on hotelling s formula for the volume of tubes and naiman s inequality abstract motivation by the question of testing for a nonlinear parameter in a regression model with independent homoscedastic normal residuals hotelling 1939 was led to consider the geometric problem of computing the volume of a tube of given radius around a curve in s to the n 1 power the unit sphere in ir to the nth power the answer involves only the arc length of the curve and not its curvature providing the radius of the tube is sufficiently small that there is no self overlap in the tube starting from a somewhat different statistical setting naiman 1986 arrived at the same geometric problem and showed that hotelling s result properly interpreted is an upper bound for the volume of a tube of arbitrary radius the purpose of this note is to give two new derivations of the hotelling naiman results the first involves differential inequalities the second is probabilistic using the concept of upcrossing borrowed from the theory of gaussian processes in the context of gaussian processes knowles 1987 has observed that approximations obtained from hotelling s result and bounds derived via upcrossings are related

erratum to existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients by combining the theory of the exponential dichotomy and liapunov function we study the existence and attractivity of almost periodic solutions for cellular neural networks cnns with distributed delays and variable coefficientsdx idt b i t x i t j 1 na i j t f j x j t j 1 nb i j t f j m j 0 k i j u x j t u du i i t we obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution and all its solutions converge to such an almost periodic solution an example is given to illustrate that the conditions of our results are feasible

existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time varying coefficients and mixed delays this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to recurrent delayed neural networks several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain furthermore several methods are applied to establish sufficient criteria for the globally exponential stability of this system the approaches are based on constructing suitable lyapunov functionals and the well known banach contraction mapping principle moreover the attractivity and exponential stability of the pseudo almost periodic solution are also considered for the system a numerical example is given to illustrate the effectiveness of our results

a note on multivariate cusum procedures cumulative sum cusum procedures are among the most powerful tools for detecting a shift from a good quality distribution to a bad quality distribution this article discusses the natural application of cusum procedures to the multivariate normal distribution it discusses two cases detecting a shift in the mean vector and detecting a shift in the covariance matrix as an example the procedure is applied to measurements taken on optical fibers

asymptotic periodicity monotonicity and oscillation of solutions of scalar neutral functional differential equations abstract we consider the periodic scalar neutral functional differential equation d dt x t c t x t h t x t h t x t where c is continuously differentiable h is increasing in its second argument and both c and h are 1 periodic in the t variable the two time lags and are not required to be the same it is shown that under certain conditions i the set of 1 periodic solutions is an ordered arc and each solution is convergent to a periodic solution ii the asymptotic and oscillatory behaviors of each solution are completely classified in terms of the value of the first integral at the initial condition

optimality of the cusum procedure in continuous time the optimality of cusum under a lorden type criterion setting is considered we demonstrate the optimality of the cusum test for ito processes in a sense similar to lorden s but with a criterion that replaces expected delays by the corresponding kullback leibler divergence

detection of random change point in one parameter exponential families abstract we consider a sequence x 1 x 2 x n of independent random variables which are susceptible to changing their distribution after the nt first observations where t is a random variable of a distribution known with support in 0 1 the object of this work is to detect the eventual change of distribution for that we study the performance of a test based on the statistic of log likelihood it shows that when the number of observations gets larger the distribution of the statistic log likelihood behaves like that of an affine function of the brownian motion this allows by using the concept of contiguity in the sense of lecam the evaluation of the asymptotic power function of the test

change point estimation using nonparametric regression we consider a regression model in which the mean function may have a discontinuity at an unknown point we propose an estimate of the location of the discontinuity based on one side nonparametric regression estimates of the mean function the change point estimate is shown to converge in probability at rate 0 n 1 and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models confidence regions for the location and size of the change are also discussed

confidence regions and tests for a change point in a sequence of exponential family random variables summary maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables with particular emphasis on the exponential distribution the exact null and alternative distributions of the test statistics are found and the power is compared with a test based on a linear trend statistic exact and approximate confidence regions for the change point are based on the values accepted by a level x likelihood ratio test and a modification of the method proposed by cox spj0tvoll 1982 the methods are applied to a classical data set on the time intervals between coal mine explosions and the change in variation of stock market returns in both cases the confidence regions for the change point cover historical events that may have caused the changes

