separability of sequential isomorphisms on quantum effects in multipartite systems in the paper we study separability of sequential isomorphisms on quantum effects in multipartite systems first we obtain necessary and sufficient conditions for separable sequential isomorphisms in bipartite systems secondly in finite dimensional bipartite systems separability of sequential endomorphisms on quantum effects is discussed furthermore we extend these conclusions to the multipartite case finally applying our results an equivalent characterization of local unitary operations is given

the nth root of sequential effect algebras in 2005 gudder int j theor phys 44 2219 2005 presented 25 problems of sequential effect algebras the 20th problem asked in a sequential effect algebra if the square root of some element exists is it unique in this paper we show that for each given positive integer n 1 there is a sequential effect algebra such that the nth root of its some element c is not unique and the nth root of c is not the kth root of c k n thus we answer the problem negatively

sequential quantum measurements a quantum effect is an operator a on a complex hilbert space h that satisfies 0 a i we denote the set of quantum effects by e h the set of self adjoint projection operators on h corresponds to sharp effects and is denoted by p h we define the sequential product of a b e h by a b a1 2ba1 2 the main purpose of this article is to study some of the algebraic properties of the sequential product many of our results show that algebraic conditions on a b imply that a and b commute for the usual operator product for example if a b satisfies certain distributive or associative laws then ab ba moreover if a b p h then ab ba and a b b or b a b if and only if ab ba b a natural definition of stochastic independence is introduced and briefly studied

structural characterization and condition for measurement statistics preservation of a unital quantum operation we investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation acting on finite dimensional quantum states by reducing this problem to the problem of simultaneous diagonalization of the kraus operators associated with we can completely characterize the kinds of quantum states that are fixed by our work has several applications it gives a simple proof of the structural characterization of a unital quantum operation that acts on finite dimensional quantum states a result not explicitly mentioned in earlier studies it also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation finally our result clarifies and extends the work of st rmer by giving a proof of a reduction theorem on the unassisted and entanglement assisted classical capacities coherent information and minimal output renyi entropy of a unital channel acting on a finite dimensional quantum state

generalized infimum and sequential product of quantum effects the quantum effects for a physical system can be described by the set e h of positive operators on a complex hilbert space h that are bounded above by the identity operator i for a b e h the operation of sequential product a b a1 2ba1 2 was proposed as a model for sequential quantum measurements a nice investigation of properties of the sequential product has been carried over gudder s and nagy g sequential quantum measurements j math phys 42 5212 2001 in this note we extend some results of this reference in particular a gap in the proof of theorem 3 2 in this reference is overcome in addition some properties of generalized infimum a b are studied

high breakdown point robust regression with censored data in this paper we propose a class of high breakdown point estimators for the linear regression model when the response variable contains censored observations these estimators are robust against high leverage outliers and they generalize the lms least median of squares s mm and estimators for linear regression an important contribution of this paper is that we can define consistent estimators using a bounded loss function or equivalently a redescending score function since the calculation of these estimators can be computationally costly we propose an efficient algorithm to compute them we illustrate their use on an example and present simulation studies that show that these estimators also have good finite sample properties

three characterisations of the sequential product it has already been established that the properties required of an abstract sequential product as introduced by gudder and greechie are not enough to characterise the standard sequential product a b aba on an operator algebra we give three additional properties each of which characterises the standard sequential product on either a von neumann algebra or a euclidean jordan algebra these properties are 1 invariance under the application of unital order isomorphisms 2 symmetry of the sequential product with respect to a certain inner product and 3 preservation of invertibility of the effects to give these characterisations we first have to study convex sequential effect algebras we show that these objects correspond to unit intervals of spectral order unit spaces with a homogeneous positive cone it has already been established that the properties required of an abstract sequential product as introduced by gudder and greechie are not enough to characterise the standard sequential product a b aba on an operator algebra we give three additional properties each of which characterises the standard sequential product on either a von neumann algebra or a euclidean jordan algebra these properties are 1 invariance under the application of unital order isomorphisms 2 symmetry of the sequential product with respect to a certain inner product and 3 preservation of invertibility of the effects to give these characterisations we first have to study convex sequential effect algebras we show that these objects correspond to unit intervals of spectral order unit spaces with a homogeneous positive cone

