a statistical approach to subspace based blind identification blind identification of single input multiple output systems is considered herein the low rank structure of the output signal is exploited to blindly identify the channel using a subspace fitting framework two approaches based on a minimal linear parameterization of a subspace are presented and analyzed the asymptotically best consistent estimate is derived for the class of blind subspace based techniques the asymptotic estimation error covariance of the subspace estimates is derived and the corresponding covariance of the statistically optimal estimates provides a lower bound on the estimation error covariance of subspace methods a two step procedure involving only linear systems of equations is presented that asymptotically achieves the bound simulations and numerical examples are provided to compare the two approaches

new approaches without postprocessing to fir system identification using selected order cumulants in this paper we address the problem of identifying the parameters of the nonminimum phase fir system from the cumulants of noisy output samples the system is driven by an unobservable zero mean independent and identically distributed i i d non gaussian signal the measurement noise may be white gaussian colored ma arma gaussian processes or even real for this problem two novel methods are proposed the methods are designed by using higher order cumulants with the following advantages i flexibility method 1 employs two arbitrary adjacent order cumulants of output whereas method 2 uses three cumulants of output two cumulants with arbitrary orders and the other one with an order equal to the summation of the two orders minus one because of this flexibility we can select cumulants with appropriate orders to accommodate different applications ii linearity both the formulations in method 1 and method 2 are linear with respect to the unknowns unlike the existing cumulant based algorithms the post processing is thus avoided extensive experiments with arma gaussian and three real noises show that the new algorithms especially algorithm 1 perform the fir system identification with higher efficiency and better accuracy as compared with the related algorithms in the literature

optimal grouping of income and wealth data abstract optimal grouping of income and wealth data under the general criterion of maximizing an inequality index for the grouped data is investigated this approach guarantees that the optimal groups correspond to nonoverlapping income ranges and minimizes the loss of distributional detail an algorithm is provided which will identify the optimal grouping arrangement precisely when the gini coefficient is used the algorithm is applied to a large microdata set statistics canada s 1984 survey of consumer finance which reports both income and wealth official and optimal groupings are compared and guidelines are suggested for devising groupings which may in practice approximate the optimal arrangement

asymptotically optimal blind fractionally spaced channel estimation and performance analysis when the received data are fractionally sampled the magnitude and phase of most linear time invariant fir communications channels can be estimated from second order output only statistics we present a general cyclic correlation matching algorithm for known order fir blind channel identification that has closed form expressions for calculating the asymptotic variance of the channel estimates we show that for a particular choice of weights the weighted matching estimator yields at least for large samples the minimum variance channel estimator among all unbiased estimators based on second order statistics furthermore the matching approach unlike existing methods provides a useful estimate even when the channel is not uniquely identifiable from second order statistics

nonparametric tests of stochastic dominance in income distributions tests for stochastic dominance based upon extensions of the goodness of fit test to the nonparametric comparison of income distributions are proposed implemented and compared with indirect tests of second order stochastic dominance currently utilized in income distribution studies

on the measurement of polarization suppose that a population of individuals may be grouped according to some vector of characteristics into clusters such that each cluster is very similar in terms of the attributes of its members but different clusters have members with very dissimilar attributes in that case we say that the society is polarized our purpose is to study polarization and to provide a theory of its measurement our contention is that polarization as conceptualized here is closely related to the generation of social tensions to the possibilities of revolution and revolt and to the existence of social unrest in general we take special care to distinguish our theory from the theory of inequality measurement we derive measures of polarization that are easily applicable to distributions of characteristics such as income and wealth

on blind identifiability of multipath channels using fractional sampling and second order cyclostationary statistics the problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered fractionally sampled data are cyclostationary rather than stationary the problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input information sequence and multiple outputs by using a time series representation of a cyclostationary process a necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived this result provides an alternative but equivalent statement of an existing result using this result it is shown that certain class of multipath channels cannot be identified from the second order statistics irrespective of how the sampling rate is chosen

fast and low complexity blind equalization via subgradient projections we propose a novel blind equalization method based on subgradient search over a convex cost surface this is an alternative to the existing iterative blind equalization approaches such as the constant modulus algorithm cma which often suffer from the convergence problems caused by their nonconvex cost functions the proposed method is an iterative algorithm called subgradient based blind algorithm sgba for both real and complex constellations with a very simple update rule it is based on the minimization of the l sub spl infin norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations the algorithm has a nice convergence behavior attributed to the convex l sub spl infin cost surface as well as the step size selection rules associated with the subgradient search we illustrate the performance of the algorithm using examples with both complex and real constellations where we show that the proposed algorithm s convergence is less sensitive to initial point selection and a fast convergence behavior can be achieved with a judicious selection of step sizes furthermore the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes

blind equalization and estimation of fir communications channels using fractional sampling we consider the problem of blind estimation and equalization of digital communication finite impulse response fir channels using fractionally spaced samples fractionally sampled data are cyclostationary rather than stationary the problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input information sequence and multiple outputs by using a time series representation of a cyclostationary process the channel parameters are estimated by first estimating various subchannels using the second and the fourth order cumulant function of the received data and then appropriately aligning and scaling them the estimated channel impulse response is then used to construct a linear equalizer two illustrative simulation examples using four and 16 qam signals are presented where effect of symbol timing phase offset is studied via simulations

cumulant based identification approaches for nonminimum phase fir systems recursive and least squares methods for identification of non minimum phase linear time invariant nmp lti fir systems are developed the methods utilize the second and third order cumulants of the output of the fir system whose input is an independent identically distributed i i d non gaussian process since knowledge of the system order is of utmost importance to many system identification algorithms new procedures for determining the order of an fir system using only the output cumulants are also presented to illustrate the effectiveness of the methods various simulation examples are presented

a cumulant interference subspace cancellation method for blind siso channel estimation we present a new linear method for blind estimation of single input single output siso finite impulse response fir channel the channel can be minimum phase or nonminimum phase channel the proposed method is based on a series of fourth order cumulant matrices where it is shown that by employing vectors chosen from the left null space of a concatenated cumulant matrix the interference subspace of the channel convolution matrix can be cancelled and thus channel information can be extracted the proposed method is robust to channel order overestimation and it has a similar computational complexity as other existing methods simulation results are included to validate the performance of the proposed algorithm

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

fir channel estimation through generalized cumulant slice weighting we study the problem of linear channel estimation with unknown channel input signals our work stems from the weighted slice algorithm in which cumulant slices of different orders are linearly combined to produce an estimate of a single input single output channel aiming to improve the reliability of estimation the new approach incorporates a certain matrix structure constraint into its weight computation criterion it provides more reliable results for channels with weak leading coefficients this generalized algorithm maintains the advantage of fonollosa and vidal s algorithm in handling the situation with channel order overestimation its natural extension to multiple input multiple output channel estimation is presented along with the channel identifiability conditions required

statistical inference for stochastic dominance and for the measurement of poverty and inequality we derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty welfare and inequality this includes estimators of most of the poverty indices currently in use as well as estimators of the curves used to infer stochastic dominance of any order these curves can be used to determine whether poverty inequality or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines we also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another the sampling distribution of convenient dual estimators for the measurement of poverty is also established the statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes our results are briefly illustrated using data for four countries drawn from the luxembourg income study data bases

mean square stabilizability via output feedback for a non minimum phase networked feedback system this work studies mean square stabilizability via output feedback for a networked linear time invariant lti feedback system with a non minimum phase plant in the feedback system the control signals are transmitted to the plant over a set of parallel communication channels with possible packet dropout our goal is to analytically describe intrinsic constraints among channel packet dropout probabilities and the plant s characteristics in the mean square stabilizability of the system it turns out that this is a very hard problem here we focus on the case in which the plant has relative degree one and each non minimum zero of the plant is only associated with one of control input channels then the admissible region of packet dropout probabilities in the mean square stabilizability of the system is obtained moreover a set of hyper rectangles in this region is presented in terms of the plant s non minimum phase zeros unstable poles and wonham decomposition forms which is related to the structure of controllable subspace of the plant a numerical example is presented to illustrate the fundamental constraints in the mean square stabilizability of the networked system

simple dependent pairs of exponential and uniform random variables the accurate characterization of input processes for simulation models can require the representation of dependencies among input values results are presented on the generation of dependent exponential and uniform pairs of random variates a random coefficient linear function of two independent exponential variables yielding a third exponential variable is used in the construction of simple dependent pairs of exponential variables to model negative dependency the constructions employ antithetic exponential variables by employing negative exponentiation the constructions yield simple multiplicative based models for dependent uniform pairs the ranges of dependency allowable in the models are assessed by correlation calculations both of the product moment and spearman types broad ranges within the theoretically allowable ranges are found because of their simplicity all models are particularly suitable for simulation and are free of point and line concentrations of probabilities