tests for a change point summary the problem considered is that of testing a sequence of independent normal random variables with constant known or unknown variance for no change in mean versus alternatives with a single change point various tests such as those based on the likelihood ratio and recursive residuals are studied power approximations are developed by integrating approximations for conditional boundary crossing probabilities a comparison of several tests is made

conditional boundary crossing probabilities with applications to change point problems abstract for normal random walks s sub 1 s sub 2 formed from independent identically distributed random variables x sub 1 x sub 2 we determine the asymptotic behavior under regularity conditions of p s sdub n mg n m for some n m sub m mxi m lambda0 xi g 1 where u sub m x sub one to the 2nd power x sub m to the 2nd power the result is applied to a normal change point problem to approximate null distributions of test statistics and to obtain approximate confidence sets for the change point

unbiased testing in exponential family regression let x ij z i i 1 2 k j 1 2 n i be independent observations such that z i is a fixed r x 1 vector r can be 0 no z s observed or 1 2 k 1 and x ij is distributed according to a one parameter exponential family which is log concave with natural parameter i we test the hypothesis that z where 1 k z is the matrix whose ith row is z i and 1 r is a vector of parameters we focus on r 2 and z i 1 z i i 1 2 k z i z i 1 the null hypothesis on hand is thus of the form i 1 2 z i in such a case the model under the null hypothesis becomes logistic regression in the binomial case poisson regression in the poisson case and linear regression in the normal case we consider mostly the one sided alternative that the second order differences of the natural parameters are nonnegative such testing problems test goodness of fit vs alternatives in which the natural parameters behave in a convex way we find classes of tests that are unbiased and that lie in a complete class we also note that every admissible test of constant size is unbiased in some discrete situations we find the minimal complete class of unbiased admissible tests generalizations and examples are given

inferences for the linear errors in variables with changepoint models abstract a new linear structural errors in variables regression with changepoint model is considered in this model we consider the likelihood ratio test based on the maximum hotelling t 2 for the test of no change against the alternative of exactly one change if there is a change either known a priori or by testing then we estimate the unknown changepoint parameter and some other related parameters by maximum likelihood the limiting distribution of the changepoint estimator is investigated and it is shown that the asymptotic efficiency increases as the absolute regression slope coefficient increases a monte carlo study shows that the proposed estimator performs satisfactorily

on the almost periodic solution of cellular neural networks with distributed delays by exponential dichotomy about differential equations a formal almost periodic solution aps of a class of cellular neural networks cnns with distributed delays is obtained then within different normed spaces several sufficient conditions guaranteeing the existence and uniqueness of an aps are proposed using two fixed point theorems based on the continuity property and some inequality techniques two theorems insuring the global stability of the unique aps are given comparing with known literatures all conclusions are drawn with slacker restrictions e g do not require the integral of the kernel function determining the distributed delays from zero to positive infinity to be one and the activation functions to be bounded etc besides all criteria are obtained by different ways finally two illustrative examples show the validity and that all criteria are easy to check and apply

decision theoretic optimality of the cusum procedure suppose x 1 x 2 are independent random variables such that for some unknown each of x 1 x 1 is distributed according to f 0 while x x 1 are all distributed according to f 1 we prove a result of moustakides that claims that the cusum procedures are optimal in the sense of lorden we do that by proving that the procedures are bayes for some stochastic mechanism of generating

the power of likelihood ratio and cumulative sum tests for a change in a binomial probability summary a simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables it is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence but that the likelihood ratio test is much more powerful near the ends an example from epidemiology is used to illustrate the results under certain conditions the cumulative sum test is identical to a two sample kolmogorov smirnov test and so the iterative procedure can be used to find the null distribution of kolmogorov smirnov and related statistics

existence and global attractivity of almost periodic solutions for neural field with time delay in this paper the problem of existence and attractivity of almost periodic solutions for delayed neural field dnf with variable coefficients is discussed first the model of dnf is established as a modified neural field model secondly by combining the theory of the exponential dichotomy employing banach fixed point theory and using differential inequality technique some conditions for the the existence and attractivity of almost periodic solutions for the dnf are proposed

robustness of the likelihood ratio test for a change in simple linear regression abstract this article examines the robustness of the likelihood ratio tests for a change point in simple linear regression we first summarize the normal theory of kim and siegmund who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope we then discuss the robustness of these tests using the convergence theory of stochastic processes we show that the test statistics converge to the same limiting distributions regardless of the underlying distribution we perform simulations to assess the distributional insensitivity of the test statistics to a weibull a lognormal and a contaminated normal distribution in two different cases fixed and random independent variables numerical examples illustrate that the test has a correct size and retains its power when the distribution is nonnormal we also study the effects of the independent variable s configuration with the

