detecting outlying cells in two way contingency table via backwards stepping when fitting a model to a contingency table a significant lack of fit can sometimes be caused by a few outlier cells with the model fitting the remaining cells well these cells can be identified by using deleted residuals the residual from the expected count with the cell deleted and tested using the drop in likelihood ratio goodness of fit statistic from the model with the cell included to the model with the cell deleted with the cells being tested from least extreme to most extreme backwards stepping this article shows that using a bonferroni bound for the outlier test at each step results in a conservative test with good power to detect multiple outliers backwards stepping and the use of deleted residuals results in the limiting of both masking and swamping effects the procedure generalizes easily to complicated probability models

fine tuning some resistant rules for outlier labeling abstract a previous study examined the performance of a standard rule from exploratory data analysis which uses the sample fourths fl and fu and labels as outside any observations below fl k fu fl or above fu k fu fl customarily with k 1 5 in terms of the order statistics x 1 x 2 x n the standard definition of the fourths is fl x f and fu x n 1 f where f n 3 2 and denotes the greatest integer function the results of that study suggest that finer interpolation for the fourths might yield smoother behavior in the face of varying sample size in this article we show that using f i n 4 5 12 to define the fourths produces the desired smoothness corresponding to a common definition of quartiles fq n 4 1 4 leads to similar results instead of allowing the some outside rate per sample the probability that a sample contains one or more outside observations analogous to the experimentwise error rate in simultaneous inference to vary some us

patient specific detection of perfusion abnormalities combining within subject and between subject variances in arterial spin labeling in this paper patient specific perfusion abnormalities in arterial spin labeling asl were identified by comparing a single patient to a group of healthy controls using a mixed effect hierarchical general linear model glm two approaches are currently in use to solve hierarchical glms 1 the homoscedastic approach assumes homogeneous variances across subjects and 2 the heteroscedastic approach is theoretically more efficient in the presence of heterogeneous variances but algorithmically more demanding in practice in functional magnetic resonance imaging studies the superiority of the heteroscedastic approach is still under debate due to the low signal to noise ratio of asl sequences within subject variances have a significant impact on the estimated perfusion maps and the heteroscedastic model might be better suited in this context in this paper we studied how the homoscedastic and heteroscedastic approaches behave in terms of specificity and sensitivity in the detection of patient specific asl perfusion abnormalities validation was undertaken on a dataset of 25 patients diagnosed with brain tumors and 36 healthy volunteers we showed evidence of heterogeneous within subject variances in asl and pointed out an increased false positive rate of the homoscedastic model in the detection of patient specific brain perfusion abnormalities with asl modeling heterogeneous variances increases the sensitivity at the same specificity level

maximal partial spreads and translation nets of small deficiency abstract partial t spreads and translation nets of small deficiency are considered meaning s d 1 2 where s is the order and d the deficiency it is proved that almost all such translation nets do in fact come from partial t spreads and some open questions about the nets belonging to maximal partial t spreads are answered some new examples of maximal partial t spreads and of unimbeddable nets of small deficiency are also constructed

stability radius and internal versus external stability in banach spaces an evolution semigroup approach in this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems these include autonomous and nonautonomous systems modeled with unbounded state space operators acting on banach spaces this approach allows one to apply the classical theory of strongly continuous semigroups to time varying systems in particular the complex stability radius may be expressed explicitly in terms of the generator of an evolution semigroup examples are given to show that classical formulas for the stability radius of an autonomous hilbert space system fail in more general settings upper and lower bounds on the stability radius are proven for banach space systems in addition it is shown that the theory of evolution semigroups allows for a straightforward operator theoretic analysis of internal stability as determined by classical frequency domain and input output operators even for nonautonomous banach space systems in particular for the nonautonomous setting internal stability is shown to be equivalent to input output stability for stabilizable and detectable systems for the autonomous setting an explicit formula for the norm of input output operator is given

bayesian identification of outliers in computerized adaptive tests abstract we consider the problem of identifying examinees with aberrant response patterns in a computerized adaptive test cat the vector y of responses of an examinee from a cat is a multivariate response vector multivariate observations may be outlying in many different directions and we characterize specific directions as corresponding to outliers with different interpretations we develop a class of outlier statistics to identify different types of outliers based on a control chart type methodology the outlier methodology is adaptable to general longitudinal discretes data structures we consider several procedures to judge how extreme a particular outlier is data from a nationally administered cat examination motivates our development and is used to illustrate the results

