on the solution of stein s equation and fisher s information matrix of an armax process the main goal of this paper consists in expressing the solution of a stein equation in terms of the fisher information matrix fim of a scalar armax process a condition for expressing the fim in terms of a solution to a stein equation is also set forth such interconnections can be derived when a companion matrix with eigenvalues equal to the roots of an appropriate polynomial associated with the armax process is inserted in the stein equation the case of algebraic multiplicity greater than or equal to one is studied the fim and the corresponding solution to stein s equation are presented as solutions to systems of linear equations the interconnections are obtained by using the common particular solution of these systems the kernels of the structured coefficient matrices are described as well as some right inverses this enables us to find a solution to the newly obtained linear system of equations

symbolic computation of fisher information matrices for parametrized state space systems the asymptotic fisher information matrix fim has several applications in linear systems theory and statistical parameter estimation it occurs in relation to the cramer rao lower bound for the covariance of unbiased estimators it is explicitly used in the method of scoring and it determines the asymptotic convergence properties of various system identification methods it defines the fisher metric on manifolds of systems and it can be used to analyze questions on identifiability of parametrized model classes for many of these applications exact symbolic computation of the fim can be of great use in this paper two different methods are described for the symbolic computation of the asymptotic fim the first method applies to parametrized mimo state space systems driven by stationary gaussian white noise and proceeds via the solution of discrete time lyapunov and sylvester equations for which a method based on faddeev sequences is used this approach also leads to new short proofs of certain well known results on the structure of the fim for siso arma systems the second method applies to parametrized siso state space systems and uses an extended faddeev algorithm for both algorithms the concept of a faddeev reachability matrix and the solution of discrete time sylvester equations in controller companion form are central issues the methods are illustrated by two worked examples the first concerns three different parametrizations of the class of stable ar n systems the second concerns a model for an industrial mixing process in which the value of exact computation to answer identifiability questions becomes particularly clear

on stein s equation vandermonde matrices and fisher s information matrix of time series processes part i the autoregressive moving average process abstract this paper introduces several forms of relationships between fisher s information matrix of an autoregressive moving average or arma process and the solution of a corresponding stein equation fisher s information matrix consists of blocks associated with the autoregressive and moving average parameters an interconnection with a solution of stein s equation is set forth for the block case as well as for fisher s information matrix as a global matrix involving all parameter blocks both cases have their importance for the interpretation of the estimated parameters the cases of distinct and multiple eigenvalues are addressed the obtained links involve equations with left and right inverses these can be expressed in terms of the inverse of appropriate vandermonde matrices a condition is set forth for establishing an equality between fisher s information matrix and a solution to stein s equation two examples are presented for illustrating some of the results obtained the global and off diagonal block case with distinct and multiple roots respectively are considered

on maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean abstract there are two approaches to maximum likelihood ml estimation of the parameter of fractionally integrated noise approximate frequency domain ml fox and taqqu 1986 and exact time domain ml sowell 1992b if the mean of the process is known then a clear finite sample mean squared error ranking of the estimators emerges the exact time domain estimator is superior we show in this paper however that the finite sample efficiency of approximate frequency domain ml relative to exact time domain ml rises dramatically when the mean is unknown and so must be estimated the intuition for our result is straightforward the frequency domain ml estimator is invariant to the true but unknown mean of the process while the time domain ml estimator is not feasible time domain estimation must therefore be based upon de meaned data but the long memory associated with fractional integration makes precise estimation of the mean difficult we conclude that the frequency domain estimator is an attractive and efficient alternative for situations in which large sample sizes render time domain estimation impractical

representing stable complexes on projective spaces abstract we give an explicit proof of a bogomolov type inequality for c 3 of reflexive sheaves on p 3 then using resolutions of rank two reflexive sheaves on p 3 we prove that the closed points of some strata of the moduli of rank two complexes that are both pt stable and dual pt stable can be given by the structure of quotient stacks using monads we apply the same techniques to p 2 and obtain similar results for some strata of the moduli of bridgeland stable complexes

root properties and convergence rates of median filters median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to additional passes of the median filter in this paper the theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals