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

existence and stability of almost periodic solution for bam neural networks with delays by using the banach fixed point theorem and constructing suitable lyapunov function some sufficient conditions are obtained ensuring existence uniqueness and global stability of almost periodic solution of the bam neural networks with variable coefficients and delays these results are helpful to design global exponential stable bam networks and almost periodic oscillatory bam networks

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

periodic solutions for general nonlinear state dependent delay logistic equations abstract in this paper by using the continuation theorem of coincidence degree theory we investigate the existence of periodic solutions for more general state dependent delay logistic equations several sufficient conditions are given and the obtained conditions possess important significance in both theories and applications

poisson disorder problem with exponential penalty for delay we solve the poisson disorder problem when the delay is penalized exponentially our objective is to detect as quickly as possible the unobservable time of the change or disorder in the intensity of a poisson process the disorder time delimits two different regimes in which one employs distinct strategies e g investment advertising manufacturing we seek a stopping rule that minimizes the frequency of false alarms and an exponential unlike previous formulations which use a linear cost function of the detection delay in the financial applications the exponential penalty is a more apt measure for the delay cost because of the compounding of the investment growth the poisson disorder problem with a linear delay cost was studied by peskir and shiryaev 2002 solving the poisson disorder problem advances in finance and stochastics springer berlin germany 295 312 which is a limiting case of ours

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

existence and exponential stability of periodic solution for impulsive cohen grossberg neural networks with time varying delays abstract this paper is concerned with the existence and global exponential stability of periodic solution for impulsive cohen grossberg neural networks with periodic coefficients and time varying delays some novel criteria on the existence and global exponential stability of periodic solution are derived by using impulsive differential inequality technique and the banach fixed point theorem the results obtained improve and extend a few of recent literature in some situations two examples with numerical simulations are given to demonstrate the efficiency of proposed methods

thresholded multivariate principal component analysis for phase i multichannel profile monitoring abstractmonitoring multichannel profiles has important applications in manufacturing systems improvement but it is nontrivial to develop efficient statistical methods because profiles are high dim

bayesian switching multiple disorder problems the switching multiple disorder problem seeks to determine an ordered infinite sequence of times of alarms which are as close as possible to the unknown times of disorders or change points at which the observable process changes its probability characteristics we study a bayesian formulation of this problem for an observable brownian motion with switching constant drift rates the method of proof is based on the reduction of the initial problem to an associated optimal switching problem for a three dimensional diffusion posterior probability process and the analysis of the equivalent coupled parabolic type free boundary problem we derive analytic form estimates for the bayesian risk function and the optimal switching boundaries for the components of the posterior probability process

global dynamics of hopfield neural networks involving variable delays abstract in this article a model describing dynamics of hopfield neural networks involving variable delays is considered existence and uniqueness of the equilibrium point under fairly general and easily verifiable conditions are also established further we derive sufficient criteria of global asymptotic stability gas of the equilibrium point

existence of periodic solutions in neutral state dependent delays equations and models sufficient conditions are obtained for the existence of positive periodic solutions of neutral equations with state dependent delays the proof is based on the theory of coincidence degree the existence results are applied to equations of population dynamics

mixed time delays dependent exponential stability for uncertain stochastic high order neural networks this paper presents a discrete and distributed time delays dependent simultaneous approach to deterministic and uncertain stochastic high order neural networks new results are proposed in terms of linear matrix inequality lmi by exploiting a novel lyapunov krasovskii functional and by making use of novel techniques for time delay systems some constraints of systems are removed and new results cover some recently published works two numerical examples are given to show the usefulness of presented approach