comparing classical and resistant outlier rules abstract in this article we compare rosner s 1983 extension of the outlier t test the generalized esd procedure to the boxplot rules tukey s 1977 resistant outlier labeling approach the underlying principles are contrasted and the behavior of the procedures is compared in a variety of sampling situations to facilitate power type comparisons of procedures that are based on different paradigms the conditional outside rate a performance criterion for assessing outlier labeling procedures is introduced this quantity represents the probability that an observation yi is labeled an outlier conditional on its distance from the center e yi e some exact expressions as well as simple approximations and a monte carlo swindle are developed the conditional outside rate together with the outside rate per observation and the some outside rate per sample are applied to compare performance of the classical and boxplot rules based on monte carlo simulation of samples of sizes n 10 30 and 50

on time regularity and related conditions for power bounded operators let t be a bounded linear operator in a complex banach space our main result gives various characterizations of the condition t is power bounded and an estimate i t t n cn 1 2 holds for all positive integers n in particular this condition holds if and only if t s 1 i for some 0 1 and some power bounded operator s or if and only if t is power bounded and the discrete semigroup t n is dominated by the continuous semigroup e t i t t 0 in a natural sense as a consequence of our main results for 1 2 1 we characterize the condition that t is power bounded and i t t n c n for all n in terms of estimates on the semigroup e t i t

decay estimates of functions through singular extensions of vector valued laplace transforms abstract let x be a banach space and let f l r x whose laplace transform extends analytically to some region containing i r 0 possibly having a pole at the origin in this paper we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its laplace transform along the imaginary axis this technique is applied to obtain decay estimates of smooth orbits of bounded c 0 semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum these results are close to those given recently by c j k batty and t duyckaerts

outlier detection and robust regression for correlated data abstract outlier detection has attracted considerable interest in various areas existing outlier detection methods usually assume independence of the modeling errors among the data points but this assumption does not hold in a number of applications in this paper we propose a probabilistic method for outlier detection and robust updating of linear regression problems involving correlated data first suspicious data points will be identified using the minimum volume ellipsoid method and the maximum trimmed likelihood method then the outlierness of each suspicious data point will be determined according to the proposed outlier probability in consideration of possible correlation among the data points the proposed method is assessed and validated through simulated and real data

stability theory for semigroups using l p l q fourier multipliers abstract we study polynomial and exponential stability for c 0 semigroups using the recently developed theory of operator valued l p l q fourier multipliers we characterize polynomial decay of orbits of a c 0 semigroup in terms of the l p l q fourier multiplier properties of its resolvent using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space we do not assume that the semigroup is uniformly bounded our results depend only on spectral properties of the generator as a corollary of our work on polynomial stability we reprove and unify various existing results on exponential stability and we also obtain a new theorem on exponential stability for positive semigroups

the identification of multiple outliers abstract one approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations in this article we define outliers in terms of their position relative to the model for the good observations the outlier identification problem is then the problem of identifying those observations that lie in a so called outlier region methods based on robust statistics and outward testing are shown to have the highest possible breakdown points in a sense derived from donoho and huber but a more detailed analysis shows that methods based on robust statistics perform better with respect to worst case behavior a concrete outlier identifier based on a suggestion of hampel is given

using simulated envelopes in the evaluation of normal probability plots of regression residuals we investigate properties of a diagnostic envelope method for evaluating normal probability plots of regression residuals that was proposed by atkinson 1981 implemented by bmdp hardwick 1987 and extended to logistic regression by landwehr pregibon and shoemaker 1984 the envelope s stability properties and joint residual vector inclusion levels undocumented so far in the literature are explored here with several examples alternative resistant techniques for creating envelopes are considered interpretations that can be derived from these plots are discussed a resistant version of the envelopes shows good stability and good sensitivity to outlying residuals both full normal and half normal probability plots with this envelope method provide useful information to the analyst