polarization concepts measurement estimation distributions can be described using density functions the main theorem uniquely characterizes a class of polarization measures that fits into what we call the identityalienation framework and simultanously satisfies a set of axioms second we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities distribution free statistical inference results are also used in order to ensure that the orderings of polarization across entities are not simply due to sampling noise an illustration of the use of these tools using data from 21 countries shows that polarization and inequality orderings can often differ in practice

identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

optimal grouping of income distribution data abstract we consider the problem of grouping income distribution data into a given number of groups such that the concealed income differences due to grouping are minimized when income differences are measured by gini s pairwise differences this means minimizing the area between the grouped and ungrouped lorenz curves in this case the necessary condition for optimal grouping is that each group limit be equal to the average income in its two adjacent groups an iterative procedure for computation and applications including fractile groupings are discussed alternative optimal groupings based on other measures of income differences are also considered

new precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal fir equalizers in this paper we propose a new precoding method for intersymbol interference isi cancellation by using non maximally decimated multirate filterbanks unlike the existing preceding methods such as the th and trellis precodings the new preceding i may be independent of the isi channel ii is linear and does not have to implement any modulo operation iii gives the ideal fir equalization at the receiver for any fir isi channel including spectral null channels iv expands the transmission bandwidth in a minimum amount the precoding is built on non maximally decimated multirate filterbanks based on multirate filterbank theory we present a necessary and sufficient condition on an fir isi transfer function in terms of its zero set such that there is a linear fir n spl times m precoder so that an ideal fir equalizer exists where the integers k and n are arbitrarily fixed the condition is easy to check as a consequence of the condition for any given fir isi transfer function not identically 0 there always exist such linear fir precoders moreover for almost all given fir isi transfer functions there exist linear fir precoders with size n spl times n 1 i e the bandwidth is expanded by 1 n in addition to the conditions on the isi transfer functions a method for the design of the linear fir precoders and the ideal fir equalizers is also given numerical examples are presented to illustrate the theory

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

blind equalization using a tricepstrum based algorithm an adaptive blind equalization method is introduced for nonminimum phase communication channels the method estimates the inverse channel impulse response by using the complex cepstrum of the fourth order cumulants tricepstrum of the synchronously sampled received signal as such the proposed adaptive method depends only on the statistics of the received sequence and is capable of reconstructing separately both the minimum and maximum phase response of the channel it is demonstrated by means of extensive simulations that the proposed tricepstrum based equalization scheme performs well and outperforms other existing blind equalizers at the expense of higher computational complexity

sampling variance and decomposable inequality measures abstract the purpose of this paper is twofold 1 to draw together and interpret results on sampling variance of this important class of inequality measures and 2 to illustrate the way in which the bivariate nature of the underlying problem affects the estimates of inequality measures and their sample variances

higher order spectrum estimation via noncausal autoregressive modeling and deconvolution a method for nonminimum phase finite impulse response fir system identification is introduced that is based on noncausal autoregressive ar modeling of the third moments of the output data the magnitude and phase response of the fir system are expressed in terms of the parameters of a noncausal ar model the set of ar parameters is obtained by solving an overdetermined linear system of equations that is formed using third moment estimates of the output data the performance of the method is illustrated with simulation examples

beyond the limitations of perturbation methods for real random eigenvalue problems using exceptional points and analytic continuation a numerical method is proposed to approximate the solution of parametric eigenvalue problem when the variability of the parameters exceed the radius of convergence of low order perturbation methods the radius of convergence of eigenvalue perturbation methods based on taylor series is known to decrease when eigenvalues are getting closer to each other this phenomenon knwon as veering in structural dynamics is a direct consequence of the existence of branch point singularity in the complex plane of the varying parameters where some eigenvalues are defective when this degeneracy referred to as exceptional point ep is close to the real axis the veering becomes stronger the main idea of the proposed approach is to combined a pair of eigenvalues to remove this singularity to do so two analytic auxiliary functions are introduced and are computed through high order derivatives of the eigenvalue pair with respect to the parameter this yields a new robust eigenvalue reconstruction scheme which is compared to taylor and puiseux series in all cases theoretical bounds are established and all approximations are compared numerically on a three degrees of freedom toy model this system illustrate the ability of the method to handle the vibrations of a structure with a randomly varying parameter computationally efficient the proposed algorithm could also be relevant for actual numerical models of large size arising from other applications involving parametric eigenvalue problems e g waveguides rotating machinery or instability problems such as squeal or flutter