detecting relevant changes in time series models summary most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form h0 1 2versush1 1 2 where 1 and 2 denote parameters of the process before and after a change point the paper takes a different perspective and investigates the null hypotheses of no relevant changes i e h0 1 2 where is an appropriate norm this formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary if the difference between the parameters before and after the change point is small a general approach to problems of this type is developed which is based on the cumulative sum principle for the asymptotic analysis weak convergence of the sequential empirical process must be established under the alternative of non stationarity and it is shown that the resulting test statistic is asymptotically normally distributed the results can also be used to establish similarity of the parameters i e h1 1 2 at a controlled type 1 error and to estimate the magnitude 1 2 of the change with a corresponding confidence interval several applications of the methodology are given including tests for relevant changes in the mean variance parameter in a linear regression model and distribution function among others the finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analysing a data example from portfolio management

the existence and uniqueness of periodic solutions for a kind of duffing type equation with two deviating arguments abstract by applying mawhin s continuation theorem and establishing new lemmas some sufficient conditions for the existence and uniqueness of periodic solutions were obtained for a duffing type equation with two deviating arguments moreover an example is given to illustrate the results

nonparametric inference on structural breaks this paper proposes estimators of location and size of structural breaks in a possibly dynamic nonparametric regression model the structural breaks can be located at given periods of time and or they can be explained by the values taken by some regressor as in threshold models no previous knowledge of the underlying regression function is required the paper also studies the case in which several regressors explain the breaks we derive the rate of convergence and provide central limit theorems for the estimators of the location s and size s a monte carlo experiment illustrates the performance of our estimators in small samples

the effect of serial correlation on tests for parameter change at unknown time it is shown that serial correlation can produce striking effects in distributions of change point statistics failure to account for these effects is shown to invalidate change point tests either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process or through diminution of the power of the tests when high frequency mass predominates these effects are characterized by the expression 2i f o fjr f a da where f is the spectral density of the noise process in sample survey work this is known as the design effect or deff simple precise adjustments to change point test statistics which account for serial correlation are provided the same adjustment applies to all commonly used regression models residual processes are derived for both stationary time series satisfying a moment condition and for general linear regression models with stationary error structure 1 introduction stochastic models for time sequenced data are generally characterized by several unknown parameters these parameters may change over time and if the changes when they occur do so unannounced and at unknown time points then the associated inferential problem is referred to as the change point problem various important application areas of statistics involve change detection in a central way two of these areas are quality assurance and environmental monitoring most of the statistics commonly applied to the change point problem involve cumulative sums or partial sums of regression residuals the distribution theory for these statistics has been computed under the assumption that the error process for the regression model is white noise in this paper we consider linear regression of a random variable against general nonstochastic functions of time but with error variables that form a serially correlated time series we then examine the large sample properties of the stochastic processes defined by the partial sums of the regression residuals large sample distribution theory for fixed sample size statistics used to detect changes in regression parameters is usually derived by computing the distributions of various functionals on

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

multiple almost periodic solutions in nonautonomous delayed neural networks a general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed we consider a general class of nonautonomous neural networks with delays and various activation functions a geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed we further derive criteria under which the n neuron network admits 2n exponentially stable sets in addition we establish the existence of 2n exponentially stable almost periodic solutions for the system when the connection strengths time lags and external bias are almost periodic functions of time through applying the contraction mapping principle finally three numerical simulations are presented to illustrate our theory

periodic two predator one prey interactions and the time sharing of a resource niche a competition model involving two competing predator species and a single renewable resource prey species is studied under the assumption that the system parameters are periodic in time it is shown by means of global bifurcation techniques that a continuum of positive periodic solutions exists as a function of a selected averaged parameter and that the stability of these solutions at least locally near bifurcation depends on the direction of bifurcation in the special autonomous case of constant parameters the bifurcation is vertical and the spectrum of the continuum is a discrete point this autonomous case supports the principle of competitive exclusion in that coexistence of the predators on the single resource prey is possible in the sense that the system equilibrates only on a parameter set of measure zero in the more general case of periodic coefficients however it is shown that the spectrum can be an interval of positive length provided the predator parameter oscillations are out of phas

bayesian sequential detection with phase distributed change time and nonlinear penalty a pomdp lattice programming approach we show that the optimal decision policy for several types of bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions this is established by using lattice programming and stochastic orders in a partially observed markov decision process pomdp framework a stochastic gradient algorithm is presented to estimate the optimal linear approximation to this threshold curve we illustrate these results by first considering quickest time detection with phase type distributed change time and a variance stopping penalty then it is proved that the threshold switching curve also arises in several other bayesian decision problems such as quickest transient detection exponential delay risk sensitive penalties stopping time problems in social learning and multi agent scheduling in a changing world using blackwell dominance it is shown that for dynamic decision making problems the optimal decision policy is lower bounded by a myopic policy finally it is shown how the achievable cost of the optimal decision policy varies with change time distribution by imposing a partial order on transition matrices

global attractivity of periodic solutions of population models abstract this paper studies periodic solutions of two types of population models with time delays and periodic coefficients the first represents one species growth with delayed recruitments and the second models a single species despersal among the n patches by developing the theory of monotone and concave operators to functional differential equations we establish conditions under which each model admits a positive periodic solution which attracts all positive solutions