bayesian analysis of contingent claim model error abstract this paper formally incorporates parameter uncertainty and model error into the implementation of contingent claim models we make hypotheses for the distribution of errors to allow the use of likelihood based estimators consistent with parameter uncertainty and model error we then write a bayesian estimator which does not rely on large sample properties but allows exact inference on the relevant functions of the parameters option value hedge ratios and forecasts this is crucial because the common practice of frequently updating the model parameters leads to small samples even for simple error structures and the black scholes model the bayesian estimator does not have an analytical solution markov chain monte carlo estimators help solve this problem we show how they extend to some generalizations of the error structure we apply these estimators to the black scholes given recent work using non parametric function to price options we nest the b s in a polynomial expansion of its inputs despite improved in sample fit the expansions do not yield any out of sample improvement over the b s also the out of sample errors though larger than in sample are of the same magnitude this contrasts with the performance of the popular implied tree methods which produce outstanding in sample but disastrous out of sample fit as dumas fleming and whaley 1997 show this means that the estimation method is as crucial as the model itself

the stability number of the timoshenko system with second sound abstract in this work we consider the timoshenko beam model with second sound we introduce a new number 0 that characterizes the exponential decay we prove that the corresponding semigroup associated to the system is exponentially stable if and only if 0 0 otherwise there is a lack of exponential stability in this case we prove that the semigroup decays as t 1 2 moreover we show that the rate is optimal

the multidimensional wave equation with generalized acoustic boundary conditions i strong stability we study the wave equation on a domain of mathbb r d d geq 2 with dynamical boundary control applied on a part of the boundary and a dirichlet boundary condition on the remaining part we prove the asymptotic stability and nonuniform stability of the associated semigroup

resistant and test based outlier rejection effects on gaussian one and two sample inference resistant and sequential test based procedures for the detection of multiple outliers are compared in gaussian one and two sample problems subsequent to statistical rejection of putative outliers operating characteristics of hypothesis tests applied to samples that are outlier free may differ from their nominal values outlier rejection rules may be calibrated however to control the rate of erroneous outlier labeling in pure gaussian samples the small sample behavior of resistant location and scale estimators used in outlier detection is examined through simulation yielding new formulas for calibration of boxplot based and shorth based outlier rejection rules effects of different outlier criteria and calibration rubrics on postrejection hypothesis tests are compared in a variety of contamination settings and real world examples tests conducted subsequent to calibrated rejection have approximately nominal operating characteristics whether or not outliers are present the selection of an outlier cr

heat wave interaction in 2 3 dimensions optimal rational decay rate abstract in this paper we consider a simplified version of a fluid structure pde model which has been of longstanding interest within the mathematical and biological sciences in it a n dimensional heat equation replaces the original stokes system so as to ultimately have a vector valued heat equation and vector valued wave equation compose the coupled pde system under study the coupling between the two disparate pde components occurs across a boundary interface as such the entire pde dynamics manifests features of both hyperbolicity and parabolicity for this heat structure system our main result of uniform stability is as follows given smooth initial data i e data in the domain of the underlying semigroup generator of the coupled pde system the corresponding solutions decay at the rate of o t 1 this establishes the long conjectured optimal rate the problem of obtaining sharp rational decay rates for the heat wave pde under present consideration has been a much considered problem with the modus operandi of earlier efforts taking place within the time domain by contrast we adopt here a frequency domain approach which is based upon a recent resolvent criterion and which was initiated in our prior effort wherein we obtained the rate of decay o 1 t the present optimal improvement o t 1 is achieved by employing an additional tool in our analysis a microlocal analysis argument to estimate a critical term involving two problematic boundary traces

direct integrals of strongly continuous operator semigroups abstract the goal of this article is to develop a theory for direct integrals of c 0 semigroups on hilbert spaces parallel to the recent approach by lachowicz and moszynski for direct sums of banach spaces diagonal operators and semigroups in it we deal with the existence and characterisation of semigroups asymptotic rates and questions of decomposability

rates of convergence to equilibrium for collisionless kinetic equations in slab geometry abstract this work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry such equations are governed by stochastic semigroups in l 1 spaces we prove convergence to equilibrium at the rate o t k 2 k 1 1 t for l 1 initial data g in a suitable subspace of the domain of the generator t where k n depends on the properties of the boundary operators near the tangential velocities to the slab this result is derived from a quantified version of ingham s tauberian theorem by showing that f g s lim e 0 i s e t 1 g exists as a c k function on r 0 such that d j d s j f g s c s 2 j 1 near s 0 and bounded as s 0 j k various preliminary results of independent interest are given and some related open problems are pointed out

asymptotic behaviour of c0 semigroups and γ boundedness of the resolvent abstract let x be a banach space with type p and cotype q and let a be the infinitesimal generator of a c 0 semigroup on x we show that if the resolvent of a has a bounded analytic extension to c then a has negative fractional growth bound of order 1 p 1 q

