lower bounds for the perron root of a nonnegative matrix abstract new lower bounds frequently better than previous bounds and readily computable for the perron root r a of a nonnegative matrix a are obtained the theoretical comparison of new bounds with the known ones is supplemented with two numerical examples

on the best constants in inequalities of the markov and wirtinger types for polynomials on the half line abstract the main topic of the paper is best constants in markov type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves the norm is the l 2 norm with laguerre weight the leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term which is the operator norm of a volterra operator are given for best constants in inequalities of the wirtinger type the limit is computed and an asymptotic formula for the error term is presented

on the geometrical structure of symmetric matrices abstract the identity ray i for 0 can be seen as the center ray of the cone of symmetric and positive definite spd matrices in that sense the angle that any spd matrix forms with the identity plays a very important role to understand the geometrical structure of the cone in this work we extend this relationship and analyze the geometrical structure of symmetric matrices including the location of all orthogonal matrices not only the identity matrix this geometrical understanding leads to new results in the subspace of symmetric matrices we also extend some of the geometrical results for the case of general not necessarily symmetric nonsingular matrices

numerical radius and zero pattern of matrices abstract let a be an n n complex matrix and r be the maximum size of its principal submatrices with no off diagonal zero entries suppose a has zero main diagonal and x is a unit n vector then letting a be the frobenius norm of a we show that a x x 2 1 1 2 r 1 2 n a 2 this inequality is tight within an additive term o r n 2 if the matrix a is hermitian then a x x 2 1 1 r a 2 this inequality is sharp moreover it implies the turan theorem for graphs

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

robust estimation in structured linear regression a structured linear regression model is one in which there are permanent dependencies among some p row vectors of the n x p design matrix to study structured linear regression we introduce a new class of robust estimators called d estimators which can be regarded as a generalization of the least median of squares and least trimmed squares estimators they minimize a dispersion function of the ordered absolute residuals up to the rank h we investigate their breakdown point and exact fit point as a function of h in structured linear regression it is found that the d and s estimators can achieve the highest possible breakdown point for h appropriately chosen it is shown that both the maximum breakdown point and the corresponding optimal value of h h op are sample dependent they hinge on the design but not on the response the relationship between the breakdown point and the design vanishes when h is strictly larger than h op however when h is smaller than h op the breakdown point depends in a complicated way on the design as well as on the response

lower bounds for the spectral radius of a matrix abstract we develop lower bounds for the spectral radius of symmetric skew symmetric and arbitrary real matrices our approach utilizes the well known leverrier faddeev algorithm for calculating the coefficients of the characteristic polynomial of a matrix in conjunction with a theorem by lucas which states that the critical points of a polynomial lie within the convex hull of its roots our results generalize and simplify a proof recently published by tarazaga for a lower bound on the spectral radius of a symmetric positive definite matrix in addition we provide new lower bounds for the spectral radius of skew symmetric matrices we apply these results to a problem involving the stability of fixed points in recurrent neural networks

generalized m estimators for errors in variables regression this paper discusses robust estimation for structural errors in variables ev linear regression models such models have important applications in many areas under certain assumptions including normality the maximum likelihood estimates for the ev model are provided by orthogonal regression or which minimizes the orthogonal distance from the regression line to the data points instead of the vertical distance used in ordinary regression or is very sensitive to contamination and thus efficient robust procedures are needed this paper examines the theoretical properties of bounded influence estimators for univariate gaussian ev models using a generalized m estimate approach the results include fisher consistency most b robust estimators and the or version of hampel s optimality problem

improving eigenvalue bounds using extra bounds abstract bounds for various functions of the eigenvalues of a hermitian matrix a based on the traces of a and a 2 are improved a technique is presented whereby these bounds can be improved by combining them with other bounds in particular the diagonal of a in conjunction with majorization is used to improve the bounds these bounds all require o n 2 multiplications

efficiency constrained bias robust estimation of location abstract it has been correctly pointed out by an anonymous referee that the results of this paper amount to a rigorous analysis of the correctness of hampel s heuristic approach in the location setup still one might conjecture by analogy that in the case of more complicated models maximizing the efficiency under a constraint on the gross error sensitivity is almost the same as putting a constraint on the bias however the extension of our technique to more complicated models is by no means straightforward if al all possible and this matter deserves further study another interesting issue brought up by an anonymous referee is that if one leaves the realm of m estimates of location there is not necessarily a pay off between bias robustness and efficiency at the central gaussian model