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

nonparametric sequential change point detection by a vertically trimmed box method this paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions a nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box as such it will be coined as the vertical box control chart v box chart its implementation requires merely to count the number of data points which fall into the box attached to the last available observation no a priori knowledge of data distributions is required and proper tuning of the box size provides a quick detection technique this is supported by establishing statistical properties of the method which explain the role of the tuning parameters used in the v box chart these theoretical results are verified by simulation studies which indicate that the v box chart may provide quick detection with zero delay for jumps of moderate sizes its averaged run length to detection is more favorable than the one for the classical ewma method by comparison with the classical shewhart chart which was optimized for normal errors our method provides comparable or better performance

boundary crossing probabilities and statistical applications abstract this paper surveys recent results involving boundary crossing probabilities and related statistical applications the first part is concerned with problems of sequential analysis especially repeated significance tests and their application to sequential clinical trials involving survival data the second part develops the probability theory motivated by the problems of part 1 a method for computing first passage distributions of brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries the third part is concerned with fixed sample statistical problems especially change point problems which involve boundary crossing probabilities examples are given of problems for which methods of part 2 appear adequate and of problems which require new methods

quickest detection of a minimum of two poisson disorder times a multisource quickest detection problem is considered assume there are two independent poisson processes x 1 and x 2 with disorder times theta 1 and theta 2 respectively i e the intensities of x 1 and x 2 change at random unobservable times theta 1 and theta 2 respectively theta 1 and theta 2 are independent of each other and are exponentially distributed define theta triangleq theta 1 wedge theta 2 min theta 1 theta 2 for any stopping time t that is measurable with respect to the filtration generated by the observations define a penalty function of the form r tau mathbb p tau 0 and tau theta is the positive part of tau theta it is of interest to find a stopping time t that minimizes the above performance index this performance criterion can be useful e g in the following scenario there are two assembly lines that produce products a and b respectively assume that the malfunctioning disorder of the machines producing a and b are independent events later the products a and b are to be put together to obtain another product c a product manager who is worried about the quality of c will want to detect the minimum of the disorder times as accurately as possible in the assembly lines producing a and b another problem to which we can apply our framework is the internet surveillance problem a router receives data from say n channels the channels are independent and the disorder times of channels are theta 1 ldots theta n the router is said to be under attack at theta theta 1 wedge cdots wedge theta n the administrator of the router is interested in detecting theta as quickly as possible since both observations x 1 and x 2 reveal information about the disorder time t even this simple problem is more involved than solving the disorder problems for x 1 and x 2 separately this problem is formulated in terms of a three dimensional sufficient statistic and the corresponding optimal stopping problem is examined the solution is characterized by iterating a suitable functional operator

approximate tail probabilities for the maxima of some random fields abstract hogan and siegmund 1986 adapt the method developed by pickands 1969 qualls and watanabe 1973 and bickel and rosenblatt 1973 to obtain explicit large deviation approximations for the maxima of several gaussian random fields arising in statistics using a special argument for one particular case they suggest a heuristic second order approximation for that case and they show by a monte carlo experiment that the second order approximation frequently gives considerably better numerical results the purpose of this paper is to show that the method developed by woodroofe 1976 1982 for problems in one dimensional time can be adapted to study maxima of random fields overall it involves simpler computations than the previous method and consequently seems potentially capable of delivering a genuine second order approximation should one seem desirable

testing for parameter constancy in linear regressions an empirical distribution function approach this paper proposes some tests for parameter constancy in linear regressions the tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free the local power analysis reveals that the proposed tests have nontrivial local power against a wide range of alternatives in particular the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances the model allows for both dynamic and trending regressors the residuals may be obtained based on any root n consistent estimator under the null of regression parameters as an intermediate result some weak convergence for stochastically weighted sequential empirical processes is established