two dimensional root structures and convergence properties of the separable median filter the root signals invariant to filtering structures of the two dimensional separable median filter are derived and presented in addition it is proved that with rare exception after repetitive passes of the separable median filter any two dimensional signal will be reduced to a signal containing only root structures

least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity summary we consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity its asymptotic normality is established when the second moments of errors and innovations are finite several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach a diagnostic tool consisting of two portmanteau tests is designed to check whether or not the estimated models are adequate the simulation experiments give further support to our model and the results for the absolute returns of the dow jones industrial average index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory conditional heteroscedasticity and heavy tails

optimal weighted median filtering under structural constraints a new expression for the output moments of weighted median filtered data is derived the noise attenuation capability of a weighted median filter can now be assessed using the l vector and m vector parameters in the new expression the second major contribution of the paper is the development of a new optimality theory for weighted median filters this theory is based on the new expression for the output moments and combines the noise attenuation and some structural constraints on the filter s behavior in certain special cases the optimal weighted median filter can be obtained by merely solving a set of linear inequalities this leads in some cases to closed form solutions for optimal weighted median filters some applications of the theory developed in this paper in 1 d signal processing and image processing are discussed throughout the analysis some striking similarities are pointed out between linear fir filters and weighted median filters

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

a direct representation for the large sample maximum likelihood estimator of a gaussian autoregressive moving average process summary a simple procedure is described for obtaining the estimator of the parameters of an autoregressive moving average process the estimator is derived from the maximum likelihood procedure assuming gaussian residuals by making two simplifying assumptions which are negligible in large samples components of the estimator are expressed as linear combinations of a suitable set of sample serial correlations or as a rational function of such linear combinations

evaluation of the covariance matrix for the maximum likelihood estimator of a gaussian autoregressive moving average process summary we present a simple procedure for deriving the covariance matrix for the maximum likelihood estimator of a gaussian autoregressive moving average process an illustration of the procedure is given

multiscale recursive medians scale space and transforms with applications to image processing a cascade of increasing scale 1 d recursive median filters produces a sieve termed an r sieve has a number of properties important to image processing in particular it 1 simplifies signals without introducing new extrema or edges that is it preserves scale space it shares this property with gaussian filters but has the advantage of being significantly more robust 2 the differences between successive stages of the sieve yield a transform to the granularity domain patterns and shapes can be recognized in this domain using idempotent matched sieves and the result transformed back to the spatial domain the r sieve is very fast to compute and has a close relationship to 1 d alternating sequential filters with flat structuring elements they are useful for machine vision applications

convergence properties of median and weighted median filters it has been shown that assuming the first and last value carry on appending strategy a finite number of passes of the same median filter to an arbitrary signal of finite length results in a root signal that will be invariant to additional filtering passes this so called convergence property is reproven using an extremely simple approach in addition the well known idempotent property i e where convergence is achieved with only one filtering pass of a recursive median filter is reproven similarly and the convergence behavior of weighted median filters is studied

a bound on the order of jumping lines let e be a stable rank 2 vector bundle on n 3 assume e is normalized i e c e 0 or 1 by grothedieck s theorem the restriction of e on a line l is isomorphic to l bl o gl bl if cl o gl bl 1 t ol b l if c1 1 for some nonnegative integer b l this b l is an upper semicontinuous function of l which in char 0 according to the grauert miilich theorem g m assumes the value 0 on an open set if be 0 then l is said to be a jumping line of order b l for c 1 0 barth b has shown that the set of jumping lines can be given a scheme structure making it a divisor s e on the grassmannian g g 1 3 which via g ip 5 has degree 2c2 e and for any line l in ip 3 b l pl se where s is the multiplicity of s t at l since any point on a projective variety of degree k has multiplicity k it follows that b l 2c 2 however this bound is not sharp in this paper we will give a sharp bound for b l valid for arbitrary c r namely if c 0

convergence behavior and n roots of stack filters the convergence behavior of two types of stack filters is investigated both types are shown to possess the convergence property and to exhibit nontrivial behavior the first type of stack filter has the erosive property it erodes any input signal to a root after a sufficient number of passes the second type of stack filter has the dilative property it dilates any input signal to a root after a sufficient number of passes for each type of stack filter an algorithm is presented which can determine a filter that has any specific signal or set of signals as roots these two algorithms are efficient in that their execution time is a linear function of the length of the input signal the width of the filter window and the number of signals to be preserved since some stack filters have the phenomenon of oscillations when they filter some input signals successively a partial ordering is defined over the set of stack filters which makes it possible to determine upper and lower bounds for these oscillations