fixed points of commutative luders operations this paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations specifically it is proved that if a quantum operation has mutually commuting operation elements that are effects forming a resolution of the identity then the fixed point set of the quantum operation is exactly the commutant of the operation elements

a uniqueness problem of the sequence product on operator effect algebra cal e h a quantum effect is an operator on a complex hilbert space h that satisfies 0 a i we denote the set of all quantum effects by in this paper we prove theorem 4 3 the theory of the sequential product on which shows in fact that there are sequential products on which are not of the generalized luders form this result answers gudder s open problem negatively

on fixed points of luders operation in this paper we give a concrete example of a luders operation la with n 3 such that la b b does not imply that b commutes with all e1 e2 and e3 in a this example answers an open problem of professor gudder

a universal property for sequential measurement we study the sequential product the operation p q pqp on the set of effects 0 1 x1d49c of a von neumann algebra x1d49c that represents sequential measurement of first p and then q in their work j math phys 49 5 052106 2008 gudder and latremoliere give a list of axioms based on physical grounds that completely determines the sequential product on a von neumann algebra of type i that is a von neumann algebra of all bounded operators on some hilbert space in this paper we give a list of axioms that completely determines the sequential product on all von neumann algebras simultaneously theorem 4

fixed points of quantum operations quantum operations frequently occur in quantum measurement theory quantum probability quantum computation and quantum information theory if an operator a is invariant under a quantum operation we call a a fixed point physically the fixed points are the operators that are not disturbed by the action of our main purpose is to answer the following question if a is a fixed point is a compatible with the operation elements of we shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von neumann algebras

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

instrumental variable estimation based on conditional median restriction abstract we develop a method named the l 1 iv estimator to estimate structural equations based on the conditional median restriction imposed on the error terms we study its asymptotic behavior and show how to estimate its asymptotic covariance matrix we also discuss the point identification in the l 1 iv estimation and propose an over identifying restriction test we further demonstrate the performance of the l 1 iv estimator in comparison with the familiar two stage least squares estimator the proposed method is applied to estimate the labor supply and wage offer functions for working married women

multiplicative jordan triple isomorphisms on the self adjoint elements of von neumann algebras abstract in this paper we consider multiplicative jordan triple isomorphisms between the sets of self adjoint elements respectively the sets of positive elements of von neumann algebras these transformations are the bijective maps which satisfy the equality aba a b a on their domains we show that all those transformations originate from linear algebra isomorphisms and linear algebra antiisomorphisms in the case when the underlying von neumann algebras do not have commutative direct summands an application of our results concerning non linear maps which preserve the absolute value of products is also presented

quantum markov chains a new approach to quantum markov chains is presented we first define a transition operation matrix tom as a matrix whose entries are completely positive maps whose column sums form a quantum operation a quantum markov chain is defined to be a pair g e where g is a directed graph and e eij is a tom whose entry eij labels the edge from vertex j to vertex i we think of the vertices of g as sites that a quantum system can occupy and eij is the transition operation from site j to site i in one time step the discrete dynamics of the system is obtained by iterating the tom e we next consider a special type of tom called a transition effect matrix in this case there are two types of dynamics a state dynamics and an operator dynamics although these two types are not identical they are statistically equivalent we next give examples that illustrate various properties of quantum markov chains we conclude by showing that our formalism generalizes the usual framework for quantum random walks

on spectra of luders operations we show that all the eigenvalues of certain generalized luders operations are non negative real numbers in two cases of interest in particular given a commuting n tuple a a1 an consisting of positive operators on a hilbert space h satisfying j 1naj i we show that the spectrum of the luders operation a b h x j 1naj1 2xaj1 2 b h is contained in 0 so the only solution of the equation a x i x is the expected one x 12i

mallows type bounded influence regression trimmed means abstract the influence functions of the regression trimmed mean estimators proposed by koenker and bassett 1978 and welsh 1987 are bounded in the dependent variable space but not in the independent variable space this article follows the approach of mallows 1973 1975 and modifies these estimators so that the resulting estimators have bounded influence functions the large sample behavior of these estimators is studied and it is shown that they have the same asymptotic distribution the small sample behaviors of the ordinary regression and bounded influence regression trimmed means are then investigated by means of a monte carlo study and by applying the estimators to water salinity data see ruppert and carroll 1980 based on these results we conclude that one can potentially gain much by using bounded influence regression trimmed means over ordinary regression trimmed means however there does not seem to be a clear choice between the koenker bassett and welsh versions