asymptotic behaviour in the robot rendezvous problem abstract this paper presents a natural extension of the results obtained by feintuch and francis in 2012a b concerning the so called robot rendezvous problem in particular we revisit a known necessary and sufficient condition for convergence of the solution in terms of cesaro convergence of the translates s k x 0 k 0 of the sequence x 0 of initial positions under the right shift operator s thus shedding new light on questions left open in feintuch and francis 2012a b we then present a new proof showing that a certain stronger ergodic condition on x 0 ensures that the corresponding solution converges to its limit at the optimal rate o t 1 2 as t after considering a natural two sided variant of the robot rendezvous problem already studied in feintuch and francis 2012a and in particular proving a new quantified result in this case we conclude by relating the robot rendezvous problem to a more realistic model of vehicle platoons

performance of some resistant rules for outlier labeling abstract the techniques of exploratory data analysis include a resistant rule for identifying possible outliers in univariate data using the lower and upper fourths fl and fu approximate quartiles it labels as outside any observations below fl 1 5 fu fl or above fu 1 5 fu fl for example in the ordered sample 5 2 0 1 8 fl 2 and fu 1 so any observation below 6 5 or above 5 5 is outside thus the rule labels 8 as outside some related rules also use cutoffs of the form fl k fu fl and fu k fu fl this approach avoids the need to specify the number of possible outliers in advance as long as they are not too numerous any outliers do not affect the location of the cutoffs to describe the performance of these rules we define the some outside rate per sample as the probability that a sample will contain one or more outside observations its complement is the all inside rate per sample we also define the outside rate per observation as the average fraction of outs

bayesian regression diagnostics with applications to international consumption and income data abstract three variants of friedman s consumption model are analyzed using houthakker s international consumption and income data and the bayesian regression analysis program brap the analysis is focussed on evaluating friedman s proportionality hypothesis various diagnostic procedures are discussed and applied using diffuse and informative prior distributions of the three models considered the logit transformation model is deemed most appropriate and results based on it suggest a departure from the proportionality hypothesis particularlyat low levels of income this result is at variance with houthakker s earlier conclusion that these data are in accord with the proportionality hypothesis

existence results for translation nets ii abstract let d be a translation bruck net of order s and degree r with translation group g and let s q 1 q n be the prime power factorization of s we prove that r min q i 1 i 1 n moreover equality can be realized provided that g is the direct sum of elementary abelian groups similar results are obtained for translation s r nets and more generally for groups with large systems of large subgroups as a corollary we considerably strengthen a known result on symmetric translation nets by showing that any translation s s net has parameters of the form s p i p j for some prime p and also necessarily has elementary abelian translation group

percentage points for a generalized esd many outlier procedure a generalized extreme studentized deviate esd many outlier procedure is given for detecting from 1 to k outliers in a data set this procedure has an advantage over the original esd many outlier procedure rosner 1975 in that it controls the type i error both under the hypothesis of no outliers and under the alternative hypotheses of 1 2 k l outliers a method is given for approximating percentiles for this procedure based on the t distribution this method is shown to be adequately accurate using monte carlo simulation for detecting up to 10 outliers in samples as small as 25 tables are given for implementing this method for n 25 1 50 10 100 50 500 k 10 05 ol 005

partial spreads over zq let p be a prime q pa and g z2nq we consider partial spreads in g i e collections of pairwise disjoint subgroups of order qn it is shown that the maximum size of such a collection is exactly pn 1 the method of proof consists in representing partial spreads in g by invertible n n matrices over zq and in finding a close relation to ordinary partial spreads over zp geometrically partial spreads over zq correspond to homogeneous translation nets

outlier labeling with boxplot procedures in this article we focus on the detection of possible outliers based on the widely used boxplot procedures the outliers in a set of data are defined to be a subset of observations that appear to be inconsistent with the remaining observations we identify the outliers by constructing a boxplot with its lower fence lf and upper fence uf either a satisfying the requirement that if the given sample is outlier free then the probability that one or more of the sample data would fall outside the region lf uf is equal to a prescribed small value or b taken to be the tolerance limits derived from an outlier free random sample within which a specified large proportion of the sampled population would be asserted to fall with a given large probability exact expressions that can be routinely used to evaluate the constants needed in the construction of the boxplot s outlier region for samples taken from the family of location scale distributions are obtained for both procedures this article sh

