parameterization of input shapers with delays of various distribution the paper introduces a new concept for composing the input shapers by combining lumped and distributed delays particularly an analytical method is proposed to parametrize zero vibration shapers with delays of various distribution involving these delays in the shaper structure the accommodation part of the shaped response can be smoothened in a predefined manner retarded spectral properties can be achieved and the response length can be optionally adjusted within the given range next following the analytical developments a numerical algorithm based on the constrained linear least squares optimization is proposed for direct design of robust distributed delay shapers

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

system reliability and component importance under dependence a copula approach abstractsystem reliability and component importance are of great interest in reliability modeling especially when the components within the system are dependent we characterize the influence of dependence structures on system reliability and component importance in coherent systems with discrete marginal distributions the effects of dependence are captured through copula theory we extend our framework to coherent multi state system applications of the derived results are demonstrated using a gaussian copula which yields simple interpretations simulations and two examples are presented to demonstrate the importance of modeling dependence when estimating system reliability and ranking of component importance proofs algorithms code and data are provided in supplementary materials available online

transmit signal design for optimal estimation of correlated mimo channels we address optimal estimation of correlated multiple input multiple output mimo channels using pilot signals assuming knowledge of the second order channel statistics at the transmitter assuming a block fading channel model and minimum mean square error mmse estimation at the receiver we design the transmitted signal to optimize two criteria mmse and the conditional mutual information between the mimo channel and the received signal our analysis is based on the recently proposed virtual channel representation which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in the correlated channel however our design framework is applicable to more general channel models which include known channel models such as the transmit and receive correlated model as special cases we show that optimal signaling is in a block form where the block length depends on the signal to noise ratio snr as well as the channel correlation matrix the block signal corresponds to transmitting beams in successive symbol intervals along fixed virtual transmit angles whose powers are determined by nonidentical water filling solutions based on the optimization criteria our analysis shows that these water filling solutions identify exactly which virtual transmit angles are important for channel estimation in particular at low snr the block length reduces to one and all the power is transmitted on the beam corresponding to the strongest transmit angle whereas at high snr the block length has a maximum length equal to the number of active virtual transmit angles and the power is assigned equally to all active transmit angles consequently from a channel estimation viewpoint a faster fading rate can be tolerated at low snrs relative to higher snrs

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

a copula transformation in multivariate mixed discrete continuous models abstract copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions especially if the density function can be represented as the product of the marginal density functions and the copula density function this leads to both an intuitive interpretation of the conditional distribution and convenient estimation procedures however this is no longer the case for copula models with mixed discrete and continuous marginal distributions because the corresponding density function cannot be decomposed so nicely in this paper we introduce a copula transformation method that allows to represent the density function of a distribution with mixed discrete and continuous marginals as the product of the marginal probability mass density functions and the copula density function with the proposed method conditional distributions can be described analytically and the computational complexity in the estimation procedure can be reduced depending on the type of copula used

limited feedback unitary precoding for spatial multiplexing systems multiple input multiple output mimo wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity spatial multiplexing is a common space time modulation technique for mimo communication systems where independent information streams are sent over different transmit antennas unfortunately spatial multiplexing is sensitive to ill conditioning of the channel matrix precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter which is often not realistic this correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter the index of the optimal precoder is conveyed from the receiver to the transmitter over a low delay feedback link criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a rayleigh fading matrix channel the design criteria are shown to be equivalent to packing subspaces in the grassmann manifold using the projection two norm and fubini study distances simulation results show that the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback

the linear model under mixed gaussian inputs designing the transfer matrix suppose a linear model y hx n where inputs x n are independent gaussian mixtures the problem is to design the transfer matrix h so as to minimize the mean square error mse when estimating x from y this problem has important applications but faces at least three hurdles firstly even for a fixed h the minimum mse mmse has no analytical form secondly the mmse is generally not convex in h thirdly derivatives of the mmse w r t h are hard to obtain this paper casts the problem as a stochastic program and invokes gradient methods the study is motivated by two applications in signal processing one concerns the choice of error reducing precoders the other deals with selection of pilot matrices for channel estimation in either setting our numerical results indicate improved estimation accuracy markedly better than those obtained by optimal design based on standard linear estimators some implications of the non convexities of the mmse are noteworthy yet to our knowledge not well known for example there are cases in which more pilot power is detrimental for channel estimation this paper explains why

pilot assisted channel estimation based on second order statistics a survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements the slowly varying channel properties are described by the channel s second order statistics first a detailed comparison of classical linear pilot based channel estimators a novel matched filter and reduced rank rr approaches is made in a common framework with respect to the model they assume for the channel their performance mse and complexity the matched filter channel estimator is introduced which exploits second order statistics with quadratic order of complexity for flat correlated rayleigh fading channels an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided it is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal to noise ratio snr range the effects of these approaches on linear equalization are briefly discussed in the context of direct sequence code division multiple access ds cdma where the focus is on a generalization of the rake receiver in space and time which reduces the channel rank based on its second order statistics resulting in a complexity reduction of the equalizer for this discussion a new notation for the generalized rake is presented which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation we conclude that exploiting second order channel statistics results in significant performance gains and rr channel estimation should only be used together with equalization in the reduced signal subspace