modeling subdiffusion using reaction diffusion systems in many types of media particularly within living cells or within their membranes diffusing species do not follow fick s laws but instead show transient subdiffusive behavior formulating spatiotemporal models that take this behavior into account is a delicate matter as one is faced with the choice of resorting either to fractional calculus or to microscopic descriptions in this article we provide an alternative designed to be easier to handle analytically and numerically than the existing approaches specifically starting from the continuous time random walk model we construct linear reaction diffusion systems that can be used as components within such a model and which capture the defining properties of subdiffusion we show how to impose physically relevant parameters and prove stability and mass conservation while applications to cellular biology are our main motivation our approach is abstract and should thus be applicable to any situation where anomalous subdiffusion is observed

bounded influence regression via local minimax mean squared error abstract the class of general m estimators for the stochastic linear regression model is considered and influence and change of variance functions are used to approximate the main term of the mean squared error mse the estimator is then found in the class that minimizes the maximum of that approximate mse over the contamination neighborhood this approach allows for additional flexibility of designing estimators optimal for prediction in specific regions of the factor space and it provides a practical way of choosing estimators tuning constants as functions of a fraction of contamination and sample size

qualitative robustness for stochastic processes in this paper we generalize hampel s concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non i i d observations defining appropriate metrics between samples we also present a different approach to qualitative robustness which formalizes the notion of resistance we give two definitions based on this approach strong and weak resistance we show that for estimating a finite dimensional real parameter pi robustness is equivalent to weak resistance and in the i i d case is also equivalent to strong resistance finally we prove the strong resistance of a class of estimators which includes common gm estimates for linear models and autoregressive processes

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

non disturbance for fuzzy quantum measurements we consider three criteria for describing non disturbance between quantum measurements while previous discussions of these criteria considered sharp measurements we shall treat more general measurements that may be unsharp or fuzzy it has been shown that in the sharp case the three criteria are equivalent to compatibility of the measurements we shall show that only the third criterion is equivalent to compatibility for the general fuzzy case moreover the first two criteria are not symmetric relative to the two measurements

estimation following a sequentially designed experiment abstract we investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function approaches to this problem include the robbins monro 1951 venter 1967 and lai robbins 1979 1981 stochastic approximation procedures and wu s 1985 1986 sequential maximum likelihood estimators because the regression function is not assumed to belong to a parametric family only experimentation near to the root is informative and the sequential design should converge to the root after the sequential design has been generated there are at least two distinct methods for estimation of the root a estimate the root by the last design point or b fit a parametric model except for ruppert 1988 and simulation studies by bodt 1985 and bodt and tingey 1990 all studies known to us of stochastic approximation procedures used the last design point as the estimator wu 1985 1986 fit a generalized linear model when the last design point is the estimator then cle

outlier induced collinearities when an observation in a regression analysis has very large values on two or more predictor variables artificial collinearities can be induced the effects of such collinearities on a regression analysis are not well documented although they can be shown to be similar in many respects to those resulting from approximate linear dependencies among the columns of predictor variable values the purpose of this article is to explore the effects of outlier induced collinearities on the estimation of regression coefficients

the breakdown point of simultaneous general m estimates of regression and scale abstract this article deals with the breakdown point of simultaneous general m estimates of the regression parameter vector and scale parameter of a linear model a general expression for is derived and its numerical values are computed for the case in which the carriers have a normal distribution the numerical results show that is in general much lower than the minimum of the breakdown points of with known and of with known the values of for some real and simulated data sets are also given

robust inference with gmm estimators the local robustness properties of generalized method of moments gmm estimators and of a broad class of gmm based tests are investigated in a unified framework gmm statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded since in many applications this function is unbounded it is useful to have procedures that modify the starting orthogonality conditions in order to obtain a robust version of a gmm estimator or test we show how this can be obtained when a reference model for the data distribution can be assumed we develop a flexible algorithm for constructing a robust gmm rgmm estimator leading to stable gmm test statistics the amount of robustness can be controlled by an appropriate tuning constant we relate by an explicit formula the choice of this constant to the maximal admissible bias on the level or and the power of a gmm test and the amount of contamination that one can reasonably assume given some information on the data finally we illustrate the rgmm methodology with some simulations of an application to rgmm testing for conditional heteroscedasticity in a simple linear autoregressive model in this example we find a significant instability of the size and the power of a classical gmm testing procedure under a non normal conditional error distribution on the other side the rgmm testing procedures can control the size and the power of the test under non standard conditions while maintaining a satisfactory power under an approximatively normal conditional error distribution