optimal rates of decay for operator semigroups on hilbert spaces abstract we investigate rates of decay for c 0 semigroups on hilbert spaces under assumptions on the resolvent growth of the semigroup generator our main results show that one obtains the best possible estimate on the rate of decay that is to say an upper bound which is also known to be a lower bound under a comparatively mild assumption on the growth behaviour this extends several statements obtained by batty et al 2016 6 in fact for a large class of semigroups our condition is not only sufficient but also necessary for this optimal estimate to hold even without this assumption we obtain a new quantified asymptotic result which in many cases of interest gives a sharper estimate for the rate of decay than was previously available and for semigroups of normal operators we are able to describe the asymptotic behaviour exactly we illustrate the strength of our theoretical results by using them to obtain sharp estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary

stabilizability and controllability of spatially invariant p d e systems in this paper we derive new readily testable criteria for exponential stabilizability approximate controllability and exact controllability for multiplicative systems arising from linear partial differential equations on an infinite domain these multiplicative systems have an unbounded semigroup generator but bounded input and output operators the theoretical results are illustrated by several examples in particular explicit easily verifiable conditions for exponential stabilizability approximate and exact controllability are given for second order p d e systems dual results for exponential detectability approximate and exact observability are also included

procedures for the identification of multiple outliers in linear models abstract we consider the problem of identifying and testing multiple outliers in linear models the available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify we introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem both procedures attempt to separate the data into a set of clean data points and a set of points that contain the potential outliers the potential outliers are then tested to see how extreme they are relative to the clean subset using an appropriately scaled version of the prediction error the procedures are illustrated and compared to various existing methods using several data sets known to contain multiple outliers also the performances of both procedures are investigated by a monte carlo study the data sets and the monte carlo indicate that both procedures are effective in the detection of multiple outliers

optimal energy decay in a one dimensional wave heat system with infinite heat part abstract using recent results in the theory of c 0 semigroups due to batty et al 2016 5 we study energy decay in a one dimensional coupled wave heat system with finite wave part and infinite heat part our main result provides a sharp estimate for the rate of energy decay of a certain class of classical solutions the present paper can be thought of as a natural sequel to a recent work by batty et al 2016 6 which studied a similar wave heat system with finite wave and heat parts using a celebrated result due to borichev and tomilov

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

active noise control with on line estimation of non gaussian noise characteristics abstract active noise control anc is a methodology for attenuating noise based on adaptive signal processing algorithms anc is well assessed for the attenuation of gaussian noise but the rejection of non gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence to overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise this can be done either by modeling the impulsive noise with a non gaussian distribution such as the symmetric stable s s distribution or by applying an outlier detection method with both approaches the accuracy in the noise description appears to be crucial for effective noise reduction this paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time varying noise distributions the first one is based on the on line estimation of an s s model of the noise probabilistic description the second relies on a simple on line recursive procedure that reliably estimates amplitude thresholds for outlier detection both methods compare favorably with competitor approaches while maintaining a sufficiently low algorithm complexity several examples are shown to demonstrate the algorithms effectiveness

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

on subdesigns of symmetric designs the proof of haemers and shrikhande uses an eigenvalue technique due to haemers 6 it is not clear whether or not 1 1 c holds provided that is a design with the parameters given above we will prove this in sect 2 by counting arguments which turn out to be much more delicate than one would expect at first this also leads to another inequality for the parameters of and which in general will not coincide with 1 1 b there are also a few further reasons to study this situation again to begin with eigenvalue techniques are less elementary than counting also a result such as theorem 1 1 should have a geometric interpretation in fact the second

on the variability of case deletion importance sampling weights in the bayesian linear model abstract i consider a standard specification of the bayesian linear model and derive necessary and sufficient conditions for the variance of the case deletion importance sampling weights to be finite the conditions have an intuitive interpretation in terms of familiar frequentist measures of leverage and influence and are easy to verify i present two real data examples in which the necessary conditions fail to hold for some observations and the corresponding importance sampling estimates are highly unreliable

string stability of interconnected systems introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems intuitively string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded it is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input output stable the authors derive sufficient weak coupling conditions which guarantee the asymptotic string stability of a class of interconnected systems under the same weak coupling conditions string stable interconnected systems remain string stable in the presence of small structural singular perturbations in the presence of parameter mismatch these weak coupling conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient based parameter adaptation law is used and that the states of all the systems go to zero asymptotically

