mathematics of granular materials this is a short and somewhat informal review on the most mathematical parts of the kinetic theory of granular media intended for physicists and for mathematicians outside the field

delay times of sequential procedures for multiple time series regression models we consider a multiple regression model in which the explanatory variables are specified by time series to sequentially test for the stability of the regression parameters in time we introduce a detector which is based on the first excess time of a cusum type statistic over a suitably constructed threshold function the aim of this paper is to study the delay time associated with this detector as our main result we derive the limit distribution of the delay time and provide thereby a theory that extends the benchmark average run length concept utilized in most of the sequential monitoring literature to highlight the applicability of the limit results in finite samples we present a monte carlo simulation study and an application to macroeconomic data

robust inference in nonstationary time series models abstract this paper studies robust inference in unit root and cointegration models the analysis covers a range of important inference problems including testing stationarity against unit roots testing for structure change in nonstationary regressions and testing for cointegration we analyze these inference problems in a unified regression framework although separate analysis is given for each specific case when it is needed the proposed inference procedures are constructed based on residuals of robust m estimations the limiting behavior of the proposed tests is investigated and a monte carlo experiment is conducted the proposed tests are easy to use and have advantages in the presence of non gaussian data

testing for structural change in dynamic models the well known cusum test for structural change is investigated whe n there are lagged dependent variables among the regressors in a linear model the authors show that both a modified cusum test suggested b y j m dufour 1982 and the straightforward cusum test retain their asymptotic significance levels in dynamic models and find that the power depends crucially on the angle between the mean regressor and the structural shift copyright 1988 by the econometric society

change point monitoring for online stochastic approximations we consider stochastic approximations in a quickly changing non stationary environment we assume the parameters of the system are subject to sudden discontinuous changes which we refer to as regime switching we are interested in problems characterized by frequent significant jumps with no a priori knowledge about the regimes our approach is based on constant step size stochastic approximation while larger step sizes have the advantage of fast adaptation smaller step sizes provide more precise estimates of the target value once the process is close to stationary we propose to use a small constant step size combined with change point monitoring and to reset the process at a value closer to the new target when a change is detected stochastic approximation and change point monitoring complement each other by achieving high precision as well as cutting down the convergence time we give a theoretical characterization and discuss the tradeoff between precision and fast adaptation we also introduce a new monitoring scheme the regression based hypothesis test which performs comparably well to page hinkley s test and the cusum of residuals the novelty of our approach is a the combination of change point monitoring to stochastic approximation in a regime switching environment and b the introduction of a new monitoring scheme we provide an asymptotic analysis of this method and we show weak convergence to a limiting switching ode for the non reset method and to a hybrid de for a reset method that we propose

detecting a shift in location some robust tests abstract the test statistic w suggested by hawkins 1977 and worsley 1979 for testing a sequence of observations for a shift in location is sensitive to the assumption that the distribution of the population being sampled is normal a modification of this statistic is proposed which is robust against heavy tailed distributions we also study the performance of several alternative testing procedures by means of a simulation experiment the farley hinich test 1975 and the homogeneity test discussed in brown durbin and evans 1975 perform well in the simulation experiment against heavy tailed distributions some applications to economic data are also discussed in the paper

testing the constancy of regression parameters against continuous structural change abstract a standard explicit or implicit assumption underlying many parameter constancy tests in linear models is that there is a single structural break in the sample in this paper that assumption is replaced by a more general one stating that the parameters of the model may change continuously over time the pattern of change is parameterized giving rise to a set of parameter constancy tests against a parameterized alternative the power properties of the lm type tests in small samples are compared to those of other tests like the cusum and fluctuation test by simulation and found very satisfactory an application is considered

wiener disorder problem with observations at fixed discrete time epochs suppose that a wiener process gains a known drift rate at some unobservable disorder time with some zero modified exponential distribution the process is observed only at known fixed discrete time epochs which may not always be spaced in equal distances the problem is to detect the disorder time as quickly as possible by means of an alarm that depends only on the observations of wiener process at those discrete time epochs we show that bayes optimal alarm times which minimize expected total cost of frequent false alarms and detection delay time always exist optimal alarms may in general sound between observation times and when the space time process of the odds that disorder happened in the past hits a set with a nontrivial boundary the optimal stopping boundary is piecewise continuous and explodes as time approaches from left to each observation time on each observation interval if the boundary is not strictly increasing everywhere then it first decreases and then increases it is strictly monotone wherever it does not vanish its decreasing portion always coincides with some explicit function we develop numerical algorithms to calculate nearly optimal detection algorithms and their bayes risks and we illustrate their use on numerical examples the solution of wiener disorder problem with discretely spaced observation times will help reduce risks and costs associated with disease outbreak and production quality control where the observations are often collected and or inspected periodically