on non linear serial dependencies in stock returns abstract this paper considers the h p tests of linearity and gaussianity of daily stock returns and their implications for non linear models of those returns

infinitesimal robustness for diffusions we develop infinitesimally robust statistical procedures for the general diffusion processes we first prove the existence and uniqueness of the times series influence function of conditionally unbiased m estimators for ergodic and stationary diffusions under weak conditions on the martingale estimating function used we then characterize the robustness of m estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators to compute these estimators we propose a general algorithm which exploits approximation methods for diffusions in the computation of the robust estimating function monte carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real data application

fixed points of dual quantum operations abstract let a be a normal completely positive map on b h with kraus operators a i i 1 denote m the subset of normal completely positive maps by m a i 1 a i a i i i 1 a i a i i and a is normal in this note the relations between the fixed points of a and a are investigated we obtain that b k h a b b b k h a b b where k h is the set of all compact operators on h and a is the dual of a m in addition we show that the map a a is a bijection on m

sequential endomorphisms of finite dimensional hilbert space effect algebras we describe the structure of all continuous sequential endomorphisms of the effect algebra of a finite dimensional hilbert space

influence functions for proportional hazards regression summary influence functions for the regression parameters in the proportional hazards model are presented it is suggested that empirical influence functions computed for each observation and each covariate can be useful in an informal way to identify influential observations this is illustrated on the stanford heart transplant data and two other examples

semiparametric robust estimation of truncated and censored regression models many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares scls are sensitive to outliers and data contamination as we document therefore we propose a semiparametric general trimmed estimator gte of truncated and censored regression which is highly robust but relatively imprecise to improve its performance we also propose data adaptive and one step trimmed estimators we derive the robust and asymptotic properties of all proposed estimators and show that the one step estimators e g one step scls are as robust as gte and are asymptotically equivalent to the original estimator e g scls the finite sample properties of existing and proposed estimators are studied by means of monte carlo simulations

characterizing sequential isomorphisms on hilbert space effect algebras let be any sequential product on the hilbert space effect algebra with and be a bijective map we show that if satisfies ab a b for then there is either a unitary or an anti unitary operator u such that a uau for every let be a borel function satisfying g 0 0 g 1 1 and let us define a binary operation g on by a gb a1 2 g a bg a a1 2 where t denotes the conjugate of the operator t we also show that a bijective map satisfies a gb a g b for if and only if there is either a unitary or an anti unitary operator u such that a uau for every

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

minimax aspects of bounded influence regression abstract bounded influence regression in the sense of hampel mallows krasker welsch is examined critically from the point of view of finite sample minimax robust estimation theory the main conclusion is that the influence of position of very high leverage points that is of points where the diagonal element of the hat matrix h x xtx 1 xt exceeds a certain bound should be cut down selectively this bound should be chosen roughly between 2 and 5 for the upper of these values the resulting estimate can be approximated very simply by scaling the residuals by their own estimated standard deviation a conflict between decision theoretic estimation and data analytic diagnostic viewpoints is pointed out and briefly discussed

almost sharp quantum effects quantum effects are represented by operators on a hilbert space satisfying 0 a i and sharp quantum effects are represented by projection operators we say that an effect a is almost sharp if a pqp for projections p and q we give simple characterizations of almost sharp effects we also characterize effects that can be written as longer products of projections for generality we first work in the formalism of von neumann algebras we then specialize to the full operator algebra b h and to finite dimensional hilbert spaces