on the uniqueness of s functionals and m functionals under nonelliptical distributions the s functionals of multivariate location and scatter including the mve functionals are known to be uniquely defined only at unimodal elliptically symmetric distributions the goal of this paper is to establish the uniqueness of these functionals under broader classes of symmetric distributions we also discuss some implications of the uniqueness of the functionals and give examples of striclty unimodal and symmetric distributions for which the mve functional is not uniquely defined the uniqueness results for the s functionals are obtained by embedding them within a more general class of functionals which we call the m functionals with auxiliary scale the uniqueness results of this paper are then obtained for this class of multivariate functionals besides the s functionals the class of multivariate m functionals with auxiliary scale include the constrained m functionals recently introduced by kent and tyler as well as a new multivariate generalization of yohai s mm functionals

geometrical properties of the frobenius condition number for positive definite matrices we study the geometrical properties of the frobenius condition number on the cone of symmetric and positive definite matrices this number related to the cosine of the angle between a given matrix and its inverse is equivalent to the classical 2 norm condition number but has a direct and natural geometrical interpretation in particular we establish bounds for the ratio between the angle that a matrix forms with the identity ray and the angle that the inverse of that matrix forms with the identity ray these bounds allow us to establish new lower bounds for the condition number that only require the trace and the frobenius norm of the matrix

new eigenvalue estimates for complex matrices abstract in a recent work 1 we have proved that all the eigenvalues j of a complex matrix a of order n lie in a disk with center at tr a n and radius n 1 n k 1 n k 2 tr a 2 n 1 2 in this paper we prove that the eigenvalues of a are contained in a rectangle with vertices on the boundary circle of the mentioned disk improving in this way the result in 1 we recall some inequalities which alloww us to bound the radius of the disk and the rectangle the bounds can be computed without knowing the eigenvalues of a

on the maximum bias functions of mm estimates and constrained m estimates of regression we derive the maximum bias functions of the mm estimates and the constrained m estimates or cm estimates of regression and compare them to the maximum bias functions of the s estimates and the t estimates of regression in these comparisons the cm estimates tend to exhibit the most favorable bias robustness properties also under the gaussian model it is shown how one can construct a cm estimate which has a smaller maximum bias function than a given s estimate that is the resulting cm estimate dominates the s estimate in terms of maxbias and at the same time is considerably more efficient

localization of eigenvalues in elliptic regions abstract we prove that the eigenvalues j of an n by n complex matrix a with its characteristic polynomial having real coefficients lie in the elliptic region defined by 2 tr a n 2 2 y 2 2 2 where n 1 n n 1 n re k 2 re te a 2 n 1 2 and n 1 n k 1 n im k 2 1 2 this region is intersected with the strip y 1 2 k 1 u im k 2 1 2 to obtain an improved eigenvalue localization region we also give bounds for the semiaxes which can be computed without knowing the eigenvalues of a when a has r n nonzero eigenvalues we obtain a smaller elliptic region containing such nonzero eigenvalues

a class of robust and fully efficient regression estimators this paper introduces a new class of robust estimators for the linear regression model they are weighted least squares estimators with weights adaptively computed using the empirical distribution of the residuals of an initial robust estimator it is shown that under certain general conditions the asymptotic breakdown points of the proposed estimators are not less than that of the initial estimator and the finite sample breakdown point can be at most 1 n less for the special case of the least median of squares as initial estimator hard rejection weights and normal errors and carriers the maximum bias function of the proposed estimators for point mass contaminations is numerically computed with the result that there is almost no worsening of bias moreover and this is the original contribution of this paper if the errors are normally distributed and under fairly general conditions on the design the proposed estimators have full asymptotic efficiency a monte carlo study shows that they have better behavior than the initial estimators for finite sample sizes