a minimum distance estimator for long memory processes this paper considers a minimum distance estimator mde of the differencing para meter of the fractionally integrated white noise model the mde minimizes the differ ence between sample and population autocorrelations the paper presents calculations of asymptotic variances to examine the efficiency of the mde relative to that of the mle for values of the differencing parameter less than l 4 the mde is consistent and asymptotically normal and the asymptotic variance of the mde using the first n auto correlations approaches that of the mle as n increases however there is a substantial efficiency loss if low order autocorrelations are omitted this implies that a non parametric treatment of short run dynamics will involve a substantial loss of efficiency

a new class of nonlinear filters neural filters a class of nonlinear filters based on threshold decomposition and neural networks is defined it is shown that these neural filters include all filters defined either by continuous functions such as linear finite impulse response fir filters or by boolean functions such as generalized stack filters adaptive least mean absolute error and adaptive least mean square error algorithms are derived for determining optimal neural filters as special cases adaptive generalized stack and adaptive generalized weighted order statistic filtering algorithms under both error criteria are derived experimental results in 1d and 2d signal processing are presented to compare the performances of the adaptive neural filters and other widely used filters

computational methods for linear matrix equations given the square matrices a b d e and the matrix c of conforming dimensions we consider the linear matrix equation a mathbf x e d mathbf x b c in the unknown matrix mathbf x our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing

stack filters the median and other rank order operators possess two properties called the threshold decomposition and the stacking properties the first is a limited superposition property which leads to a new architecture for these filters the second is an ordering property which allows an efficient vlsi implementation of the threshold decomposition architecture motivated by the success of rank order filters in a wide variety of applications and by the ease with which they can now be implemented we consider in this paper a new class of filters called stack filters they share the threshold decomposition and stacking properties of rank order filters but are otherwise unconstrained they are shown to form a very large class of easily implemented nonlinear filters which includes the rank order operators as well as all compositions of morphological operators the convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters the results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals the output distribution for these filters is also found all the stack filters of window width 3 are determined along with their convergence properties among these filters are found two which we have named asymmetric median filters they share all the properties of median filters except that they remove impulses of one sign only that is one removes only positive going edges the other removes only negative going edges while the median filter removes impulses of both signs this investigation of the properties of stack filters thus produces several new useful and easily implemented filters

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

some statistical properties of median filters some statistical properties of median filters are analyzed it is shown that median filters can remove impulsive plus gaussian white noise better than hanning filters when the amplitude of the impulses is large or the energy of the gaussian noise is relatively low it is also shown that unlike linear filters median filters preserve sharp changes in signals when the noise energy is not too high

rank order operators and the mean absolute error criterion the author shows that among all randomizing stack filters whose output decisions are based on the sum of the bits in the window on each level of the threshold decomposition architecture rank order operators are optimal under an error criterion which is the sum of the absolute error incurred on each level of the threshold decomposition architecture he also shows that if the filtering class being optimized obeys a deterministic stacking property then the traditional multilevel mean absolute error criterion reduces to the sum of the absolute error incurred to each level this leads to an efficient algorithm for choosing the rank order filter which minimizes the multilevel mean absolute error criterion

on second moment properties of median filtered sequences of independent data in this paper we present the derivation of the bivariate distribution function for median filtered sequences of independent arbitrary second order random variables this result is then used to qualitatively analyze second moment properties of median filtered data the results hint towards a low pass characteristic of the median filters and a low dependency of the output spectrum on input alphabet size and distribution

state description for the root signal set of median filters median filtering is a simple digital technique for smoothing signals one main characteristic of the filter is that it maps the input signal space into a root signal space where signals invariant to median filters are called roots of the signal in this paper we develop the theory for the root signal set of median filters a tree structure for the root signal set is obtained for binary signals the number of roots r n for a signal of length n and window size filter 2s 1 is exactly represented by the difference equation r n r n 1 r n s a general solution is obtained in a z domain approach finally a method for faster one dimensional median filter operation is introduced