efficient bayesian inference for gaussian copula regression models a gaussian copula regression model gives a tractable way of handling a multivariate regression when some of the marginal distributions are non gaussian our paper presents a general bayesian approach for estimating a gaussian copula model that can handle any combination of discrete and continuous marginals and generalises gaussian graphical models to the gaussian copula framework posterior inference is carried out using a novel and efficient simulation method the methods in the paper are applied to simulated and real data

analysis of multivariate probit models summary this paper provides a practical simulation based bayesian and non bayesian analysis of correlated binary data using the multivariate probit model the posterior distribution is simulated by markov chain monte carlo methods and maximum likelihood estimates are obtained by a monte carlo version of the em algorithm a practical approach for the computation of bayes factors from the simulation output is also developed the methods are applied to a dataset with a bivariate binary response to a four year longitudinal dataset from the six cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the panel survey of income dynamics

multivariate logit copula model with an application to dental data applications of copulas for multivariate continuous data abound but there are only a few that treat multivariate binary data in the present paper we model multivariate binary data based on copulas using mixtures of max infinitely divisible copulas introduced by joe and hu j multivar anal 1996 57 2 240 265 when applying copulas to binary data the marginal distributions also contribute to the dependence measures we propose the use of covariate information in the copula parameters to obtain a direct effect of a covariate on dependence to deal with model uncertainty due to selecting among several candidate models we use a model averaging technique we apply the model to data from the signal tandmobiel dental study and in particular to four binary responses that refer to caries experience in the mandibular and maxillary left and right molars we aim to model kendall s tau associations between them and examine how covariate information affects these associations we found that there are systematically larger associations between the two mandibular and the two maxillary molars using covariates to model these associations more closely we found that the systematic fluoride and age of the children affect the associations note that such relationships could not have been revealed by methods that focus on the marginal models copyright 2008 john wiley sons ltd

solving inverse problems with piecewise linear estimators from gaussian mixture models to structured sparsity a general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper the approach is based on gaussian mixture models which are estimated via a maximum a posteriori expectation maximization algorithm a dual mathematical interpretation of the proposed framework with a structured sparse estimation is described which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques we demonstrate that in a number of image inverse problems including interpolation zooming and deblurring of narrow kernels the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art

training based mimo channel estimation a study of estimator tradeoffs and optimal training signals in this paper we study the performance of multiple input multiple output channel estimation methods using training sequences we consider the popular linear least squares ls and minimum mean square error mmse approaches and propose new scaled ls sls and relaxed mmse techniques which require less knowledge of the channel second order statistics and or have better performance than the conventional ls and mmse channel estimators the optimal choice of training signals is investigated for the aforementioned techniques in the case of multiple ls channel estimates the best linear unbiased estimation blue scheme for their linear combining is developed and studied

inverse feedback shapers for coupled multibody systems the concept of inverse feedback shapers is fully developed in this report for the case of multibody systems with strongly coupled dynamics the presented results constitute a nontrivial extension of the previous papers by the authors on input shaping focusing on effectively decoupled controlled and flexible parts as the main technical result the target mode for the inverse shaper design is identified based on an input output transformation of the multibody system into the controlled subsystem the attached residual oscillatory dynamics and an internal feedback loop representing the dynamical coupling a state feedback controller applied for the selected generalized coordinate is considered throughout this paper

pair copula constructions for multivariate discrete data multivariate discrete response data can be found in diverse fields including econometrics finance biometrics and psychometrics our contribution through this study is to introduce a new class of models for multivariate discrete data based on pair copula constructions pccs that has two major advantages first by deriving the conditions under which any multivariate discrete distribution can be decomposed as a pcc we show that discrete pccs attain highly flexible dependence structures second the computational burden of evaluating the likelihood for an m dimensional discrete pcc only grows quadratically with m this compares favorably to existing models for which computing the likelihood either requires the evaluation of 2 m terms or slow numerical integration methods we demonstrate the high quality of inference function for margins and maximum likelihood estimates both under a simulated setting and for an application to a longitudinal discrete dataset on headache severity this article has onli

joint regression analysis for discrete longitudinal data we introduce an approximation to the gaussian copula likelihood of song li and yuan 2009 biometrics 65 60 68 used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes our approximation allows estimation of parameters from response vectors of length much larger than three and is asymptotically equivalent to the gaussian copula likelihood we estimate regression parameters from the toenail infection data of de backer et al 1996 british journal of dermatology 134 16 17 which consist of binary response vectors of length seven or less from 294 subjects although maximizing the gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation gee estimators our simulation study illustrates that for finite samples gee estimators can actually be as much as 20 more efficient