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

eigenvalue estimates for symmetric matrices abstract we use the fact that the set of symmetric positive semidefinite matrices of order n form a cone with a special structure in order to find bounds for the eigenvalues of a symmetric matrix

adaptive symbol by symbol reception of mpsk on the gaussian channel with unknown carrier phase characteristics an adaptive version of the optimum decision aided symbol by symbol receiver obtained in our previous works for m ary phase shift keying over the gaussian channel with unknown carrier phase characteristics is considered it uses a first order adaptive filter for carrier reference tracking and the filter gain is adapted on line based on the observed signal samples using a least mean square error criterion the phase tracking performance of the filter in the steady state tracking mode is analyzed using a linearized model the phase tracking error variance is minimized due to the risk function used in designing the filter gain adaptation algorithm the bit error probability for quadrature phase shift keying is obtained both analytically and via computer simulations

on the cone of positive semidefinite matrices abstract a survey of some general properties of the cone of positive semidefinite matrices its faces two isometric isomorphisms and linear transformations on it is given

efficient bounded influence regression estimation abstract the least squares estimator for in the classical linear regression model is strongly efficient under certain conditions however in the presence of heavy tailed errors and or anomalous data the least squares efficiency can be markedly reduced in this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first order condition for strong efficiency subject to the constraint we then show that the estimator is asymptotically normal the article concludes with an outline of an algorithm for computing a bounded influence regression estimator and with an example comparing least squares robust regression as developed by huber and the estimator proposed in this article

the automatic robustness of minimum distance functionals on montre que les estimateurs de distance minimale forment une classe d estimateurs automatiquement robustes dans le meme sens que l estimateur du maximum de vraisemblance

bounds for eigenvalues using the trace and determinant abstract let a be a square matrix with real and positive eigenvalues 1 n 0 and let 1 k l n bounds for kl l and k l involving k l n tr a and det a only are presented

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

more estimates for eigenvalues and singular values abstract there is an interesting relation between the angle that a matrix forms with the identity and its eigenvalues then we show for symmetric matrices that some information about the matrix can be known if the angle is computed a lower bound for the maximum eigenvalue is obtained for symmetric positive semidefinite matrices this inequality and the upper bound for eigenvalues given in 5 provide us an interval in which must lie the maximum eigenvalue finally some results from 5 and the first part of this paper are generalized for the non symmetric case

robust regression based on infinitesimal neighbourhoods we study robust estimation in the general normal regression model with random carriers permitting small departures from the model the framework is that of bickel 1981 we obtain solutions of huber 1982 kraskerhampel 1980 and krasker welsch 1982 as special cases as well as some new procedures our calculations indicate that the optimality properties of these estimates are more limited than suggested by krasker and welsch

alternatives to the median absolute deviation abstract in robust estimation one frequently needs an initial or auxiliary estimate of scale for this one usually takes the median absolute deviation mad n 1 4826 med xi med j x j because it has a simple explicit formula needs little computation time and is very robust as witnessed by its bounded influence function and its 50 breakdown point but there is still room for improvement in two areas the fact that mad n is aimed at symmetric distributions and its low 37 gaussian efficiency in this article we set out to construct explicit and 50 breakdown scale estimators that are more efficient we consider the estimator sn 1 1926 med med j xi xj and the estimator qn given by the 25 quantile of the distances xi x j i j note that sn and qn do not need any location estimate both sn and qn can be computed using o n log n time and o n storage the gaussian efficiency of sn is 58 whereas qn attains 82 we study sn and qn by means of their influence functions their b

influence function and maximum bias of projection depth based estimators location estimators induced from depth functions increasingly have been pursued and studied in the literature among them are those induced from projection depth functions these projection depth based estimators have favorable properties among their competitors in particular they possess the best possible finite sample breakdown point robustness however robustness of estimators cannot be revealed by the finite sample breakdown point alone the influence function gross error sensitivity maximum bias and contamination sensitivity are also important aspects of robustness in this article we study these other robustness aspects of two types of projection depth based estimators projection medians and projection depth weighted means the latter includes the stahel donoho estimator as a special case exact maximum bias the influence function and contamination and gross error sensitivity are derived and studied for both types of estimators sharp upper bounds for the maximum bias and the influence functions are established comparisons based on these robustness criteria reveal that the projection depth based estimators enjoy desirable local as well as global robustness and are very competitive among their competitors

lower bounds for the numerical radius abstract let a be a complex n n matrix we find lower bounds for its numerical radius r a max x ax x c n x x 1 first we choose x satisfying x x 1 and compute x ax we also improve the simple bound so obtained second we apply r a max z a z a 2 z c z 1 where denotes the largest eigenvalue