geometrical validity of curvilinear finite elements in this paper we describe a way to compute accurate bounds on jacobian determinants of curvilinear polynomial finite elements our condition enables to guarantee that an element is geometrically valid i e that its jacobian determinant is strictly positive everywhere in its reference domain it also provides an efficient way to measure the distortion of curvilinear elements the key feature of the method is to expand the jacobian determinant using a polynomial basis built using bezier functions that has both properties of boundedness and positivity numerical results show the sharpness of our estimates

non restarting cumulative sum charts and control of the false discovery rate cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations e g shifts in the mean usually after signalling the chart is restarted by setting it to some value below the signalling threshold we propose a non restarting cusum chart which is able to detect periods during which the stream is out of control further we advocate an upper boundary to prevent the cusum chart rising too high which helps to detect a change back into control we present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data we consider two definitions of a false discovery signalling out of control when the observations have been in control since the start and signalling out of control when the observations have been in control since the last time the chart was at zero we prove that the false discovery rate is controlled under both these definitions simultaneously simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery copyright 2013 oxford university press

average run length to false alarm for surveillance schemes designed with partially specified pre change distribution observations are taken independently and sequentially detection of a change in distribution is studied when the problem has an invariance structure the prechange distribution is assumed to be a member of a specified family and is assumed known up to a nuisance parameter we provide a general method of constructing surveillance schemes in the presence of a nuisance parameter and give sufficient conditions for approximating their average run lengths to false alarm applications include detecting a change in scale of i i d gamma variates with unknown initial scale detecting a change in location of i i d normal variates with unknown initial mean and a non parametric scheme based on ranks for detecting a change to a stochastically larger distribution

lagrangian numerical approximations to one dimensional convolution diffusion equations this work focuses on the numerical analysis of one dimensional nonlinear diffusion equations involving a convolution product first homogeneous friction equations are considered algorithms follow recent ideas on mass transportation methods and lead to simple schemes which can be proved to be stable to decrease entropy and to converge toward the unique solution of the continuous problem in particular for the first time homogeneous cooling states are displayed numerically further we present results on the more delicate fourth order thin film equation for which a nonnegativity preserving scheme is derived the dead core phenomenon is presented for the hele shaw cell

tests for changes in models with a polynomial trend abstract in this paper we propose a class of tests for changes in models with a polynomial trend based on the generalized fluctuation testing principle of kuan and hornik 1995 we derive the asymptotic null distributions of the proposed tests and tabulate their asymptotic critical values we also show that these tests are consistent and have non trivial local power against a wide class of alternatives the simulation results suggest that the proposed tests can complement the existing tests in different time trend models

the invertibility of the isoparametric mapping for pyramidal and prismatic finite elements we consider the isoparametric transformation which maps a given reference element onto a global element given by its vertices for multi linear finite elements on pyramids and prisms we present easily computable conditions on the position of the vertices which ensure that the isoparametric transformation is bijective

a new test for structural stability in the linear regression model abstract we propose a new test for the constancy of regression coefficients in linear models the test does not require that possible change points be known we derive the limiting null distribution of the test statistic prove that the test has non trivial power against many local alternatives and show that it compares favourably to both the cusum and cusum of squares tests

a trend resistant test for structural change based on ols residuals abstract we discuss the null distribution and local power of an ols based version of the cusum test and show that this contrary to other tests for structural change like e g the ploberger kontrus kramer fluctuation test can also be applied to trending data