estimating the differencing parameter via the partial autocorrelation function this paper provides an explanation for the puzzling phenomenon in tieslau et al 1996 journal of econometrics 71 249 264 that a substantial e ciency loss occurs if low order autocorrelations are omitted when estimating the di erencing parameter d this is because for all n strictly bigger than 1 the nth order autocorrelation function does not depend uniquely on the di erencing parameter we construct a new estimator for the di erencing parameter based on the partial autocorrelation function comparisons of the asymptotic and nite sample variance of our estimator and those of tsb are made a substantial e ciency gain is achieved by our estimator as compared to tsb s 2000 elsevier science s a all rights reserved jel classixcation c22

on the convergence and roots of order statistics filters we propose a comprehensive theory of the convergence and characterization of roots of order statistics filters conditions for the convergence of iterations of order statistics filters are proposed criteria for the morphological characterization of roots of order statistics filters are also proposed

espaces abstraits de morphismes et mutations i try to extend here some results of the paper moduli spaces of decomposable morphisms of sheaves and quotients by non reductive groups let e f be decomposable sheaves on a smooth projective variety i find more linearizations of the natural action of the group mathop rm aut nolimits e times mathop rm aut nolimits f on mathop rm hom nolimits e f such that a good quotient of the open set of semi stable morphisms exists to obtain this one associates to mathop rm hom nolimits e f another space of morphisms mathop rm hom nolimits e f in such a way that there is a natural bijection between the set of orbits of an open subset of mathop rm hom nolimits e f and the set of orbits of an open subset of mathop rm hom nolimits e f we can in this case deduce the existence of good quotients of some open subsets of mathop rm hom nolimits e f from the existence of good quotients of the corresponding open subsets of mathop rm hom nolimits e f

computation of the fisher information matrix for time series models the fisher information matrix is useful in time series modeling mainly because the significance of estimated parameters can also be derived from it it can also be used in iterative procedures of parameter estimation the paper is mainly concerned with algorithmic aspects related to the computation of that matrix either asymptotically or exactly after a review of the literature on the subject several recent methods are described and compared from the point of view of a complexity b accuracy and c the class of models for which they can be used

a goodness of fit test for time series with long range dependence we propose a test statistic for goodness of fit in time series with slowly decaying serial correlations the asymptotic distribution of the test statistic originally proposed by milhoj for time series with smooth spectra turns out to be the same under the null hypothesis even if the spectrum has a pole at 0 in particular the test is suitable to detect lack of independence in the observations or estimated residuals if the first few correlations are small but the decay of the correlations is slow

the classification and associative memory capability of stack filters the notion of the on set of a positive boolean function is used to classify stack filters into three different types called decreasing increasing and mixed the associative memory capability of each of these three types of stack filters is then investigated the associative memory of a stack filter is defined to be the set of root signals of that filter in a class of stack filters in which each filter s root set contains a desired set of patterns those filters whose root sets have the smallest cardinality are said to be minimal among all filters in that class for that set of patterns some learning schemes are proposed to find minimal decreasing and increasing stack filters it is also shown that for any specified set of patterns there is always a mixed stack filter which is minimal when one considers all stack filters which preserve those patterns in this sense mixed stack filters are always at least as good as decreasing or increasing stack filters

tuning the smoothness of the recursive median filter the median filter is a special case of nonlinear filters used for smoothing signals since the output of the median filter is always one of the input samples it is conceivable that certain signals could pass through the median filter unaltered these signals define the signature of a filter and are referred to as root signals median filters are known to possess the convergence property meaning that by repeating median filtering a root signal will be found starting from any input signal by associating the nonlinear operation of median filtering with a two terms cost function an optimization process that minimizes that function is obtained cost functions of the same type are associated with different recursive median filtering schemes by replacing the actual values inside the filter s window with the original signal the convergence behavior of these filters and their smoothness are studied by changing the positions of the replacements during filtering a tuning effect of the smoothness is obtained simulation results show that the proposed filtering schemes provide improved performance over the standard recursive median filter succeeding in preserving small details and fine textures