two criteria for evaluating risk prediction models summary we propose and study two criteria to assess the usefulness of models that predict risk of disease incidence for screening and prevention or the usefulness of prognostic models for management following disease diagnosis the first criterion the proportion of cases followed pcf q is the proportion of individuals who will develop disease who are included in the proportion q of individuals in the population at highest risk the second criterion is the proportion needed to follow up pnf p namely the proportion of the general population at highest risk that one needs to follow in order that a proportion p of those destined to become cases will be followed pcf q assesses the effectiveness of a program that follows 100q of the population at highest risk pnf p assess the feasibility of covering 100p of cases by indicating how much of the population at highest risk must be followed we show the relationship of those two criteria to the lorenz curve and its inverse and present distribution theory for estimates of pcf and pnf we develop new methods based on influence functions for inference for a single risk model and also for comparing the pcfs and pnfs of two risk models both of which were evaluated in the same validation data

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

recovering the poles from third order cumulants of system output the problem of identifying the poles of single input single output siso linear stochastic systems from the higher order statistics of noisy observations is considered it is assumed that the system is driven by an independent and identically distributed non gaussian process with nonzero third order cumulant function at zero lag there is no other restriction of the probability distribution of the driving noise the system is assumed to be of known order causal and exponentially stable but is not required to be minimum phase the system output is observed in additive possibly non gaussian noise it is shown that if there are no pole zero cancellations in the transfer function of the given system then it is necessary and sufficient for a block hankel matrix to have rank equal to the system order where the matrix is constructed from a partial set of third order cumulants of the noisy output sequence this fundamental result then leads to a linear solution to the problem of estimating the coefficients of the system characteristic polynomial from which the system poles can be found via root finding

a novel recursive approach to estimating ma parameters of causal arma models from cumulants the estimation of ma moving average parameters of causal arma autoregressive moving average models using the third order cumulants alone is treated a novel recursive approach is proposed under certain conditions the approach applies to noncausal models

statistical inference for testing inequality indices with dependent samples this paper develops asymptotically distribution free inference for testing inequality indices with dependent samples it considers the interpolated gini coefficient and the generalized entropy class which includes several commonly used inequality indices we first establish inference tests for changes in inequality indices with completely dependent samples i e matched pairs and then generalize the inference procedures to cases with partially dependent samples the effects of sample dependency on standard errors of inequality changes are examined through simulation studies as well as through applications to the cps and psid data

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

approaches of fir system identification with noisy data using higher order statistics the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is discussed the system is driven by an independently identically distributed nongaussian sequence that is not observed the noise is additive and may be colored and nongaussian following some existing linear parametric approaches to this problem a linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known both recursive closed form and batch least squares versions of the parameter estimators are presented the existing and the proposed linear methods utilize only a partial set of the relevant output statistics this restriction being necessary to obtain a linear estimator whereas there exist nonlinear method that exploit a much larger set of output statistics a simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods is presented

arma bispectrum approach to nonminimum phase system identification an identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase fir finite impulse response system the method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving average arma models the magnitude and phase response of the system are expressed in terms of the ar parameters of the arma models in particular the ar part of the causal arma model captures the minimum phase component of the system and the ar part of the anticausal arma captures the maximum phase component both sets of parameters are obtained by solving overdetermined linear systems of equations a model order selection criterion based on third order moments is proposed the arma bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction it is demonstrated that the proposed identification procedure exhibits improved modeling performance the method does not require knowledge of the non gaussian noise distribution

closed form recursive estimation of ma coefficients using autocorrelations and third order cumulants the authors derive a simple recursive closed form algorithm for estimating the parameters of a moving average ma model of known order using only the autocorrelation and the 1 d diagonal slice of the third order cumulant of its response to excitation by an unobservable non gaussian iid process the output may be corrupted by zero mean nonskewed white noise of unknown variance the autoregressive moving average arma case is briefly discussed

blind equalization and estimation of digital communication fir channels using cumulant matching we consider the problem of blind estimation and equalization of digital communication fir finite impulse response channels the channel parameters are estimated by nonlinear batch optimization of a quadratic cumulant matching criterion involving second and fourth order cumulants of the received data a new algorithm is proposed for asymptotically globally convergent linear estimation of the fir channel parameters where the fir model order is not necessarily known the nonlinear cumulant matching algorithm is initialized by the linear parameter estimator the estimated channel impulse response is then used to construct a linear equalizer two illustrative simulation examples using 4 16 and 64 qam signals are presented