higher order interpolatory vector bases on pyramidal elements in the numerical solution of three dimensional 3 d electromagnetic field problems the regions of interest can be discretized by elements having tetrahedral brick or prismatic shape however such different shape elements cannot be linked to form a conformal mesh to this purpose pyramidal elements are required in this paper we define interpolatory higher order curl and divergence conforming vector basis functions on pyramidal elements with extension to curved pyramids and discuss their completeness properties a general procedure to obtain vector bases of arbitrary polynomial order is given and bases up to second order are explicitly reported these new elements ensure the continuity of the proper vector components across adjacent elements of equal order but different shape results to confirm the faster convergence of higher order functions on pyramids are presented

small sample properties of forecasts from autoregressive models under structural breaks this paper develops a theoretical framework for the analysis of smallsample properties of forecasts from general autoregressive models under structural breaks finite sample results for the mean squared forecast error of one step ahead forecasts are derived both conditionally and unconditionally and numerical results for different types of break specifications are presented it is established that forecast errors are unconditionally unbiased even in the presence of breaks in the autoregressive coefficients and or error variances so long as the unconditional mean of the process remains unchanged insights from the theoretical analysis are demonstrated in monte carlo simulations and on a range of macroeconomic time series from g7 countries the results are used to draw practical recommendations for the choice of estimation window when forecasting from autoregressive models subject to breaks

information bounds and quickest change detection in decentralized decision systems the quickest change detection problem is studied in decentralized decision systems where a set of sensors receive independent observations and send summary messages to the fusion center which makes a final decision in the system where the sensors do not have access to their past observations the previously conjectured asymptotic optimality of a procedure with a monotone likelihood ratio quantizer mlrq is proved in the case of additive gaussian sensor noise if the signal to noise ratios snr at some sensors are sufficiently high this procedure can perform as well as the optimal centralized procedure that has access to all the sensor observations even if all snrs are low its detection delay will be at most pi 2 1ap 57 larger than that of the optimal centralized procedure next in the system where the sensors have full access to their past observations the first asymptotically optimal procedure in the literature is developed surprisingly the procedure has the same asymptotic performance as the optimal centralized procedure although it may perform poorly in some practical situations because of slow asymptotic convergence finally it is shown that neither past message information nor the feedback from the fusion center improves the asymptotic performance in the simplest model

asymptotic minimax robust quickest change detection for dependent stochastic processes with parametric uncertainty in this paper we consider the problem of quickly detecting an unknown change in the conditional densities of a dependent stochastic process in contrast to the existing quickest change detection approaches for dependent stochastic processes we propose minimax robust versions of the popular lorden pollak and bayesian criteria for when there is uncertainty about the parameter of the post change conditional densities under an information theoretic pythagorean inequality condition on the uncertainty set of possible post change parameters we identify asymptotic minimax robust solutions to our lorden pollak and bayesian problems finally through simulation examples we illustrate that asymptotically minimax robust rules can provide detection performance comparable to the popular but more computationally expensive generalized likelihood ratio rule

a mathematical framework for new fault detection schemes in nonlinear stochastic continuous time dynamical systems in this work a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous time dynamical systems is developed these schemes are based on a stochastic process called the residual which reflects the system behavior and whose changes are to be detected a quickest detection scheme for the residual is proposed which is based on the computed likelihood ratios for time varying statistical changes in the ornstein uhlenbeck process several expressions are provided depending on a priori knowledge of the fault which can be employed in a proposed cusum type approximated scheme this general setting gathers different existing fault detection schemes within a unifying framework and allows for the definition of new ones a comparative simulation example illustrates the behavior of the proposed schemes

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

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

homogeneous cooling states are not always good approximations to granular flows a widespread belief in the study of granular flow is the existence of homogeneous cooling states i e self similar solutions which would attract all solutions faster than the equilibrium solution does in most cases the existence of these self similar solutions is an open problem here we consider a one dimensional model which has been used for some years and for which simple self similar solutions do exist however we prove that the approximation is quite poor our proof makes use of the powerful and simple tools of mass transportation and exploits the structure of the evolution equation seen as a nonlinear transport equation

stability convergence to self similarity and elastic limit for the boltzmann equation for inelastic hard spheres we consider the spatially homogeneous boltzmann equation for inelastic hard spheres in the framework of so called constant normal restitution coefficients alpha in 0 1 in the physical regime of a small inelasticity that is alpha in alpha 1 for some constructive alpha in 0 1 we prove uniqueness of the self similar profile for given values of the restitution coefficient alpha in alpha 1 the mass and the momentum therefore we deduce the uniqueness of the self similar solution up to a time translation