df dd for channels with phase noise in this letter we design decision feedback differential detection df dd schemes for channels with phase noise if the df dd feedback filter is properly optimized a performance similar to that of a more complex scheme recently reported by chiavaccini and vitetta based on expectation maximization can be achieved however it is also shown that an error floor is unavoidable for channels with phase noise if a constraint is introduced the df dd receiver can be made robust against unknown frequency offsets

higher order infinitesimal robustness using the von mises expansion we study the higher order infinitesimal robustness of a general m functional and characterize its second order properties we show that second order robustness is equivalent to the boundedness of both the estimator s estimating function and its derivative with respect to the parameter it implies at the same time i variance robustness and ii robustness of higher order saddlepoint approximations to the estimator s finite sample density the proposed construction of second order robust m estimators is fairly general and potentially useful in a variety of relevant settings besides the theoretical contributions we discuss the main computational issues and provide an algorithm for the implementation of second order robust m estimators finally we illustrate our theory by monte carlo simulation and in a real data estimation of the maximal losses of nikkei 225 index returns our findings indicate that second order robust estimators can improve on other widely applied robus

minimax bias robust estimation of the dispersion matrix of a multivariate distribution maronna defines affine equivariant m estimators for multivariate location and scatter they are particularly suited for estimating the pseudo covariance or scatter matrix of an elliptical population by defining the bias of dispersion matrix properly we consider the maximum bias of an m estimator over an e neighborhood of the underlying elliptical distribution location known we find that tyler s estimator minimizes the maximum bias

on the structure of the set of symmetric matrices with the perron frobenius property abstract in this paper we explore the geometry of the set of symmetric perron frobenius matrices whose spectral radius is an eigenvalue with a nonnegative associated eigenvector we prove that the set which is not convex is star convex with the identity matrix as the center we also describe a few aspects of the geometric structure of the set

depth weighted scatter estimators general depth weighted scatter estimators are introduced and investigated for general depth functions we find out that these affine equivariant scatter estimators are fisher consistent and unbiased for a wide range of multivariate distributions and show that the sample scatter estimators are strong and n consistent and asymptotically normal and the influence functions of the estimators exist and are bounded in general we then concentrate on a specific case of the general depth weighted scatter estimators the projection depth weighted scatter estimators which include as a special case the well known stahel donoho scatter estimator whose limiting distribution has long been open until this paper large sample behavior including consistency and asymptotic normality and efficiency and finite sample behavior including breakdown point and relative efficiency of the sample projection depth weighted scatter estimators are thoroughly investigated the influence function and the maximum bias of the projection depth weighted scatter estimators are derived and examined unlike typical high breakdown competitors the projection depth weighted scatter estimators can integrate high breakdown point and high efficiency while enjoying a bounded influence function and a moderate maximum bias curve comparisons with leading estimators on asymptotic relative efficiency and gross error sensitivity reveal that the projection depth weighted scatter estimators behave very well overall and consequently represent very favorable choices of affine equivariant multivariate scatter estimators

bias robust estimation of scale in this paper we consider the problem of robust estimation of the scale of the location residuals when the underlying distribution of the data belongs to a contamination neighborhood of a parametric location scale family we define the class of m estimates of scale with general location and show that under certain regularity assumptions these scale estimates converge to their asymptotic functionals uniformly with respect to the underlying distribution and with respect to the m estimate defining score function chi we establish expressions for the maximum asymptotic bias of m estimates of scale over the contamination neighborhood as a function of the fraction of contamination using these expressions we construct asymptotically min max bias robust estimates of scale in particular we show that a scaled version of the madm median of absolute residuals about the median is approximately min max bias robust within the class of huber s proposal 2 joint estimates of location and scale we also consider the larger class of m estimates of scale with general location and show that a scaled version of the shorth the shortest half of the data is approximately min max bias robust in this class finally we present the results of a monte carlo study showing that the shorth has attractive finite sample size mean squared error properties for contaminated gaussian data

topological indices of the line graph of subdivision graphs and their schur bounds in this paper we investigate topological indices of the line graphs of the tadpole graphs wheel graphs and ladder graphs using the subdivision concept which generalize the results of ranjini et al 2011 in addition we present the schur bound for the general sum connectivity co index