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

bussgang zero crossing equalization an integrated hos sos approach an integrated higher order statistics hos and second order statistics sos based equalization technique is presented as an extension of the bussgang equalization algorithm this extension allows one to simultaneously take account of the statistical knowledge about the data source as done in the conventional hos approaches and in particular by bussgang like equalization algorithms such as super exponential constant modulus etc and the spectral redundancy usually present in pulse amplitude modulation pam and quadrature amplitude modulation qam modulated signals exploited by sos based approaches the technique presented employs a new form of sos equalization that naturally integrates into the bussgang scheme it is based on a zero crossing zc property of the received signal when it is passed through a suitable filter the novel equalization scheme is presented in a bayesian estimation framework after illustration of the general bussgang paradigm and of the principles of the zc approach from simulated experiments results show that the extended bussgang zc equalizer not only outperforms conventional bussgang equalizers but is also robust to situations where hos and sos approaches individually fail

nonminimum phase fir channel estimation using cumulant matrix pencils this paper studies the blind estimation of single input single output channels with finite impulse response fir and nonminimum phase based on higher order statistics we introduce a new algorithm that exploits a matrix pencil constructed from a set of cumulant matrices by solving a generalized eigenvalue problem channel estimates up to a scalar ambiguity can be obtained from nontrivial generalized eigenvectors of this cumulant matrix pencil with multiple estimation results available different schemes are given to extract channel information effectively the proposed algorithm does not require exact knowledge of the channel length and can function properly under channel length overestimation numerical simulations demonstrate the robustness of this new algorithm to various adverse conditions

nonparametric estimation and inference about the overlap of two distributions this paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques this quantity has been proposed as a measure of economic polarization between two groups anderson 2004 and anderson et al 2010 in ecology it has been used to measure the overlap of species we give the asymptotic distribution theory of our estimator which in some cases of practical relevance is nonstandard due to a boundary value problem we also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider we investigate the finite sample properties of our methods by simulation methods we give an application to the study of polarization within china in recent years using household survey data from two provinces taken in 1987 and 2001 we find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space

consistent parameter estimation for non causal autoregressive model via higher order statistics abstract the problem of estimating the parameters of a non causal autoregressive ar model given the noisy observations of the system output is considered the system is driven by an i i d independent and identically distributed non gaussian sequence that is not observed the measurement noise is additive i i d and possibly non gaussian a parameter estimator that involves simultaneous matching of data autocorrelations and third order auto cumulants was recently proposed for the estimation of the parameters of non causal ar models in the proposed method the maximum cumulant lag used in cumulant matching was specified as large but finite in this paper we give a specific lower bound to the maximum cumulant lag and we prove the strong consistency of the parameter estimator under the specified choice of lags some recently developed fundamental results concerning the recovery of the poles of a causal system from the third order statistics of the system output play a crucial role in this paper

large sample properties of two inequality indices this paper provides the large sample properties of two inequality indices atkinson s 1970 index and the generalized entropy index cowell and kuga 1981 shorrocks 1984 the large sample properties of the equally distributed equivalent e d e income measures associated with these indices are also derived the asymptotic distributions of these inequality and welfare measures allow the construction of confidence intervals and tests for differences in the measures these confidence intervals and tests are asymptotically distribution free given the increasing availability of large micro data sets on incomes these results are directly applicable to empirical work on income distributions the sampling distributions of some inequality indices such as the gini coefficient and pietra index are known but the ethical bases of these indices have been subject to criticism and some researchers may prefer the atkinson or generalized entropy indices on ethical grounds these researchers are confronted with a choice between using an ethically unattractive index with a known sampling distribution or using an ethically preferable index whose sampling properties are unknown the increasing use of the atkinson and generalized entropy indices in empirical analyses of income distributions suggests many are choosing the second option it then becomes important to understand the sampling properties of these indices so that statistical inference procedures may be applied the analysis in this paper complements the recent research on sampling properties and inference for lorenz curves for example beach and davidson 1983 and gastwirth and gail 1985 propose tests for equality of lorenz curves and beach and richmond 1985 provide joint confidence intervals for the lorenz ordinate vector bishop chakraborti and thistle 1987 1988a 1988b and bishop formby and thistle 1989 provide a number of extensions these papers utilize results from the theory of linear functions of order statistics 2 however this approach is not directly applicable to the atkinson and generalized entropy indices these indices are not linear functions of order statistics the atkinson and generalized entropy indices are functions of fractional and negative moments of the distribution and their large sample properties follow from the properties of the sample moments