regularity analysis for an abstract system of coupled hyperbolic and parabolic equations abstract in this paper we provide a complete regularity analysis for the following abstract system of coupled hyperbolic and parabolic equations u t t a u a w w t a u t k a w u 0 u 0 u t 0 v 0 w 0 w 0 where a is a self adjoint positive definite operator on a complex hilbert space h and 0 1 0 1 we are able to decompose the unit square of the parameter into three parts where the semigroup associated with the system is analytic of specific order gevrey classes and non smoothing respectively moreover we will show that the orders of gevrey class is sharp under proper conditions

groups with a large number of large disjoint subgroups it is known that if g is a group of order 4n2 and g contains n mutually disjoint subgroups of order 2n then the nonidentity elements of these subgroups form a difference set in g gluck recently discovered a nonabelian example with n 4 and showed it to be the only case with n 4 and g not elementary abelian we show here that the only examples with n 4 are elementary abelian 2 groups

asymptotically independent scale free spacings with applications to discordancy testing de facon analogue a la construction des espacements independants et independants de l echelle pour la distribution exponentielle on definit des quantites pour une distribution arbitraire et on etudie leur comportement asymptotique conjoint

asymptotics for infinite systems of differential equations this paper investigates the asymptotic behavior of solutions to certain infinite systems of ordinary differential equations in particular we use results from ergodic theory and the asymptotic theory of c 0 semigroups to obtain a characterization in terms of convergence of certain cesaro averages of those initial values which lead to convergent solutions moreover we obtain estimates on the rate of convergence for solutions whose initial values satisfy a stronger ergodic condition these results rely on a detailed spectral analysis of the operator describing the system which is made possible by certain structural assumptions on the operator the resulting class of systems is sufficiently broad to cover a number of important applications including in particular both the so called robot rendezvous problem and an important class of platoon systems arising in control theory our method leads to new results in both cases

asymptotics and approximation of large systems of ordinary differential equations abstract in this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations under the mild assumption that the so called characteristic function of our system is completely monotonic we obtain a drastically simplified condition which ensures boundedness of the associates semigroup if the characteristic function satisfies certain additional conditions we deduce sharp rates of convergence to equilibrium we moreover address the important and delicate issue of the role of the infinite system in understanding the asymptotic behaviour of large but finite systems and we provide a precise way of obtaining size independent rates of convergence for families of finite dimensional systems finally we illustrate our abstract results in the setting of the well known platoon problem

maximal rings associated with covers of abelian groups abstract for a finite abelian group a we investigate the problem of determining those rings r which are maximal as rings in the near ring m 0 a of all 0 preserving functions on a we find this problem is related to properties of certain covers of a by subgroups special attention is given to the case where a is an elementary abelian p group

on the decay rate for the wave equation with viscoelastic boundary damping abstract we consider the wave equation with a boundary condition of memory type under natural conditions on the acoustic impedance of the boundary a corresponding semigroup of contractions is known to exist with the help of quantified tauberian theorems we establish energy decay rates via resolvent estimates on the generator of the semigroup using a variational approach we reduce resolvent estimates to estimates for a sesquilinear form induced by an operator characteristic function arising form the matrix representation of the generator under not too strict additional assumptions on the acoustic impedance we establish an upper bound on the resolvent for the wave equation on the interval or the disc we prove our estimates to be sharp

an integrability condition on the resolvent for hyperbolicity of the semigroup abstract in this paper we present necessary and sufficient conditions on the resolvent of the generator of a strongly continuous semigroup in order that the corresponding semigroup is hyperbolic the proof is based on a new characterization of the growth bound in terms of the resolvent as an application we discuss three examples

system theoretic properties of a class of spatially invariant systems in this paper we develop new readily testable criteria for system theoretic properties such as stability controllability observability stabilizability and detectability for a class of spatially invariant systems our approach uses the well established theory developed to solve infinite dimensional systems the theoretical results are illustrated by several examples