times series segmentation a sliding window approach the aim of this paper is to present two on line sliding window segmentation algorithms detection nonstationarity is based on parameter fluctuations and change point localization of the akaike information criterion asymptotic properties of the proposed algorithms are analyzed specifically the limiting distributions are derived and the asymptotic threshold values are tabulated for future reference finite sample simulations are performed to illustrate the usefulness of these algorithms

performance analysis of sequential tests between poisson processes the problem of performance computation for sequential tests between poisson processes is considered the average sample numbers and error probabilities of the sequential probability ratio test sprt between two homogeneous poisson processes are known to solve certain delay differential equations ddes exact numerically stable solutions to these ddes are developed here and their asymptotic properties are explored these solutions are seen to be superior to earlier solutions of dvoretsky kiefer and wolfowitz 1953 which suffer from severe numerical instability in some ranges of parameters of interest in applications the application of these results is illustrated in the problem of performance approximation for the cumulative sum cusum quickest detection procedure

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

powerful tests for structural changes in volatility abstract detecting structural changes in volatility is important for understanding volatility dynamics and stylized facts observed for financial returns such as volatility persistence we propose modified cusum and lm tests that are built on a robust estimator of the long run variance of squared series we establish conditions under which the new tests have standard null distributions and diverge faster than standard tests under the alternative the theory allows smooth and abrupt structural changes that can be small the smoothing parameter is automatically selected such that the proposed test has good finite sample size and meanwhile achieves decent power gain

inference of time varying regression models we consider parameter estimation hypothesis testing and variable selection for partially time varying coefficient models our asymptotic theory has the useful feature that it can allow dependent nonstationary error and covariate processes with a two stage method the parametric component can be estimated with a n 1 2 convergence rate a simulation assisted hypothesis testing procedure is proposed for testing significance and parameter constancy we further propose an information criterion that can consistently select the true set of significant predictors our method is applied to autoregressive models with time varying coefficients simulation results and a real data application are provided

detecting a suddenly arriving dynamic profile of finite duration this paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change in contrast to the traditional abrupt change detection where the post change period is assumed to be infinitely long the detection of a suddenly arriving transient change should be done before it disappears the detection of transient changes after their disappearance is considered as missed hence the traditional quickest change detection criterion minimizing the average detection delays provided a prescribed false alarm rate is compromised the proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded a suboptimal cusum type transient change detection algorithm based on a subclass of truncated sequential probability ratio tests is proposed the optimization of the proposed algorithm in this subclass leads to a specially designed finite moving average test the proposed method is analyzed theoretically and by simulation a special attention is paid to the case of gaussian observations with a dynamic profile

wavelet analysis of change points in a non parametric regression with heteroscedastic variance abstract in this paper we develop wavelet methods for detecting and estimating jumps and cusps in the mean function of a non parametric regression model an important characteristic of the model considered here is that it allows for conditional heteroscedastic variance a feature frequently encountered with economic and financial data wavelet analysis of change points in this model has been considered in a limited way in a recent study by chen et al 2008 with a focus on jumps only one problem with the aforementioned paper is that the test statistic developed there has an extreme value null limit distribution the results of other studies have shown that the rate of convergence to the extreme value distribution is usually very slow and critical values derived from this distribution tend to be much larger than the true ones here we develop a new test and show that the test statistic has a convenient null limit n 0 1 distribution this feature gives the proposed approach an appealing advantage over the existing approach another attractive feature of our results is that the asymptotic theory developed here holds for both jumps and cusps implementation of the proposed method for multiple jumps and cusps is also examined the results from a simulation study show that the new test has excellent power and the estimators developed also yield very accurate estimates of the positions of the discontinuities

does modeling a structural break improve forecast accuracy mean square forecast error loss implies a bias variance trade off that suggests that structural breaks of small magnitude should be ignored in this paper we provide a test to determine whether modeling a structural break improves forecast accuracy the test is near optimal even when the date of a local to zero break is not consistently estimable the results extend to forecast combinations that weight the post break sample and the full sample forecasts by our test statistic in a large number of macroeconomic time series we find that structural breaks that are relevant for forecasting occur much less frequently than existing tests indicate