resistant estimation for simultaneous equations models using weighted instrumental variables in this paper we present a weighted instrumental variables estimator that is resistant2 to heavy tailed errors aberrant data in either the endogenous or exogenous variables and certain other model failures the estimator is analogous to the weighted least squares approach to robustness proposed by krasker and welsch 21 for ordinary regression we will discuss the theory that motivated this estimator derive some of its properties describe our computational algorithm and using an empirical example illustrate the estimator s utility as a tool for data analysis in structural models the evolution of robust estimators for simultaneous equations models has closely resembled the development of robust methods for ordinary regression in both cases research focused at first on the well documented effects of long tailed error distributions on the classical procedures for ordinary regression models statisticians have studied the properties of least absolute deviations lad estimators see bassett and koenker 2 and amemiya 1 and maximum likelihood type estimators called m estimators see huber 14 for simultaneous equations models lad can be generalized in several different ways to modify two stage least squares or instrumental variables amemiya 1 has presented these estimators in a unified framework and powell 31 has proven their asymptotic normality under weak assumptions fair 8 has compared two stage lad estimates of a u s macroeconomic model with two stage least squares and full information maximum likelihood estimates the m estimator concept can also be generalized to simultaneous equations for example prucha and kelejian 32 have considered maximum likelihood estimation under the assumption that the disturbance vector is multivariate student t although lad and m estimators maintain a high efficiency when the error distribution is heavy tailed they are not robust in the stronger sense of hampel 10 which roughly speaking requires an estimator to have a limited sensitivity to any small fraction of the data 3 lad and m estimators fail under this criterion because a single observation whose values for the right side variables are highly anomalous can have an arbitrarily large effect on lad estimates or m estimates just as on the classical procedures consequently these estimators do not provide insurance against the sort of gross errors that occur in some data sets nor do they serve as reliable diagnostics for departures from linearity occurring in extreme regions of the space of right side variables for linear models the estimators that satisfy the strong hampel robustness criterion have become known as bounded influence estimators several such estimators have been

maps preserving operator pairs whose products are projections abstract let b h be the algebra of all bounded linear operators on a complex hilbert space h with dim h 2 it is proved that a surjective map on b h preserves operator pairs whose products are nonzero projections in both directions if and only if there is a unitary or an anti unitary operator u on h such that a u au for all a in b h for some constants with 2 1 related results for surjective maps preserving operator pairs whose triple jordan products are nonzero projections in both directions are also obtained these show that the operator pairs whose products or triple jordan products are nonzero projections are isometric invariants of b h

bounded influence estimators for the sure model abstract this paper considers robust estimation of the seemingly unrelated regression equations sure model following the infinitesimal approach to robustness we characterize the class of optimal bounded influence estimators and we propose two computationally simple estimators we also present the results of a set of monte carlo experiments carried out to study the behavior of these estimators

a generalization of gudder nagy s theorem with numerical ranges of operators in this paper we prove that for a b c which are bounded linear operators on a separable complex hilbert space h ax x bx x cx x for all x h with x 1 if and only if there exists a complex number c c such that a ci and c cb or b ci and c ca

nondisturbing quantum measurements we consider pairs of discrete quantum observables povms and analyze the relation between the notions of nondisturbance joint measurability and commutativity we specify conditions under which these properties coincide or differ depending for instance on the interplay between the number of outcomes and the hilbert space dimension or on algebraic properties of the effect operators we also show that non disturbance is in general not a symmetric relation and that it can be decided and quantified by means of a semidefinite program

change of variance sensitivities in regression analysis the change of variance function is defined for estimators of regression coefficients both an unstandardized and a standardized form of the change of variance sensitivity are introduced and their relation with the corresponding gross error sensitivities is investigated the problems of optimal robustness lead to the hampel krasker and the krasker welsch estimators at the same time also the scale parameter has to be estimated robustly by means of the change of variance sensitivity optimal robust redescending scale estimators are constructed

preservers on hilbert space effects in this paper we study a new class of transformations on the set of all hilbert space effects this consists of the bijective maps which preserve the order and zero product in both directions the main result of the paper gives a complete description of the structure of those transformations as applications we obtain additional new results and some former ones as easy corollaries in particular we obtain the form of the ortho order automorphisms as well as that of the sequential automorphisms in the last paragraph of the paper we show that the automorphisms of these two kinds belong to our class of transformations even when their domain is the set of all effects in a general von neumann algebra