bounds for singular values using traces abstract bounds for the singular values ratios of singular values and rank of a square matrix a involving tr a tr a 2 and tr a h a are presented some of the results are analogous to the well known bounds for the eigenvalues ratios of eigenvalues and rank of a involving tr a and tr a 2

lower bounds for the smallest singular value abstract let a aij be an n n complex matrix suppose that g a the undirected graph of a has no isolated vertex let e be the set of edges of g a we prove that the smallest singular value of a n satisfies n min ij i j e where gij ai aj ai aj 2 ri ci rj cj 1 2 2 with ai aii and ri ci are the ith deleted absolute row sum and column sum of a respectively the result simplifies and improves that of johnson and szulc n mini j ij see 1

a decreasing sequence of eigenvalue localization regions abstract we construct a decreasing sequence of rectangles rp in such a way that all the eigenvalues of a complex matrix a are contained in each rectangle when a is a matrix with real spectrum or a normal matrix each rp can be obtained without knowing the eigenvalues of a

lower bounds for contamination bias globally minimax versus locally linear estimation we study how robust estimators can be in parametric families obtaining a lower bound on the contamination bias of an estimator that holds for a wide class of parametric families this lower bound includes as a special case the bound used to establish that the median is bias minimax among location equivariant estimators and it is tight or nearly tight in a variety of other settings such as scale estimation discrete exponential families and multiple linear regression the minimum variation distance estimator has contamination bias within a dimension free factor of this bound a second lower bound applies to locally linear estimates and implies that such estimates cannot be bias minimax among all fisher consistent estimates in higher dimensions in linear regression this class of estimates includes the familiar m estimates gm estimates and s estimates in discrete exponential families yet another lower bound implies that the proportion of zeros estimate has minimax bias if the median of the distribution is zero a common situation in some fields this bound also implies that the information standardized sensitivity of every fisher consistent estimate of the poisson mean and of the binomial proportion is unbounded

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

on one step gm estimates and stability of inferences in linear regression abstract the folklore on one step estimation is that it inherits the breakdown point of the preliminary estimator and yet has the same large sample distribution as the fully iterated version as long as the preliminary estimate converges faster than n 1 4 where n is the sample size we investigate the extent to which this folklore is valid for one step gm estimators and their associated standard errors in linear regression we find that one step gm estimates based on newton raphson or scoring inherit the breakdown point of high breakdown point initial estimates such as least median of squares provided the usual weights that limit the influence of extreme points in the design space are based on location and scatter estimates with high breakdown points moreover these estimators have bounded influence functions and their standard errors can have high breakdown points the folklore concerning the large sample theory is correct assuming the regression errors are symmetrically distributed and homoscedastic

a class of locally and globally robust regression estimates abstract we present a new class of regression estimates called generalized estimates these estimates are defined by minimizing the scale of the weighted residuals with weights that penalize high leverage observations like the estimates the generalized estimates utilize for their definition two loss functions 1 and 2 which together with the weights can be chosen to achieve simultaneously high breakdown point finite gross error sensitivity and high efficiency we recommend however choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step the generalized estimate with loss functions 1 and 2 is related to the hill ryan gm estimate with a loss function which is a linear combination of 1 and r in fact both estimates have the same influence function and asymptotic distribution under the central model we show that a certain generalized estima

generalized s estimators abstract in this article we introduce a new type of positive breakdown regression method called a generalized s estimator or gs estimator based on the minimization of a generalized m estimator of residual scale we compare the class of gs estimators with the usual s estimators including least median of squares it turns out that gs estimators attain a much higher efficiency than s estimators at the cost of a slightly increased worst case bias we investigate the breakdown point the maxbias curve and the influence function of gs estimators we also give an algorithm for computing gs estimators and apply it to real and simulated data