generalized runs tests for the iid hypothesis we provide a family of tests for the iid hypothesis based on generalized runs powerful against unspecified alternatives providing a useful complement to tests designed for specific alternatives such as serial correlation garch or structural breaks our tests have appealing computational simplicity in that they do not require kernel density estimation with the associated challenge of bandwidth selection simulations show levels close to nominal asymptotic levels our tests have power against both dependent and heterogeneous alternatives as both theory and simulations demonstrate

estimating a change point in a sequence of very high dimensional covariance matrices this article considers the problem of estimating a change point in the covariance matrix in a sequence of high dimensional vectors where the dimension is substantially larger than the sample size

mosum tests for parameter constancy summary in this paper tests for structural change based on moving sums mosums of recursive and least squares residuals are investigated we obtain and tabulate the asymptotic critical values of the mosum test with recursive residuals and show that the asymptotic critical values of the mosum test with least squares residuals can easily be obtained from already existing tables for the moving estimates test we also show that these mosum tests are consistent and have nontrivial local power against a general class of alternatives our simulations further indicate that the proposed mosum tests can complement other tests when there is a single structural change and have power advantage when there are certain double structural changes

self similar blowup solutions to an aggregation equation in r n we present numerical simulations of radially symmetric finite time blowup for the aggregation equation ut u k u where the kernel k x x the dynamics of the blowup exhibits self similar behavior in which zero mass concentrates at the core at the blowup time computations are performed in r n for n between 2 and 10 using a method based on characteristics in all cases studied the self similarity exhibits second kind anomalous scaling

the cusum test with ols residuals we show that the cusum test of the stability over time of the coefficients of a linear regression model which is usually based on recursive residuals can also be applied to ordinary least squares residuals we derive the limiting null distribution of the resulting test and compare its local power to that of the standard procedure it turns out that neither version is uniformly superior to the other henceforth bde on the cusum and cusum of squares tests for the constancy over time of the coefficients of a linear regression model both tests are based on recursive residuals which are independent n o o 2 under ho and therefore ideal ingredients for all types of tests while the cusum of squares test has been generalized to ordinary least squares ols residuals mccabe and harrison 1980 a generalization of the cusum test to ols residuals which are dependent and heteroskedastic even under ho has not yet been made except for a very special case macneill 1978 in fact both bde 1975 p 151 and mccabe and harrison 1980 p 142 argue that a least squares variant of the cusum test poses intractable problems due to an alleged difficulty in assessing the significance of the departure of the cumulated ols residuals from their mean value zero below we show that it is no more difficult to derive the limiting distribution for a cusum test based on ols residuals than for a cusum test based on recursive residuals while the cusums of the recursive residuals properly standardized tend in distribution to a standard wiener process sen 1982 krimer ploberger and alt 1988 henceforth kpa we show that the ols based cusums tend in distribution to a brownian bridge or tied down brownian motion see billingsley 1968 p 64 this generalizes macneill s 1978 polynomial regression result to arbitrary regressor sequences we also demonstrate that the resulting cusum test has higher local power for certain types of structural change than the one based on recursive residuals though neither variant is uniformly superior to the other

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

a non local perspective on the power properties of the cusum and cusum of squares tests for structural change abstract we consider the power properties of the cusum and cusum of squares cusq tests in the presence of a one time change in the parameters of a linear regression model a result due to ploberger and kramer 1990 the local power of the cusum and cusum of squares tests econometric theory 6 335 347 is that the cusq test has only trivial asymptotic local power in this case while the cusum test has non trivial local asymptotic power unless the change is orthogonal to the mean regressor the main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finite samples the approach we take is to derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis this enables us to analyze what happens for non local to zero breaks our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors a static regression with correlated errors a dynamic regression with lagged dependent variables or whether a correction for non normality is applied in the case of the cusq we discuss in which cases the tests are subject to a non monotonic power function that goes to zero as the magnitude of the change increases and uncover some curious properties all theoretical results are verified to yield good guides to the finite sample power through simulation experiments we finally highlight the practical importance of our results