sequential product on standard effect algebra cal e h a quantum effect is an operator a on a complex hilbert space h that satisfies is the set of all quantum effects on h in 2001 professors gudder and nagy studied the sequential product for in 2005 professor gudder asked is the only sequential product on recently liu and wu have presented an example to show that the answer is negative in this paper first we characterize some algebraic properties of the abstract sequential product on second we present a general method for constructing sequential products on and finally we study some properties of the sequential products constructed by the method

a framework for worst case and stochastic safety verification using barrier certificates this paper presents a methodology for safety verification of continuous and hybrid systems in the worst case and stochastic settings in the worst case setting a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region no explicit computation of reachable sets is required in the construction of barrier certificates which makes it possible to handle nonlinearity uncertainty and constraints directly within this framework in the stochastic setting our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set a bound whose validity is proven by the existence of a barrier certificate for polynomial systems barrier certificates can be constructed using convex optimization and hence the method is computationally tractable some examples are provided to illustrate the use of the method

two time scale markov chains and applications to quasi birth death queues aiming at reduction of complexity this work is concerned with two time scale markov chains and applications to quasi birth death queues asymptotic expansions of probability vectors are constructed and justified lumping all states of the markov chain in each subspace into a single state an aggregated process is shown to converge to a continuous time markov chain whose generator is an average with respect to the stationary measures then a suitably scaled sequence is shown to converge to a switching diffusion process extensions of the results are presented together with examples of quasi birth death queues

generalized continuous time random walks master equations and fractional fokker planck equations continuous time random walks which generalize random walks by adding a stochastic time between jumps provide a useful description of stochastic transport at mesoscopic scales the continuous time random walk model can accommodate certain features such as trapping which are not manifest in the standard macroscopic diffusion equation the trapping is incorporated through a waiting time density and a fractional diffusion equation results from a power law waiting time a generalized continuous time random walk model with biased jumps has been used to consider transport that is also subject to an external force here we have derived the master equations for continuous time random walks with space and time dependent forcing for two cases when the force is evaluated at the start of the waiting time and at the end of the waiting time the differences persist in low order spatial continuum approximations however the two processes are shown to be governed by the same fokker planck equations in the diffusi

sequential product spaces are jordan algebras we show that finite dimensional order unit spaces equipped with a continuous sequential product as defined by gudder and greechie are homogeneous and self dual as a consequence of the koecher vinberg theorem these spaces therefore correspond to euclidean jordan algebras we remark on the significance of this result in the context of reconstructions of quantum theory in particular we show that sequential product spaces must be c algebras when their vector space tensor product is also a sequential product space in the parlance of operational theories when the space allows a local composite we also show that sequential product spaces in infinite dimension correspond to jb algebras when a few additional conditions are satisfied finally we remark on how changing the axioms of the sequential product might lead to a new characterization of homogeneous cones we show that finite dimensional order unit spaces equipped with a continuous sequential product as defined by gudder and greechie are homogeneous and self dual as a consequence of the koecher vinberg theorem these spaces therefore correspond to euclidean jordan algebras we remark on the significance of this result in the context of reconstructions of quantum theory in particular we show that sequential product spaces must be c algebras when their vector space tensor product is also a sequential product space in the parlance of operational theories when the space allows a local composite we also show that sequential product spaces in infinite dimension correspond to jb algebras when a few additional conditions are satisfied finally we remark on how changing the axioms of the sequential product might lead to a new characterization of homogeneous cones

characterizations of fixed points of quantum operations let a be a general quantum operation an operator b is said to be a fixed point of a if a b b in this note we shall show conditions under which b a fixed point a implies that b is compatible with the operation element of a in particular we offer an extension of the generalized luders theorem

continuous jordan triple endomorphisms of p2 abstract we describe the structure of all continuous jordan triple endomorphisms of the set p 2 of all positive definite 2 2 matrices thus completing a recent result of ours we also mention an application concerning sorts of surjective generalized isometries on p 2 and as second application we complete another former result of ours on the structure of sequential endomorphisms of finite dimensional effect algebras

a note on operator probability theory involving numerical ranges abstract in this note the relationships between the expectation and variance in operator probability theory and numerical range of operators are considered

the structure of simultaneous equation estimators a generalization towards nonnormal disturbances a general linear simultaneous equation system with a multivariate student t disturbance vector is considered the normal equations of the corresponding maximum likelihood estimator are used as estimator generating equations to introduce a new class of estimators properties of large subclasses of these estimators are determined for disturbance vectors other than the multivariate student t

