsity principle it models all voxels of the tensor response jointly while accounting for the inherent structural information among the voxels it effectively reduces the number of free parameters leading to feasible computation and improved interpretation we achieve model estimation through a nascent technique called the envelope method which identifies the immaterial information and focuses the estimation based upon the material information in the tensor response we demonstrate that the resulting estimator is asymptotically efficient

a bernstein type inequality and moderate deviations for weakly dependent sequences in this paper we present a bernstein type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded the class considered includes geometrically and subgeometrically strongly mixing sequences the result is then used to derive asymptotic moderate deviation results applications are given for classes of markov chains iterated lipschitz models and functions of linear processes with absolutely regular innovations

estimation of a multiplicative covariance structure in the large dimensional case abstract we propose a kronecker product model for correlation or covariance matrices in the large dimensional case the number of parameters of the model increases logarithmically with the dimension of the matrix we propose a minimum distance md estimator based on a log linear property of the model as well as a one step estimator which is a one step approximation to the quasi maximum likelihood estimator qmle we establish rates of convergence and central limit theorems clt for our estimators in the large dimensional case a specification test and tools for kronecker product model selection and inference are provided in a monte carlo study where a kronecker product model is correctly specified our estimators exhibit superior performance in an empirical application to portfolio choice for s p500 daily returns we demonstrate that certain kronecker product models are good approximations to the general covariance matrix

an asymptotic extraction technique for evaluating sommerfeld type integrals an asymptotic extraction process is developed which leads to an efficient method for the evaluation of the electric field from a hertzian dipole in a layered geometry this technique allows for a rapidly converging expression for the electric field which remains well behaved as the source and observation heights z z coincide a useful application of this method is in the calculation of mutual impedance between printed dipoles

maximum likelihood estimation for the tensor normal distribution algorithm minimum sample size and empirical bias and dispersion recently there has been a growing interest in the analysis of multi dimensional data arrays e g when a univariate response is sampled in 3 d space or when a multivariate response is sampled in time and 2 d space in this article we scrutinize the problem of maximum likelihood estimation mle for the tensor normal distribution of order 3 or more which is characterized by the separability of its variance covariance structure there is one variance covariance matrix per dimension in the 3 d case the system of likelihood equations for the three variance covariance matrices has no analytical solution and therefore needs to be solved iteratively we studied the convergence of an iterative three stage algorithm mle 3d that we propose for this determined the minimum sample size required for matrix estimates to exist and computed by simulation the empirical bias and dispersion of the kronecker product of the three variance covariance matrix estimators in eight scenarios we found that the standardized bias and a matrix measure of dispersion decrease monotonically and tend to vanish with increasing sample size so the kronecker product estimator is consistent an example with 3 d spatial measures of glucose content in the brain is also presented finally results are discussed and the 4 d case is presented with simulation results in an appendix software is available for interested users

efficient evaluation of the finite part of pole free sommerfeld integrals in half space problems with predefined accuracy this communication presents a novel simple and robust approach for the computation of the finite part of pole free sommerfeld integrals sis in half space problems with high and controllable accuracy over a large range of source observer distances the approach includes the following techniques 1 cancellation of the branch point singularities based on the square root change of variables for numerical integration 2 approximation of real axis integration path in order to enhance the singularity cancellation for arbitrary low loss dielectrics 3 thresholds for truncation of the interval of integration for given accuracy which improve the efficiency of computation and 4 prediction formulas that estimate the required number of integration points for a given accuracy up to 1000 wavelengths of source observer distance the proposed approach is verified through numerical examples and comparison to reference methods

high dimensional covariance matrix estimation using a factor model abstract high dimensionality comparable to sample size is common in many statistical problems we examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to as the sample size n increases motivated by the arbitrage pricing theory in finance a multi factor model is employed to reduce dimensionality and to estimate the covariance matrix the factors are observable and the number of factors k is allowed to grow with p we investigate the impact of p and k on the performance of the model based covariance matrix estimator under mild assumptions we have established convergence rates and asymptotic normality of the model based estimator its performance is compared with that of the sample covariance matrix we identify situations under which the factor approach increases performance substantially or marginally the impacts of covariance matrix estimation on optimal portfolio allocation and portfolio risk assessment are studied the asymptotic results are supported by a thorough simulation study

a novel analysis of microstrip structures using the gaussian green s function method a novel closed form expression is derived for spatial green s functions of microstrip structures by expanding the spectral green s function into a gaussian series this innovative method is called the gaussian green s function ggf method due to the gaussian form in the closed form green s function representation the main advantage of the ggf method lies in its precision as well as rapid convergence to demonstrate the versatility of this method the current distribution of a microstrip antenna is achieved via the combination of the method of moments mom and ggf method it is shown that this method can be computationally very efficient with less than 1 error compared to the numerical integration of the spectral integral also the results of the ggf method have been compared to the results of the commercial full wave software of agilent ads