stable rank 2 reflexive sheaves on with small and applications we investigate the moduli spaces of stable rank two reflexive sheaves on p3 with small chern classes as an application to curves of low degree in p3 we prove the curve has maximal rank and that the corresponding hilbert scheme is irreducible and unirational introduction in the past few years the subject of vector bundles on projective spaces and in particular the case of rank 2 on p3 has received much attention several basic theorems have been proved e g the existence of the moduli space of stable vector bundles m though so far very few of these moduli spaces have been studied in detail the interest of vector bundles partly stems from their connection with curves however the class of curves obtained in this way is rather restricted recently hartshorne srs has focused attention on reflexive sheaves of rank 2 on p3 on the one hand most results proved for vector bundles also turn out to be true for reflexive sheaves on the other hand reflexive sheaves have two significant advantages first they correspond to quite general curves second and most importantly one has the reduction step introduced by hartshorne which is an effective tool in studying vector bundles by relating them to simpler reflexive sheaves in this paper we investigate the moduli spaces of stable rank 2 reflexive sheaves on p3 with c2 3 for c2 2 we prove the moduli spaces are irreducible nonsingular and rational we also classify the related unstable planes for c2 3 in most cases we show that the moduli space is irreducible and unirational as one of the applications to curves of low degree in p3 cf srs 4 1 we prove that the curve has maximal rank and that the corresponding hilbert scheme is irreducible and unirational hence as a corollary we conclude that the variety of moduli 1g of curves of genus g is unirational for g 5 6 7 8 in 1 we give facts on multiple lines and deduce a criterion for unstable planes 2 contains our classification of semistable sheaves with c2 2 3 is about sheaves with c2 3 4 gives the applications to curves acknowledgment i would like to thank my thesis advisor robin hartshorne he has been very generous in his advice and time in addition he attracted to received by the editors september 1 1982 and in revised form march 18 1983 1980 mathematics subject classification primary 14f05 secondary 14d22 i1984 american mathematical society 0002 9947 84 1 00 25 per page

nonrecursive and recursive stack filters and their filtering behavior it is shown that stack filters that are based on symmetric threshold functions and preserve median filter roots make all inputs converge to roots or to cycles of period two this is an important result since these filters have useful roots the median filter roots and they are time symmetric i e time reversal of an input sequence of such a filter is equivalent to time reversal of the output sequence of the filter in order to construct stack filters without cycles the recursive stack filter which is an extension of the recursive median filter is introduced it is shown that a recursive stack filter has the same roots as the corresponding nonrecursive stack filter also given a nonrecursive filter from the class mentioned above the corresponding recursive filter will make every input signal of finite converge to a root in a finite number of passes

computation of the fisher information matrix for siso models closed form expressions and an algorithm for obtaining the fisher information matrix of gaussian single input single output siso time series models are presented it enables the computation of the asymptotic covariance matrix of maximum likelihood estimators of the parameters the procedure makes use of the autocovariance function of one or more autoregressive processes under certain conditions the siso model can be a special case of a vector autoregressive moving average arma model for which there is a method to evaluate the fisher information matrix that method is compared with the procedure described in the paper

on the computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

a general linear prediction approach to the complex split inversion algorithm a general linear prediction framework is developed for the derivation of the complex split levinson algorithm which leads naturally to a structural interpretation of the redundancy present in the classical levinson durbin algorithm a novel order recursive predictor structure is presented it is conceptually simpler than a lattice realization since it propagates only one generalized prediction error when the usual prediction error is desired it can be recovered through a simple terminal stage

weighted order statistics filters their classification some properties and conversion algorithm stack filters that are based on threshold logic with nonnegative weights and threshold value are called weighted order statistics wos filters and are classified into four different types type 0 trivial type 1 decreasing type 2 increasing and type 3 mixed a significant property of the threshold logic is that it only needs n 1 tuples to represent its function representation if the input of this function has it variables this associative representation is very useful in neural computing nonlinear filtering etc the authors propose a significant classification of threshold logic such that the behaviors of wos filters can be understood easily based on this classification in the paper all type 0 type 1 and type 2 wos filters are shown to possess the convergence property however type 3 wos filters do not necessarily possess the convergence property hence the authors investigate the convergence behaviors of some type 3 wos filters including symmetric weighted median filters and the type 3 filters proposed in wendt 1990 finally an efficient algorithm to determine whether a positive boolean function corresponds to a weighted median filter is proposed the authors use the property all threshold logics are regular to make the algorithm tractable