nonparametric sequential signal change detection under dependent noise a nonparametric version of the sequential signal detection problem is studied our signal model includes a class of time limited signals for which we collect data in the sequential fashion at discrete points in the presence of correlated noise for such a setup we introduce a novel signal detection algorithm relying on the postfiltering smooth correction of the classical whittaker shannon interpolation series given a finite frame of noisy samples of the signal we design a detection algorithm being able to detect a departure from a reference signal as quickly as possible our detector is represented as a normalized partial sum continuous time stochastic process for which we obtain a functional central limit theorem under weak assumptions on the correlation structure of the noise particularly our results allow for noise processes such as arma and general linear processes as well as mixing processes the established limit theorems allow us to design monitoring algorithms with the desirable level of the probability of false alarm and able to detect a change with probability approaching one

detecting a change in regression first order optimality observations are generated according to a regression with normal error as a function of time when the process is in control the process potentially changes at some unknown point of time and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions the problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a constraint on the average run length to a false alarm a bound on the expected delay is first obtained it is then shown that the cusum and shiryayev roberts procedures achieve this bound to first order

sequential monitoring for changes from stationarity to mild non stationarity abstract we develop and study sequential testing procedures a la chu et al 1996 for on line detection of changes in a time series from stationarity to mild forms of non stationarity the proposed tests are based on sequential cusum and kpss type detector processes and are shown to provide consistent detection under a wide range of change point models including changes in the parameters of arma and garch series from values within the model s stationarity parameter region to values close converging to the stationarity boundary local asymptotic results are established giving precise descriptions of the time to detection under several of these models which show that such procedures are powerful to detect a wide range of non stationary characteristics including changes in mean volatility and unit root behaviour the proposed methods are investigated by means of a simulation study and in applications to monitoring for changes in trend and unit root behaviour in macroeconomic production series and to detect changes in volatility of the s p 500 stock market index

misspecified and asymptotically minimax robust quickest change detection we investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations we develop new bounds on the performance of misspecified cumulative sum cusum rules and pose minimax robust versions of the popular lorden and pollak criteria with polynomial or higher order moment detection delay penalties by exploiting our results for misspecified cusum rules we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms in contrast to previous robust quickest change detection treatments our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions we illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal to noise ratio settings i e dim target manoeuvre detection

geometrical validity of curvilinear pyramidal finite elements a method to efficiently determine the geometrical validity of curvilinear finite elements of any order was recently proposed in 1 the method is based on the adaptive expansion of the jacobian determinant in a polynomial basis built using bezier functions that has both properties of boundedness and positivity while this technique can be applied to all usual finite elements triangles quadrangles tetrahedra hexahedra and prisms it cannot readily be applied to pyramids due to non polynomial nature of pyramidal finite element spaces in this short paper we extend the results from 1 to pyramidal elements by making use of the high order nodal pyramidal finite element proposed by bergot et al 10 which exhibits optimal convergence properties inh1 norm the paper is organized as follows we begin by briefly recalling the pyramidal finite element space in section 2 before constructing the function space of the jacobian determinant in section 3 section 4 then introduces a generalized bezier function basis which can be used to obtain adaptive bounds on the pyramidal jacobian determinant numerical results showing the sharpness of the estimates are given in section 5

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

risk adjusted monitoring of time to event recently there has been interest in risk adjusted cumulative sum charts cusums to monitor the performance of e g hospitals taking into account the heterogeneity of patients even though many outcomes involve time only conventional regression models are commonly used in this article we investigate how time to event models may be used for monitoring purposes we consider monitoring using cusums based on the partial likelihood ratio between an out of control state and an in control state we consider both proportional and nonproportional alternatives as well as a head start against proportional alternatives we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events in a stationary set up the former is roughly proportional to the average run length in calendar time adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion however it changes the threshold substantially if a false alarm probability is used in simulation studies charts based on survival analysis perform better than simpler monitoring schemes we present one example from retail finance and one medical application