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

quantum operations fixing a convex cone of density operators on t h nsf of china 11001230 nsf of fujian 2013j01022 fundamental research funds for the central universities 2012121001

on b robust instrumental variable estimation of the linear model with panel data the aim of this paper is to demonstrate how to acquire robust consistent estimates of the linear model when the fundamental orthogonality condition is not fulfilled with this end in view we develop two estimation procedures two stage generalized m 2sgm and robust generalized method of moments rgmm both estimators are b robust i e their associated influence function is bounded consistent and asymptotic normally distributed our simulation results indicate that the relatively efficient rgmm estimator in regressions with heteroskedastic and or autocorrelated errors provides accurate parameter estimates of a panel data model with all variables subject to measurement errors even if a substantial portion of the data is contaminated with aberrant observations the traditional estimation techniques such as 2sls and gmm break down when outliers corrupt the data

a natural robustification of the ordinary instrumental variables estimator summary instrumental variables estimators are designed to provide consistent parameter estimates for linear regression models when some covariates are correlated with the error term we propose a new robust instrumental variables estimator riv which is a natural robustification of the ordinary instrumental variables estimator oiv specifically we construct riv using a robust multivariate location and scatter s estimator to robustify the solution of the estimating equations that define oiv riv is computationally inexpensive and readily available for applications through the r library riv it has attractive robustness and asymptotic properties including high resilience to outliers bounded influence function consistency under weak distributional assumptions asymptotic normality under mild regularity conditions and equivariance we further endow riv with an iterative algorithm which allows for the estimation of models with endogenous continuous covariates and exogenous dummy covariates we study the performance of riv when the data contains outliers using an extensive monte carlo simulation study and by applying it to a limited access dataset from the framingham heart study cohort to estimate the effect of long term systolic blood pressure on left atrial size

robust regression using repeated medians abstract the repeated median algorithm is a robustified u statistic in which nested medians replace the single mean unlike many generalizations of the univariate median repeated median estimates maintain the high 50 breakdown value and can resist the effects of outliers even when they comprise nearly half of the data because they are calculated directly not iteratively repeated median procedures can be used as starting values for iterative robust estimation methods for bivariate linear regression with symmetric errors repeated median estimates are unbiased and fisher consistent and their efficiency under gaussian sampling can be comparable to the efficiency of the univariate median author

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

conditionally unbiased bounded influence estimation in general regression models with applications to generalized linear models abstract in this article robust estimation in generalized linear models for the dependence of a response y on an explanatory variable x is studied a subclass of the class of m estimators is defined by imposing the restriction that the score function must be conditionally unbiased given x within this class of conditionally fisher consistent estimators optimal bounded influence estimators of regression parameters are identified and their asymptotic properties are studied the estimators studied in this article and the efficient bounded influence estimators studied by stefanski carroll and ruppert 1986 depend on an auxiliary centering constant and nuisance matrix the centering constant can be given explicitly for the conditionally fisher consistent estimators and thus they are easier to compute than the estimators studied by stefanski et al 1986 in addition estimation of the nuisance matrix has no effect on the asymptotic distribution of the conditionally fisher consistent estimators the sam

robust estimation with many instruments abstract linear instrumental variables models are widely used in empirical work but often associated with low estimator precision this paper proposes an estimator that is robust to outliers and shows that the estimator is minimax optimal in a class of estimators that includes the limited maximum likelihood estimator liml intuitively this optimal robust estimator combines liml with winsorization of the structural residuals and the winsorization leads to improved precision under thick tailed error distributions consistency and asymptotic normality of the estimator are established under many instruments asymptotics and a consistent variance estimator which allows for asymptotically valid inference is provided

analogs of renormalization group transformations in random processes abstract we review the properties of a real space renormalization group transformation of the free energy including the existence of oscillatory terms multiplying the non analytic part of the free energy we then construct stochastic processes which incorporate into probability distributions the features of the free energy scaling equation the essential information is obtainable from the scaling equation and a direct solution for a probability is not necessary these random processes are shown to be generated directly from cantor sets in a spatial representation the ensuing random process exhibits a transition between gaussian and fractal behavior in the fractal regime the trajectories will in an average sense form self similar clusters in a temporal representation the random process exhibits a transition between an asymptotically constant renewal rate and fractal behavior the fractal regime represents a frozen state with only transient effects allowed and is related to charge transport in glasses