bayesian wavelet based methods for the detection of multiple changes of the long memory parameter long memory processes are widely used in many scientific fields such as economics physics and engineering change point detection problems have received considerable attention in the literature because of their wide range of possible applications here we describe a wavelet based bayesian procedure for the estimation and location of multiple change points in the long memory parameter of gaussian autoregressive fractionally integrated moving average models arfima p d q with unknown autoregressive and moving average parameters our methodology allows the number of change points to be unknown the reversible jump markov chain monte carlo algorithm is used for posterior inference the method also produces estimates of all model parameters performances are evaluated on simulated data and on the benchmark nile river dataset

bayesian analysis of long memory and persistence using arfima models abstract this paper provides a bayesian analysis of autoregressive fractionally integrated moving average arfima models we discuss in detail inference on impulse responsens and show how bayesian methods can be used to i test arfima models against arima alternatives and ii take model uncertainty into account when making inferences on quantities of interest our methods are then used to investigate the persistence properties of real u s gnp

asymptotic behavior of random vandermonde matrices with entries on the unit circle analytical methods for finding moments of random vandermonde matrices with entries on the unit circle are developed vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation precoding and sparse sampling theory just to name a few within this framework we extend classical freeness results on random matrices with independent and identically distributed i i d entries and show that vandermonde structured matrices can be treated in the same vein with different tools we focus on various types of matrices such as vandermonde matrices with and without uniform phase distributions as well as generalized vandermonde matrices in each case we provide explicit expressions of the moments of the associated gram matrix as well as more advanced models involving the vandermonde matrix comparisons with classical i i d random matrix theory are provided and deconvolution results are discussed we review some applications of the results to the fields of signal processing and wireless communications

modeling persistence in hydrological time series using fractional differencing the class of autoregressive integrated moving average arima time series models may be generalized by permitting the degree of differencing d to take fractional values models including fractional differencing are capable of representing persistent series d 0 or short memory series d 0 the class of fractionally differenced arima processes provides a more flexible way than has hitherto been available of simultaneously modeling the long term and short term behavior of a time series in this paper some fundamental properties of fractionally differenced arima processes are presented methods of simulating these processes are described estimation of the parameters of fractionally differenced arima models is discussed and an approximate maximum likelihood method is proposed the methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures

a generalized convergence theorem for neural networks a neural network model is presented in which each neuron performs a threshold logic function the model always converges to a stable state when operating in a serial mode and to a cycle of length at most 2 when operating in a fully parallel mode this property is the basis for the potential applications of the model such as associative memory devices and combinatorial optimization the two convergence theorems for serial and fully parallel modes of operation are reviewed and a general convergence theorem is presented that unifies the two known cases new relations between the neural network model and the problem of finding a minimum cut in a graph are obtained

restarted global fom and gmres algorithms for the stein like matrix equation x m x c abstract in this paper we propose the restarted global full orthogonalization method gl fom and global generalized minimum residual gl gmres method to solve the stein like matrix equation x m x c with m x a x b m x a x b m x a x b or m x a x h b respectively where x is an unknown matrix to be solved first by using a real inner product in complex matrix spaces a generalized global arnoldi process is given then we demonstrate how to employ the restarted gl fom and gl gmres algorithms for solving the stein like matrix equation the proposed algorithms take advantage of the shifted structure of the matrix equation and are implemented by the original coefficient matrices finally some numerical examples are given to illustrate the effectiveness with comparison to some existing methods

duality and other properties of multiplicative seasonal autoregressive moving average models model duality is defined between four models referred to as the primal the dual the autoregressive adjoint and the moving average adjoint a duality theorem which generalizes the results of box pierce 1970 and pierce 1970 is presented applications of this duality theorem to autoregressive moving average models and multiplicative seasonal autoregressive moving average models are discussed these applications include i a convenient method for calculating the covariance matrix of the estimated parameters ii convenient formulae for the variances of the residual autocorrelations iii the distribution of the inverse partial autocorrelations finally a useful approximation to the covariance determinant of multiplicative seasonal models is derived