long time asymptotics of kinetic models of granular flows we analyze the long time asymptotics of certain one dimensional kinetic models of granular flows which have been recently introduced in 22 in connection with the quasi elastic limit of a model boltzmann equation with dissipative collisions and variable coefficient of restitution these nonlinear equations classified as nonlinear friction equations split naturally into two classes depending on whether or not the temperature of their similarity solutions homogeneous cooling states reduce to zero in finite time for both classes we show uniqueness of the solution by proving decay to zero in the wasserstein metric of any two solutions with the same mass and mean velocity furthermore if the temperature of the similarity solution decays to zero in finite time we prove by computing explicitly upper bounds for the lifetime of the solution in terms of the length of the support that the temperature of any other solution with initially bounded support must also decay to zero in finite time

monitoring structural change contemporary tests for structural change deal with detections of the one shot type given an historical data set of fixed size these tests are designed to detect a structural break within the data set due to the law of the iterated logarithm one shot tests cannot be applied to monitor out of sample stability each time new data arrive without signalling a nonexistent break with probability one we propose and analyze two real time monitoring procedures with controlled size asymptotically the fluctuation and cusum monitoring procedures we extend an invariance principle in the sequential testing literature to obtain our results simulation results show that the proposed monitoring procedures indeed have controlled asymptotic size detection timing depends on the magnitude of parameter change the signal to noise ratio and the location of the out of sample break point

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

a likelihood ratio approach to sequential change point detection for a general class of parameters in this article we propose a new approach for sequential monitoring of a general class of parameters of a d dimensional time series which can be estimated by approximately linear functionals of t

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

tanaka theorem for inelastic maxwell models we show that the euclidean wasserstein distance is contractive for inelastic homogeneous boltzmann kinetic equations in the maxwellian approximation and its associated kac like caricature this property is as a generalization of the tanaka theorem to inelastic interactions even in the elastic classical boltzmann equation we give a simpler proof of the tanaka theorem than the ones in 29 31 consequences are drawn on the asymptotic behavior of solutions in terms only of the euclidean wasserstein distance

input design for detection of abrupt changes in dynamical systems the detection and diagnosis of changes in stationary dynamical systems via statistical methods and using input design to improve detection performance are discussed a cumulative sum test to detect a change towards one of several hypotheses is obtained by exploiting connections with the sequential probability ratio test for input design the objectives are taken to be to decrease the detection time and at the same time to ensure a tolerable false alarm rate both off line auxiliary inputs and on line generation of the input signal by a linear output feedback are considered the problem is first introduced for the two hypotheses case and then the design techniques are extended to the general multiple hypotheses case

strong rules for detecting the number of breaks in a time series this paper proposes a new approach for detecting the number of structural breaks in a time series when estimation of the breaks is performedone at the time we consid er the case of shifts in the mean of a possibly nonlinear process allowing for dependent and heterogeneous observations this is accomplishedthrough a simple sequential almost sure rule ensuring that in large samples both the probabilities of overestimating andund erestimating the number of breaks are zero a new estimator for the long run variance which is consistent also in the presence of neglectedbreaks is proposed the 0nite sample behavior is investigatedvia a simulation exercise a tendency to overreject the null hypothesis emerges for sample of moderate size and so we suggest a small sample correction the sequential procedure applied to the weekly eurodollar interest rate detects multiple breaks over the period 1973 1995 c 2003 elsevier b v all rights reserved jel classi cation c20 c22

grouped data sequential probability ratio tests and cumulative sum control charts methodology is proposed for the design of sequential methods when data are obtained by gauging articles into groups exact expressions are obtained for the operating characteristics and average sampling number of wald sequential probability ratio tests and for the average run length of cumulative sum cusum schemes based on grouped data step by step design algorithms are provided to assist the practitioner the methodology is illustrated assuming a normal process with known standard deviation in which we wish to detect shifts in the mean an example from a progressive die operation is presented the methods proposed are simple to implement and are an economical alternative to variables data based sequential sampling plans and cusum control charts

an efficient sequential nonparametric scheme for detecting a change of distribution ble and remarkably efficient the method is based on the sequential vectors of signs and ranks of the observations the methodology is one of likelihood ratio a sequence of likelihood ratios for these vectors is computed and the shiryayev roberts approach to changepoint detection is then applied to yield a class of statistics and associated stopping rules inequalities and asymptotic approximations for the operating characteristics of these rules are developed these are found to be valid also for small average run lengths and early changepoints as well the relative efficiency of these schemes with respect to a normal parametric shift detection policy is very high making them a robust alternative to parametric methof s