continuity of the sequential product of sequential quantum effect algebras in order to study quantum measurement theory sequential product defined by a b a1 2ba1 2 for any two quantum effects a b has been introduced physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology in this paper we study the continuity problems of the sequential product a b a1 2ba1 2 with respect to other important topologies such as norm topology weak operator topology order topology and interval topology

order preserving bijections of c x i abstract let x be a compact hausdorff space which satisfies the first axiom of countability i 0 1 and c x i the set of all continuous functions from x to i in the paper we will give a description of bijective maps on c x i which preserve the order in both directions

efficient robust regression via two stage generalized empirical likelihood large and finite sample efficiency and resistance to outliers are the key goals of robust statistics although often not simultaneously attainable we develop and study a linear regression estimator that comes close efficiency is obtained from the estimator s close connection to generalized empirical likelihood and its favorable robustness properties are obtained by constraining the associated sum of weighted squared residuals we prove maximum attainable finite sample replacement breakdown point and full asymptotic efficiency for normal errors simulation evidence shows that compared to existing robust regression estimators the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance the estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers

robust estimators for simultaneous equations models this paper presents a class of robust estimators for linear and non linear simultaneous equations models which are a direct generalization of the maximum likelihood estimator the new estimators are obtained as solutions of a generalized likelihood equation they are resistant to deviations from the model distribution to outlying observations and to some model misspecifications an optimality principle leads to the construction of an optimal robust estimator which is the best trade off between efficiency at the model and robustness

bounded influence rank regression a one step estimator based on wilcoxon scores abstract the krasker welsch 1982 approach to bounding influence is merged with rank regression i propose a one step estimator that is analogous to bickel s 1975 one step m estimator of type 1 but uses weights that depend on the design vector and the residuals to reduce the influence of outliers in fact the standardized sensitivity of the estimator is made equal to a prechosen constant it is based however on a second derivative approximation to a dispersion surface that is not convex this one step variant avoids the problem of multiple roots the estimator is shown to be consistent and asymptotically multivariate normal an example shows that it yields results similar to those of the krasker welsch estimator

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

bounded error identification of time varying parameters by rls techniques the performance of the recursive least squares algorithm with constant forgetting factor in the identification of time varying parameters is studied in a stochastic framework it is shown that the mean square tracking error keeps bounded if and only if the so called covariance matrix of the algorithm is l sup 1 bounded then a feasibility range for the forgetting factor is worked out in correspondence of which the covariance matrix and therefore the tracking error keeps bounded

on the standard k loop structure of positive invertible elements in a c algebra abstract we investigate the algebraic properties of the operation a b a b a on the set of all positive invertible elements of a c algebra a we show that its commutativity associativity and distributivity are each equivalent to the commutativity of a we present abstract characterizations of the operation and a few related ones too

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

on the bounded influence regression estimator of krasker and welsch abstract recently krasker and welsch 1982 considered a class of bounded influence regression estimators they showed that within this class the so called krasker welsch estimator is the only solution to a first order necessary condition for strong optimality that is for minimizing in the sense of positive definiteness the asymptotic covariance matrix however whether any strongly optimal estimator in fact exists remained an open question in this article an example is given where no strongly optimal estimator exists moreover the practical significance of the lack of a strongly optimal estimator is discussed

asymptotic behavior of general m estimates for regression and scale with random carriers let xini y i be a sequence of independent identically distributed random variables where x i r p and y i r and let r p be an unknown vector such that y i x i u i where u i is independent of x i and has distribution function f u where 0 is an unknown parameter this paper deals with a general class of m estimates of regression and scale defined as solutions of the system sum limits i phi text x i r i x i 0 sum limits i chi r i 0 where r y i xi1 with r p r r and r r this class contains estimators of proposed by huber mallows and krasker and welsch the consistency and asymptotic normality of the general m estimators are proved assuming general regularity conditions on and and assuming the joint distribution of x i y i to fulfill the model only approximately

characterization of the sequential product on quantum effects we present a characterization of the standard sequential product of quantum effects the characterization is in terms of algebraic continuity and duality conditions that can be physically motivated