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

computation of the exact information matrix of gaussian dynamic regression time series models in this paper the computation of the exact fisher information matrix of a large class of gaussian time series models is considered this class which is often called the single input single output siso model includes dynamic regression with autocorrelated errors and the transfer function model with autoregressive moving average errors the method is based on a combination of two computational procedures recursions for the covariance matrix of the derivatives of the state vector with respect to the parameters and the fast kalman filter recursions used in the evaluation of the likelihood function it is much faster than existing procedures an expression for the asymptotic information matrix is also given

a recursive variant of mallows filter class mallows 1980 nonlinear fir filter class includes most of the nonlinear digital filters in wide use today this filter class is defined in terms of five axioms and this paper modifies two of these axioms to obtain a class of symmetric recursive nonlinear filters one of the main points considered in this paper is the consequence of mallows location invariance axiom a2 and general prescriptions are given for both mallows original fir filter class and its recursive extension this representation is also extremely useful in discussing the root sequences of both the recursive and nonrecursive structures since recursive filters can exhibit various forms of instability a number of stability results are presented for this class of filters finally some simple examples are considered that illustrate the potential utility of the results presented

a horrocks theorem for reflexive sheaves abstract in this paper we define m tail reflexive sheaves as reflexive sheaves on projective spaces with the simplest possible cohomology we prove that the rank of any m tail reflexive sheaf e on p n is greater or equal to n m m we completely describe m tail reflexive sheaves on p n of minimal rank and we construct huge families of m tail reflexive sheaves of higher rank

stack filters and the mean absolute error criterion a method to determine the stack filter which minimizes the mean absolute error between its output and a desired signal given noisy observations of this desired signal is presented specifically an optimal window width b stack filter can be determined with a linear program with o b2 sup b variables this algorithm is efficient since the number of different inputs to a window width b filter is m sup b if the filter has m valued input and the number of stack filters grows faster than 2 raised to the 2 sup b 2 power it is shown that optimal stack filtering under the mean absolute error criterion is analogous to optimal linear filtering under the mean squared error criterion both linear filters and stack filters are defined by superposition properties both classes are implementable and both have tractable procedures for finding the optimal filter under an appropriate error criterion

efficiency improvements in inference on stationary and nonstationary fractional time series we consider a time series model involving a fractional stochastic component whose integration order can lie in the stationary invertible or nonstationary regions and be unknown and an additive deterministic component consisting of a generalized polynomial the model can thus incorporate competing descriptions of trending behavior the stationary input to the stochastic component has parametric autocorrelation but innovation with distribution of unknown form the model is thus semiparametric and we develop estimates of the parametric component which are asymptotically normal and achieve an m estimation efficiency bound equal to that found in work using an adaptive lam lan approach a major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies this is relevant also when the innovation density is parameterized and we provide a result for that case also our semiparametric estimates employ nonparametric series estimation which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models our work thus also contributes to methods and theory for nonfractional time series models such as autoregressive moving averages a monte carlo study of finite sample performance of the semiparametric estimates is included

statistical analysis of dwt coefficients of fgn processes using arfima p d q models abstract fractional gaussian noise fgn provides an important parametric representation for the data recorded from long memory processes also it has been well established in literature that the orthogonal wavelet transforms prove to be the optimal bases to represent the data as fgn or fbm fractional brownian motion models this paper highlights the statistical properties of discrete wavelet transform dwt coefficients in the wavelet expansion of fgn statistical analysis was carried out by analyzing the inter scale and intra scale correlations of the dwt coefficients for wavelets with varying vanishing moments two types of auto regressive moving average arma models were fit to the wavelet coefficients of fgn namely i arma p q and ii arfima p d q models the latter represents the arma models with fractional differencing using the akaike information criteria aic and the bayesian information criteria bic it has been shown that arfima models best represent the wavelet coefficients of fgn the above observation holds good when wavelets with increasing number of vanishing moments are used for obtaining dwt coefficients after estimating the optimal model and its parameters different properties pertaining to the inter scale and intra scale correlations were verified using these models