on training optimization for estimation of correlated mimo channels in the presence of multiuser interference in this paper the problem of estimating multiple input multiple output mimo channels in a realistic environment involving correlated channel fading and multiuser interference is considered four estimation schemes are studied including the linear minimum mean squared error lmmse least squares ls and gauss markov gm estimators as well as a novel scheme which is derived here as an alternative to lmmse estimation the mse optimal training sequences for each of them are provided and their requirements for side information feedback are assessed the new scheme is shown to exhibit a performance comparable to or even better than lmmse at a significantly lower feedback and computational cost the analytical comparison of the estimation schemes is supported by numerous simulation results that cover a wide range of antenna configurations relative interference power and channel correlation strengths the results of this paper provide a complete picture for a palette of estimation schemes with their relative performance and costs of training

joint regression analysis of correlated data using gaussian copulas this article concerns a new joint modeling approach for correlated data analysis utilizing gaussian copulas we present a unified and flexible machinery to integrate separate one dimensional generalized linear models glms into a joint regression analysis of continuous discrete and mixed correlated outcomes this essentially leads to a multivariate analogue of the univariate glm theory and hence an efficiency gain in the estimation of regression coefficients the availability of joint probability models enables us to develop a full maximum likelihood inference numerical illustrations are focused on regression models for discrete correlated data including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes in the simulation studies the proposed copula based joint model is compared to the popular generalized estimating equations which is a moment based estimating equation method to join univariate glms two real world data examples are used in the illustration

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

vines a new graphical model for dependent random variables a new graphical model called a vine for dependent random variables is introduced vines generalize the markov trees often used in modelling high dimensional distributions they differ from markov trees and bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence

estimation of copula models with discrete margins via bayesian data augmentation estimation of copula models with discrete margins can be difficult beyond the bivariate case we show how this can be achieved by augmenting the likelihood with continuous latent variables and computing inference using the resulting augmented posterior to evaluate this we propose two efficient markov chain monte carlo sampling schemes one generates the latent variables as a block using a metropolis hastings step with a proposal that is close to its target distribution the other generates them one at a time our method applies to all parametric copulas where the conditional copula functions can be evaluated not just elliptical copulas as in much previous work moreover the copula parameters can be estimated joint with any marginal parameters and bayesian selection ideas can be employed we establish the effectiveness of the estimation method by modeling consumer behavior in online retail using archimedean and gaussian copulas the example shows that elliptical copulas can be poor at modeling depend

mixture model and least squares based packet video error concealment a gaussian mixture model gmm based spatio temporal error concealment approach has recently been proposed for packet video the method improves peak signal to noise ratio psnr compared to several famous error concealment methods and it is asymptotically optimal when the number of mixture components goes to infinity there are also drawbacks however the estimator has high online computational complexity which implies that fewer surrounding pixels to the lost area than desired are used for error concealment moreover gmm parameters are estimated without considering maximization of the error concealment psnr in this paper we propose a mixture based estimator and a least squares approach for solving the spatio temporal error concealment problem compared to the gmm scheme the new method may base error concealment on more surrounding pixels to the loss while maintaining low computational complexity and model parameters are found by an algorithm that increases psnr in each iteration the proposed method outperforms the gmm based scheme in terms of computation performance tradeoff

mapping based algorithm for large scale computation of quasi polynomial zeros a method for computing all zeros of a retarded quasi polynomial that are located in a large region of the complex plane is presented the method is based on mapping the quasi polynomial and on utilizing asymptotic properties of the chains of zeros first the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi polynomial secondly large regions free of zeros are defined finally the zeros are located as the intersection points of the zero level curves of the real and imaginary parts of the quasi polynomial which are evaluated over the areas of the region outside those free of zeros

training signal design for estimation of correlated mimo channels with colored interference in this paper we study the problem of estimating correlated multiple input multiple output mimo channels in the presence of colored interference the linear minimum mean square error mmse channel estimator is derived and the optimal training sequences are designed based on the mse of channel estimation we propose an algorithm to estimate the long term channel statistics needed for the construction of the optimal training sequences we also design an efficient scheme to feed back the required information to the transmitter where we can approximately construct the optimal sequences numerical results show that the optimal training sequences provide substantial performance gain for channel estimation when compared with other training sequences

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

meta analysis of diagnostic tests accounting for disease prevalence a new model using trivariate copulas in real life and somewhat contrary to biostatistical textbook knowledge sensitivity and specificity and not only predictive values of diagnostic tests can vary with the underlying prevalence of disease in meta analysis of diagnostic studies accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects in this paper a new model is proposed using trivariate copulas and beta binomial marginal distributions for sensitivity specificity and prevalence as an expansion of the bivariate model two different copulas are used the trivariate gaussian copula and a trivariate vine copula based on the bivariate plackett copula this model has a closed form likelihood so standard software e g sas proc nlmixed can be used the results of a simulation study have shown that the copula models perform at least as good but frequently better than the standard model the methods are illustrated by two examples

on mmse estimation a linear model under gaussian mixture statistics in a bayesian linear model suppose observation y hx n stems from independent inputs x and n which are gaussian mixture gm distributed with known matrix h the minimum mean square error mmse estimator for x has analytical form however its performance measure the mmse itself has no such closed form because existing bayesian mmse bounds prove to have limited practical value under these settings we instead seek analytical bounds for the mmse both upper and lower this paper provides such bounds and relates them to the signal to noise ratio snr