a cholesky factorization based approach for blind fir channel identification for blind channel identification various techniques including transmitter induced cyclostationarity based approaches have been proposed in literature to induce cyclostationarity at the transmitter zero padding to every symbol packet can be considered some subspace methods are proposed for the channel estimation by exploiting the induced cyclostationarity due to zero padding the covariance matrix of received signal vectors can have a special structure utilizing this structure we can estimate channel impulse responses through factorization in this correspondence we propose a factorization based approach to estimate channel impulse responses in general the proposed factorization based approach can work with a small number of samples and becomes much more computationally efficient than the subspace method when the length of packets is long

fir system identification using higher order cumulants a generalized approach estimation of the parameters of an fir system driven by a white non gaussian process using only higher order cumulants of its corrupted output is considered new methods which generalize existing methods and which do not impose any restriction on the additive gaussian noise are proposed and their performance studied

adaptive iir algorithms based on high order statistics recursive estimation algorithms are derived for moving average and autoregressive moving average processes these algorithms can be used for adaptive infinite impulse response iir filtering of non gaussian processes the behavior of these algorithms is illustrated by extensive numerical examples

identification and deconvolution of multichannel linear non gaussian processes using higher order statistics and inverse filter criteria this paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple input multiple output mimo system given only the measurements of the vector output of the system the system is assumed to be driven by a temporally i i d and spatially independent non gaussian vector sequence which is not observed an iterative inverse filter criteria based approach is developed using the third order or the fourth order normalized cumulants of the inverse filtered data at zero lag stationary points of the proposed cost functions are investigated the approach is input iterative i e the input sequences are extracted and removed one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed the strong consistency of the proposed approach is also briefly discussed computer simulation examples are presented to illustrate the proposed approaches

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

singular value decomposition based ma order determination of non gaussian arma models singular value decomposition svd based moving average ma order determination of non gaussian processes using higher order statistics is addressed it is shown that the ma order determination of autoregressive moving average arma models is equivalent to the rank determination of a certain error matrix and a svd approach is proposed its simplified form is applied to pure ma models to improve the robustness of the order selection a combination of the svd and the product of diagonal entries pode test is proposed some interesting applications of the two svd approaches are presented and simulations verify their performance

coupling of eigenvalues of complex matrices at diabolic and exceptional points the paper presents a general theory of coupling of eigenvalues of complex matrices of an arbitrary dimension depending on real parameters the cases of weak and strong coupling are distinguished and their geometric interpretation in two and three dimensional spaces is given general asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios two physical examples illustrate effectiveness and accuracy of the presented theory

sensitivity analysis of generalised eigenproblems and application to wave and finite element models abstract the first and second order sensitivity analysis of the eigenvalue problem of generalised non symmetric matrices using perturbation theory is developed these results are then applied to sensitivity analysis of wave propagation in structures modelled using the wave and finite element wfe method three formulations of the wfe eigenvalue problem are considered the transfer matrix method the projection method and zhong s method the sensitivities with respect to system parameters of wavenumbers and wave mode shapes are derived expressions for the group velocity are presented numerical results for a thin beam a foam core panel and a cross laminated timber panel are used to demonstrate the proposed approach it is shown that sensitivities can be calculated at negligible computational cost

blind identification of simo systems and simultaneous estimation of multiple time delays from hos based inverse filter criteria higher order statistics based inverse filter criteria ifc have been effectively used for blind equalization of single input multiple output simo systems recently chi and chen reported a relationship between the unknown simo system and the optimum equalizer designed by the ifc for finite signal to noise ratio snr in this paper based on this relationship an iterative fast fourier transform fft based nonparametric blind system identification bsi algorithm and an fft based multiple time delay estimation mtde algorithm are proposed with a given set of non gaussian measurements the proposed bsi algorithm allows the unknown simo system to have common subchannel zeros and its performance estimation accuracy is superior to that of the conventional ifc based methods the proposed mtde algorithm can simultaneously estimate all the p 1 time delays with respect to a reference sensor with space diversity of sensors exploited therefore its performance estimation accuracy is robust to the nonuniform distribution of snrs of p spl ges 2 sensors due to channel fading some simulation results are presented to support the efficacy of the proposed bsi algorithm and mtde algorithm

interaction of eigenvalues in multi parameter problems the paper presents a new general theory of interaction of eigenvalues of matrix operators depending on parameters both complex and real eigenvalues are considered strong and weak interactions are distinguished and their geometric interpretation on the complex plane is given mechanical examples are presented and discussed in detail