on the existence of translation nets abstract the existence of a translation net of order s and degree r with translation group g is equivalent to the existence of r mutually disjoint subgroups of g of order s in this paper we consider p groups g of odd square order p2n and improve the known general upper bound on the number of mutually disjoint subgroups of order pn in g provided that g is not elementary abelian this solves problem 8 2 14 in d jungnickel latin squares their geometries and their groups a survey in coding theory and design theory ii d k ray chaudhuri ed pp 166 225 springer berlin new york 1990 we determine all groups of order p4 which are translation groups of translation nets with at least three parallel classes for all prime numbers p furthermore we construct p3 p2 1 translation nets with non abelian translation group of order p6 for all odd prime numbers p

a generalized extreme studentized residual multiple outlier detection procedure in linear regression this article is concerned with procedures for detecting multiple y outhers in linear regression a generalized extreme studentized residual gesr procedure which controls type i error rate is developed an approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n 25 are tabulated the performance of this procedure is compared with others by monte carlo techniques and found to be superior the procedure however fails in detecting y outliers that are on high leverage cases for this a two phase procedure is suggested in phase 1 a set of suspect observations is identified by gesr and one of the diagnostics applied sequentially in phase 2 a backward testing is conducted using the gesr procedure to see which of the suspect cases are outlicrs several examples are analyzed

residual plots for repeated measures multivariate data are difficult to analyse partly because of difficulty in looking at the data repeated measures data have a special structure that makes the parallel plot1 2 particularly effective for viewing the data in this paper we use parallel plots to display not just raw data but also residuals from standard models fit to repeated measures data the plots are useful for determining how well a particular model fits the data identifying outlying observations and suggesting terms missing from the linear predictor

location of several outliers in multiple regression data using elemental sets the outlying tendency of any case in a multiple regression of p predictors may be estimated by drawing all subsets of size p from the remaining cases and fitting the model each such subset yields an elemental residual for the case in question and a suitable summary statistic of them can be used as an estimate of the case s outlying tendency we propose two such summary statistics an unweighted median which is of bounded influence and a weighted median which is more efficient but less robust the computational load of the procedure is reduced by using random samples in place of the full set of subsets of size p as a byproduct the method yields useful information on the influence or leverage of cases and the mutual masking of high leverage points

brief paper infinite chains of kinematic points in formulating the stability problem for an infinite chain of cars state space is traditionally taken to be the hilbert space 2 wherein the displacements of cars from their equilibria or the velocities from their equilibria are taken to be square summable but this obliges the displacements or velocity perturbations of cars that are far down the chain to be vanishingly small and leads to anomalous behaviour in this paper an alternative formulation is proposed wherein state space is the banach space allowing the displacements or velocity perturbations of cars from their equilibria to be merely bounded

a bayesian approach to outlier detection and residual analysis summary an approach to detecting outliers in a linear model is developed an outlier is defined to be an observation with a large random error generated by the linear model under consideration outliers are detected by examining the posterior distribution of the random errors an augmented residual plot is also suggested as a graphical aid in finding outliers we propose a precise definition of an outlier in a linear model which appears to lead to simple ways of exploring data for the possibility of outliers the definition is such that if the parameters of the model are known then it is also known which observations are outliers alternatively if the parameters are unknown the posterior distribution can be used to calculate the posterior probability that any observation is an outlier in a linear model with normally distributed random errors ei with mean zero and variance a 2we declare the ith observation to be an outlier if iei i ko for some choice of k the value of k can be chosen so that the prior probability of an outlier is small and thus outliers are observations which are more extreme than is usually expected realizations of normally distributed errors of more than about three standard deviations from the mean are certainly surprising and worth further investigation such outlying observations can occur under the assumed model however and this should be taken into account when deciding what to do with outliers and in choosing k note that ei is the actual realization of the random error not the usual estimated residual i the problem of outliers is studied and thoroughly reviewed by barnett lewis 1984 hawkins 1980 beckman cook 1983 and pettit smith 1985 the usual bayesian approach to outlier detection uses the definition given by freeman 1980 freeman defines an outlier to be any observation that has not been generated by the mechanism that generated the majority of observations in the data set freeman s definition therefore requires that a model for the generation of outliers be specified and is implemented by for example box tiao 1968 guttman dutter freeman 1978 and abraham box 1978 our method differs in that we define outliers as arising from the model under consideration rather than arising from a separate expanded model our approach is similar to that described by zellner moulton 1985 and is an extension of the philosophy