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

a bounded influence high breakdown efficient regression estimator abstract we consider the multiple linear regression model y i x i e i i 1 2 n with random carriers and focus on the estimation of this article s main contribution is to present an estimator that is affine regression and scale equivariant has both a high breakdown point and a bounded influence function and has an asymptotic efficiency greater than 95 versus least squares under gaussian errors we give conditions under which the estimator a one step general m estimator that uses schweppe weights and is based on a high breakdown initial estimator satisfies these properties the major conditions necessary for the estimator are a it must be based on a n consistent initial estimator with a 50 breakdown point and b it must be based on a psi function that is odd bounded and strictly increasing the advantage of this estimator over previous approaches is that it does not downweight high leverage points without first considering how they fit the bulk of the data methods of computi

the influence function and maximum bias of tukey s median tukey s median is among one of the earliest known high breakdown point multivariate location statistics aside from its breakdown point though little else appears to be known about its robustness properties in this paper we investigate other aspects of tukey s median and in particular we derive and study its influence function and its maximum contamination bias function when judged by these other robustness criteria tukey s median again proves to be highly robust

projection estimators for generalized linear models we introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression these projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter we found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction e of outlier contamination for small e this bias is approximately twice the maximum bias of the initial estimator independently of the number of regressors since these projection estimators are not asymptotically normal we define one step weighted m estimators starting at the projection estimators these estimators have the same asymptotic normal distribution as the m estimator and a degree of robustness close to the one of the projection estimator we perform a monte carlo simulation for the case of binomial and poisson regression with canonical links this study shows that the proposed estimators compare favorab

the least trimmed differences regression estimator and alternatives abstract this article proposes and studies the performance in theory and practice of the least trimmed differences ltd linear regression estimator the estimator minimizes the sum of the smallest quartile of the squares of the differences in each pair of residuals we obtain the breakdown point maxbias curve and large sample properties of a class of estimators including the ltd as special case the ltd estimator has a 50 breakdown point and gaussian efficiency of 66 substantially higher than other common high breakdown estimators such as least median of squares and least trimmed squares the ltd estimator is difficult to compute but can be performed using a feasible solution algorithm half sample jackknifing is effective in producing standard errors in simulations we find the ltd to be more stable than other high breakdown estimators in an example the ltd still shows instability like other high breakdown estimators when there are small changes in the data

min max bias robust regression abstract this paper considers the problem of minimizing the maximum asymptotic bias of regression estimates over epsilon contamination neighborhoods for the joint distribution of the response and carriers two classes of estimates are treated 1 m estimates with bounded function rho applied to the scaled residuals using a very general class of scale estimates and 2 bounded influence function type generalized m estimates estimates in the first class are obtained as the solution of a minimization problem while estimates in the second class are specified by an estimating equation the first class of m estimates is sufficiently general to include both huber proposal 2 simultaneous estimates of regression coefficients and residuals scale and rousseeuw yohai s estimates of regression it is shown than an s estimate based on a jump function type rho solves the min max bias problem for the class of m estimates with very general scale this estimate is obtained by the minimization of the alpha quantile of the squared residuals where alpha epsilon depends on the fraction of contamination epsilon when epsilon approaches limit of 5 alpha epsilon approaches limit of 5 and the min max estimator approaches the least median of squared residuals estimator introduced by rousseeuw for the bounded influence class of gm estimates it is shown the a sign type nonlinearity yields the min max estimate this estimate coincides with the minimum gross error sensitivity gm estimate

matricial inner products and pointed cones of hermitian preserving linear transformations abstract let be a conjugate homogeneous reflector on a vector space v over r or c with p a pointed cone contained in spec v a mapping on v v whose range is contained in p which generalizes the usual inner product properties is called a vectorial inner product a certain family of these vectorial inner products on matrices which we call matricial inner products is used to generate a set of pointed cones in the ambient space of hermitian preserving linear transformations some basic results on these cones including psd psd and c p and on the partial orders that they induce are given

characterizations and lower bounds for the spread of a normal matrix abstract the spread of an n n matrix a with eigenvalues 1 n is defined by spr a max j k j k we prove that if a is normal then spr a max x ax y ay x y c n x y 1 max x ay y ax x y c n x y 1 re x y 0 max x ay y ax x y c n x y 1 x y 0 max spr z a z a 2 z c z 1 2 max x a 2 x x ax 2 x a ax x ax 2 1 2 x c n x 1 we also present several lower bounds for spr a given by these characterizations

propagation of outliers in multivariate data we investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers i e contamination in each variable is independent from the other variables this model brings up a possible new source of statistical error that we call propagation of outliers this source of error is unusual in the sense that it is generated by the data processing itself and takes place after the data has been collected we define and derive the influence function of robust multivariate location estimates under flexible contamination models and use it to investigate the effect of propagation of outliers furthermore we show that standard high breakdown affine equivariant estimators propagate outliers and therefore show poor breakdown behavior under componentwise contamination when the dimension d is high