parameter updating in a bayes network abstract a bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables the primary use of the network is to provide an efficient method for updating conditional probabilities in the graph we consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model a discrete time bayesian model we show that using the network characterizes the dynamic linear model and its computations in a unified way the generality of the network permits nonsequential data collection and thereby provides a straightforward method of incorporating delayed data an on line diagnostic is offered to complement the conventional forecast error and an approximation to the posterior distribution is proposed algorithms for data propagation in multivariate gaussian causal trees are presented

sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models by using the theory of coincidence degree the existence of positive periodic solutions is studied for the neutral model with periodic delaysn t n t a t email protected t n t email protected i 1 nb i t n email protected i t email protected i 1 nc i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

the cusum test of homogeneity with an application in spontaneous abortion epidemiology we test the hypothesis of homogeneity over time in the rate of an event with a modification of page s cumulative sum cusum procedure the modification draws on an indifference zone approach to testing that is well suited to the epidemiologic study of retrospective data we provide procedures for evaluating the significance level of the largest observed cusum value occurring in a sequence of fixed length we draw inferences unconditionally with a known baseline rate of the event and conditionally on observed margins with unknown baseline rate data collected over a five year period from one new york city hospital serve to illustrate the modified cusum test in a study of fluctuations in the proportions of chromosomally normal trisomic x monosomic and triploid spontaneous abortions

inclusion exclusion bonferroni identities and inequalities for discrete tube like problems via euler characteristics identity for the union of finitely many balls in d dimensional euclidean space with a single correction term this result also holds in the d dimensional sphere these results form the basis for a discrete theory of tubes which up to now has been continuous in nature the spherical result is used to give a simulation method for finding critical probabilities for multiple comparisons procedures and a computer program implementing the method is described numerical results are presented which demonstrate that in the tails of the distribution probability estimates based on the method tend to exhibit less variability than estimates based on naive simulation 1 introduction this paper touches on several areas of mathematics statistics and elementary probability theory the main results are somewhat technical in proof but easily stated consider a finite collection of measurable subsets ai n the classical inclusion exclusion identity is n

identifying optimal risk windows for self controlled case series studies of vaccine safety in vaccine safety studies subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window to our knowledge risk windows for vaccine safety studies have tended to be pre defined and not to use information from the current study inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period which can introduce bias we propose a data based approach for identifying the optimal risk windows for self controlled case series studies of vaccine safety the approach involves fitting conditional poisson regression models to obtain incidence rate ratio estimates for different risk window lengths for a specified risk window length l the average time at risk t l is calculated when the specified risk window is shorter than the true the incidence rate ratio decreases with 1 t l increasing but there is no explicit relationship when the specified risk window is longer than the true the incidence rate ratio increases linearly with 1 t l increasing theoretically the risk window with the maximum incidence ratio is the optimal risk window because of sparse data problem we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long risk windows

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

a note on ritov s bayes approach to the minimax property of the cusum procedure 1 introduction page 1954 proposed the cusum procedures as a solu tion to the problem of sequential detection of a change in distribution lorden 1971 introduced a notion of minimax optimality for change point models andshowed that the cusum procedures are asymptotically optimal in his sense moustakides 1986 then showed the minimax optimality of the cusum pro cedures when the initial and nal distribution are both known ritov 1990 used a bayes approach and gave an interesting argument for moustakides result similar to that of lehmann 1959 on the optimality of the sequentialprobability ratio test we transfer his approach to a continuous time modeland discuss the structure of the bayes risk let be an arbitrary but known constant we will consider a process wwithw

testing for a two phase multiple regression maximum likelihood methods are used to estimate the parameters of two separate multiple regressions that switch at an unknown point in the data normal errors with constant variance are assumed and likelihood ratio statistics are used to test for the presence of two separate regressions our main result is a conservative bound on the null distribution function of the test statistic this bound is based on an improved bonferroni inequality and a simple power series approximation is provided similar bounds are given for likelihood ratio statistics that test for a shift in the constant term of the regression only the accuracies of the bounds and approximations are evaluated on a number of examples