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

the finite sample properties of simultaneous equations estimates and estimators bayesian and non bayesian approaches abstract after discussing the need for good finite sample estimation procedures for simultaneous equations models and showing the inadequacies of asymptotically justified estimators it is shown how the bayesian method of moments bmom provides an exact finite sample analysis of unrestricted reduced form systems then optimal finite sample estimates of structural coefficients are derived using three standard loss functions and they are compared to traditional bayesian optimal estimates monte carlo experimental evidence from four studies on the relative performance of bayesian and non bayesian estimators is reviewed with the finding that the performance of bayesian estimators is better

brief paper riccati equations for second order spatially invariant partial differential systems recently the class of spatially invariant systems was introduced with motivating examples of partial differential equations on an infinite domain for these it was shown that by taking fourier transforms one obtains infinitely many finite dimensional systems with a scalar parameter the idea is that for the lqr controller design for these systems one can solve the parameterized lqr riccati equation pointwise while for simple first order systems like the heat equations this approach works for second order systems like wave or beam equations it is easy to construct examples for which this approach fails here we give a correct formulation for second order partial differential systems including wave and beam type equations

packing and covering groups with subgroups abstract we study the problem of covering or packing a finite group with subgroups of a specified order and obtain bounds on the size of such covers and packings our main results provide characterizations of the elementary abelian groups by the existence of large packings or small covers respectively hence large packings and small covers can be thought of as geometric objects they correspond to large partial t spreads and small t covers of a suitable projective space pg d p for some prime p we shall also exhibit some series of examples which show that our bounds are reasonable

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

bivariate extensions of the boxplot the boxplot has proven to be a very useful tool for summarizing univariate data several options of bivariate boxplot type constructions are discussed these include both elliptic and asymmetric plots an inner region contains 50 of the data and a fence identifies potential outliers such a robust plot shows location scale correlation and a resistant regression line alternative constructions are compared in terms of efficiency of the relevant parameters additional properties are given and recommendations made emphasis is given to the bivariate biweight m estimator several practical examples illustrate that standard least squares ellipsoids can give graphically misleading summaries

optimal polynomial decay of functions and operator semigroups we characterize the polynomial decay of orbits of hilbert space c 0 semigroups in resolvent terms we also show that results of the same type for general banach space semigroups and functions obtained recently in batty and duyckaerts j evol eq 8 765 780 2008 are sharp this settles a conjecture posed in batty and duyckaerts 2008

the non analytic growth bound of a c0 semigroup and inhomogeneous cauchy problems abstract the non analytic growth bound t of a c0 semigroup t measures the extent to which t can be approximated by a holomorphic function and it is related to spectral properties of the generator a in regions of c far from the real axis we show that t can be characterised by means of fourier multiplier properties of the resolvent of a far from the real axis and also by existence and uniqueness of mild solutions of inhomogeneous cauchy problems of the form u t au t f t on r where the carleman spectra of f and u are far from the origin the corresponding results for the exponential growth bound 0 t have been established earlier by other authors

determining amplitude limits for vibration spectra a method for determining vibration amplitude limits of a mechanical device the method comprises identifying a mechanical device and a frequency range for a spectrum to be analyzed retrieving vibration spectra comprising individual spectrum for the mechanical device and the frequency range calculating frequency for the individual spectrum and identifying the individual spectrum with the smallest number of frequency lines in addition the method comprises calculating noise bandwidths and a largest noise bandwidth removing outlier data calculating conditional kernel density and calculating vibration amplitude limits to detect faults in the mechanical device

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

optimal rates of decay in the katznelson tzafriri theorem for operators on hilbert spaces abstract the katznelson tzafriri theorem is a central result in the asymptotic theory of discrete operator semigroups it states that for a power bounded operator t on a banach space we have t n i t 0 if and only if t t 1 the main result of the present paper gives a sharp estimate for the rate at which this decay occurs for operators on hilbert space assuming the growth of the resolvent norms r e i t as 0 satisfies a mild regularity condition this significantly extends an earlier result by the second author which covered the important case of polynomial resolvent growth we further show that under a natural additional assumption our condition on the resolvent growth is not only sufficient but also necessary for the conclusion of our main result to hold by considering a suitable class of toeplitz operators we show that our theory has natural applications even beyond the setting of normal operators for which we in addition obtain a more general result

forcing linearity numbers abstract for a module over a ring r we introduce the concept of a forcing linearity number which is a type of measure of how much local linearity is needed to imply global linearity we determine this number for vector spaces for modules over integral domains not fields and for modules over local rings not integral domains