a per survivor phase estimation algorithm for detection of psk signals an expectation maximization em technique for maximum a posteriori map estimation of a random parameter is employed to devise a per survivor phase tracking algorithm for phase shift keyed signals transmitted over channels with phase jitter simulation results show that the proposed algorithm can provide substantial performance gains over recursive and nonrecursive phase estimators in the presence of a strong phase jitter

upper bounds for singular values abstract let a be an n n matrix with singular values 1 n if 1 r n then r min h s r h where sr is the set of n n matrices h such that rank a h r 1 and denotes the spectral norm i e the largest singular value we find upper bounds for r by choosing h suitably

normalized frobenius condition number of the orthogonal projections of the identity abstract this paper deals with the orthogonal projection in the frobenius sense a n of the identity matrix i onto the matrix subspace a s a r n n s being an arbitrary subspace of r n n lower and upper bounds on the normalized frobenius condition number of matrix a n are given furthermore for every matrix subspace s r n n a new index f a s which generalizes the normalized frobenius condition number of matrix a is defined and analyzed

inequalities for the numerical radius the norm and the maximum of the real part of bounded linear operators in hilbert spaces some inequalities for the numerical radius the operator norm and the maximum of the real part of bounded linear operators in hilbert spaces under suitable assumptions for the involved operator are given

bounds for ratios of eigenvalues using traces abstract let a be an n n matrix with real eigenvalues 1 n and let 1 k l n bounds involving tr a and tr a 2 are introduced for k l k l k l and k k n l 1 l 2 k 2 k n l 1 2 l also included are conditions for l 0 and for k l 0

bounds for the spectral radius and the largest singular value abstract we derive an increasing sequence of lower bounds for the spectral radius of a matrix with real spectrum and progressively improved bounds for the largest singular value of a complex matrix we also find estimates for the rank of normal matrices with real spectrum and for the rank of normal nonnegative matrices including some sufficient condition for such matrices to be invertible

a dynamic programming algorithm for simultaneous phase estimation and data decoding on random phase channels the problem of simultaneously estimating phase and decoding data symbols from baseband data is posed the phase sequence is assumed to be a random sequence on the circle and the symbols are assumed to be equally likely symbols transmitted over a perfectly equalized channel a dynamic programming algorithm viterbi algorithm is derived for decoding a maximum em a posteriori map phase symbol sequence on a finite dimensional phase symbol trellis a new and interesting principle of optimality for simultaneously estimating phase and decoding phase amplitude coded symbols leads to an efficient two step decoding procedure for decoding phase symbol sequences simulation results for binary 8 ary phase shift keyed psk and 16 quadrature amplitude shift keyed qask symbol sets transmitted over random walk and sinusoidal jitter channels are presented and compared with results one may obtain with a decision directed algorithm or with the binary viterbi algorithm introduced by ungerboeck when phase fluctuations are severe and when occasional large phase fluctuations exist map phase symbol sequence decoding on circles is superior to ungerboeck s technique which in turn is superior to decision directed techniques

high breakdown point estimates of regression by means of the minimization of an efficient scale abstract a new class of robust estimates estimates is introduced the estimates have simultaneously the following properties a they are qualitatively robust b their breakdown point is 5 and c they are highly efficient for regression models with normal errors they are defined by minimizing a new scale estimate applied to the residuals asymptotically a estimate is equivalent to an m estimate with a function given by a weighted average of two functions one corresponding to a very robust estimate and the other to a highly efficient estimate the weights are adaptive and depend on the underlying error distribution we prove consistency and asymptotic normality and give a convergent iterative computing algorithm finally we compare the biases produced by gross error contamination in the estimates and optimal bounded influence estimates

approximate ml decoding of coded psk with no explicit carrier phase reference an approximate method is discussed for maximum likelihood estimation of coded psk sequences in the presence of an unknown carrier phase this method makes use of the viterbi algorithm to find an optimum path in the encoder trellis diagram phase estimation is embedded into the structure of the detection algorithm and the branch metrics in the trellis are modified with respect to those employed with known carrier phase comparisons with traditional decoding schemes show that the proposed solution has better performance in terms of acquisition time and cycle slips