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

dynamic linear models with markov switching abstract in this paper hamilton s 1988 1989 markov switching model is extended to a general state space model this paper also complements shumway and stoffer s 1991 dynamic linear models with switching by introducing dependence in the switching process and by allowing switching in both measurement and transition equations building upon ideas in hamilton 1989 cosslett and lee 1985 and harrison and stevens 1976 a basic filtering and smoothing algorithm is presented the algorithm and the maximum likelihood estimation procedure is applied in estimating lam s 1990 generalized hamilton model with a general autoregressive component the estimation results show that the approximation employed in this paper performs an excellent job with a considerable advantage in computation time a state space representation is a very flexible form and the approach taken in this paper therefore allows a broad class of models to be estimated that could not be handled before in addition the algorithm for calculating smoothed inferences on the unobserved states is a vastly more efficient one than that in the literature

positive periodic solutions of neutral lotka volterra system with periodic delays in this paper several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral lotka volterra system with unbounded delays by using the theory of coincidence degree our results extend and improve existing results and have further applications in population dynamics

existence and stability of almost periodic solutions in impulsive neural network models abstract the existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting the approach transforms the original network into a matrix analysis problem where a set of sufficient conditions based on spectral radius is presented a concrete hopfield model shows the advantages in comparison with a classical norm approach

quickest detection with exponential penalty for delay the problem of detecting a change in the probability distribution of a random sequence is considered stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria in both cases the detection delay is penalized exponentially rather than linearly as has been the case in previous formulations of this problem the first of these two criteria is to minimize a worst case measure of the exponential detection delay within a lower bound constraint on the mean time between false alarms expressions for the performance of the optimal detection rule are also developed for this case it is seen for example that the classical page cusum test can be arbitrarily unfavorable relative to the optimal test under exponential delay penalty the second criterion considered is a bayesian one in which the unknown change point is assumed to obey a geometric prior distribution in this case the optimal stopping time effects an optimal trade off between the expected exponential detection delay and the probability of false alarm finally generalizations of these results to problems in which the penalties for delay may be path dependent are also considered

the likelihood ratio test for a change point in simple linear regression summary we consider likelihood ratio tests to detect a change point in simple linear regression a when the alternative specifies that only the intercept changes and b when the alternative permits the intercept and the slope to change approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable the approximations are compared with simulations in order to assess their accuracy for the model in which only the intercept is allowed to change a confidence region for the change point and an approximate joint confidence region for the change point the difference in intercepts and the slope are obtained by inversion of the appropriate likelihood ratio tests

existence and global attractivity of almost periodic solution for cellular neural network with distributed delays this paper is devoted to the existence and global attractivity of almost periodic solution for a class of cellular neural network with distributed delays and variable coefficients some sufficient conditions ensuring the existence and global attractivity of almost periodic solution are derived by employing banach fixed point theory and using differential inequality technique the results allow for the consideration of all unbounded neuron signal functions but not necessarily surjective thus these conditions obtained have highly important significance in designs and applications of the networks we extend and improve previously known results an example is also worked out to demonstrate the advantages of our results

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

a general regression changepoint test for time series data abstractthis article develops a test for a single changepoint in a general setting that allows for correlated time series regression errors a seasonal cycle time varying regression factors and covariate information within a changepoint statistic is constructed from likelihood ratio principles and its asymptotic distribution is derived the asymptotic distribution of the changepoint statistic is shown to be invariant of the seasonal cycle and the covariates should the latter obey some simple limit laws however the limit distribution depends on any time varying factors a new test based on arma residuals is developed and is shown to have favorable properties with finite samples driving our work is a changepoint analysis of the mauna loa record of monthly carbon dioxide concentrations this series has a pronounced seasonal cycle a nonlinear trend heavily correlated regression errors and covariate information in the form of climate oscillations in the end we find a prominent changepoint in the ea

a simple method for studying run length distribution of exponentially weighted moving average charts a numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average ewma charts both average run lengths arl s and standard deviations of run lengths sdrl s are presented for the twosided ewma chart assuming normal observations along with an example illustrating how to design such a chart the procedure given extends easily to many nonnormal cases and to one sided versions of the ewma chart

on the exponential stability and periodic solutions of delayed cellular neural networks a set of criteria is presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks dcnns by constructing suitable lyapunov functionals introducing many parameters and combining with the elementary inequality technique these criteria have important leading significance in the design and applications of globally stable dcnns and periodic oscillatory dcnns in addition earlier results are extended and improved other results are contained two examples are given to illustrate the theory