pseudolinear estimation of fractionally integrated arma arfima models with automotive application a novel pseudolinear method for the estimation of fractionally integrated arma arfima models that are capable of representing combined long and short term dependency is introduced the method is based on the relationship of the ar ma parameters and the coefficients of the fractional power operator binomial series expansion with the model s inverse function these lead to the formulation of a special form regression problem that can be decomposed into a univariate nonlinear and a multivariate linear regression and may be thus tackled via a special pseudolinear procedure this decomposition in turn leads to the elimination of the need for initial guess parameter values drastic simplification in the detection and handling of potential local extrema problems as well as computational simplicity the method s strong consistency is established whereas its performance characteristics are assessed via monte carlo experiments and comparisons with the maximum likelihood method the pseudolinear method is also used for the arfima modeling and prediction of power consumption in an experimental automobile fully active suspension system the consumption of which is shown to exhibit long term dependency a comparison with arma arima type modeling is also made and the obtained arfima models are shown to achieve improved predictive performance at a drastically reduced parametric complexity

divisors on general curves and cuspidal rational curves in t roduc t ion 371 0 pre l iminar ies 377 1 a pl i icker formula 378 2 d imens iona l t ransversa l i ty 380 3 d i m e n s i o n of families of r a t iona l curves with fixed degree and ass igned cusps in a project ive space 383 4 l inear series on curves with universa l s ingular i t ies 386 5 l inear series and project ive embedd ings of general curves 391 6 embedd ings of general cuspidal curves 400 7 degenera t ion of schuber t in tersect ions some special cases 403 8 degene ra t ion of schuber t in tersect ions ma in results 407 9 g c is reduced for general cuspidal r a t iona l c 414

approximating long memory dna sequences by short memory process abstract this paper analyzes the approximation of a general long memory arfima p d q process by a short memory arma 1 1 process to validate this approximation a mean square error forecast criterion is considered and the calculation of the mean square error between the observation x t l of an arfima process and the l step ahead forecast of the arma 1 1 process is presented the performance of the arma 1 1 approximation to an arfima model is illustrated by using an application to a dna sequence of orf virus this paper gives some theoretical justification on the mean square error forecast criterion based on a selected arma 1 1 model when compared to the general arfima p d q process the paper also provides a dna sequence of orf virus analysis when the time series is originated from the tangent values of the chaos game representation coordinates for each nucleotide the conclusions of this paper work well because the estimator value of d is small d 0 16 the paper also gives the other parameter estimate of the fitted arfima 0 d 1 model and one step predictions using arma 1 1 model

on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity abstract this article considers fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity which combines the popular generalized autoregressive conditional heteroscedastic garch and the fractional arma models the fractional differencing parameter d can be greater than 1 2 thus incorporating the important unit root case some sufficient conditions for stationarity ergodicity and existence of higher order moments are derived an algorithm for approximate maximum likelihood ml estimation is presented the asymptotic properties of ml estimators which include consistency and asymptotic normality are discussed the large sample distributions of the residual autocorrelations and the square residual autocorrelations are obtained and two portmanteau test statistics are established for checking model adequacy in particular non stationary farima p d q garch r s models are also considered some simulation results are reported as an illustration

median filtering by threshold decomposition median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to further passes of the median filter in this paper it is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals filtering each binary signal to a root with a binary median filter and then reversing the decomposition this equivalence allows problems in the analysis and the implementation of median filters for arbitrary level signals to be reduced to the equivalent problems for binary signals since the effects of median filters on binary signals are well understood this technique is a powerful new tool

factored forms for solutions of ax xb c and x axb c in companion matrices abstract the main concern of this paper is linear matrix equations with block companion matrix coefficients it is shown that general matrix equations ax xb c and x axb c can be transformed to equations whose coefficients are block companion matrices c l x xc m diag i 0 0 and x c l xc m diag i 0 0 respectively where l and cm stand for the first and second block companion matrices of some monic r r matrix polynomials l si s 1j 0 jlj and m ti t7minus 1j 0 jmj the solution of the equat with block companion coefficients is reduced to solving vector equations sx where the matrix s is r2l r2l l max s t and enjoys some symmetry properties