change point testing in logistic regression models with interaction term a threshold effect takes place in situations where the relationship between an outcome variable and a predictor variable changes as the predictor value crosses a certain threshold change point threshold effects are often plausible in a complex biological system especially in defining immune responses that are protective against infections such as hiv 1 which motivates the current work we study two hypothesis testing problems in change point models we first compare three different approaches to obtaining a p value for the maximum of scores test in a logistic regression model with change point variable as a main effect next we study the testing problem in a logistic regression model with the change point variable both as a main effect and as part of an interaction term we propose a test based on the maximum of likelihood ratios test statistic and obtain its reference distribution through a monte carlo method we also propose a maximum of weighted scores test that can be more powerful than the maximum of likelihood ratios test when we know the direction of the interaction effect in simulation studies we show that the proposed tests have correct type i error and higher power than several existing methods we illustrate the application of change point model based testing methods in a recent study of immune responses that are associated with the risk of mother to child transmission mtct of hiv 1

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

an improved bonferroni inequality and applications summary we present an improved bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events the bound is constructed in terms of the joint probability of pairs of events which are represented by edges on a graph examples of applications to periodicity location shift detection kolmogorovsmirnov tests and outlier detection are given

human motion classification using 2d stick model matching regression coefficients a 2d human motion model developed based on polynomial regression data fit human motion modeled in three segments backbone upper body and lower body tolerance rate considers the acceptable range for reliable motion estimations classification accuracy for developed estimation model is on par with the actual motion estimation methods have been proposed via different approaches such as silhouette based model based and image based estimations however these methods are highly dependent on the quality of motion data for optimal classification accuracy further because of the complexity of existing algorithms for motion estimation there are difficulties in interpretation hence the contribution of this work is to model simple human motions for the purpose of recognizing different activity behavior patterns for classification analysis the model is made up of three body component integrations backbone bb upper body ub and lower body lb to form a simple 2d human stick figure two case studies involving a publicly available video of walking running and jumping motions as well as experimental captures of yoga motions are studied video motions are simplified into time step image snapshots which are later translated into a numeric 2d coordinate system initially the human pelvis is considered the origin of the stick figure the stick model was drawn by integrating the bb ub and lb components based on the 2d body joint coordinates the motion estimation model applies the concept of polynomial fitting to the coordinates data computations on the polynomial fitting coefficient deviations at sequential time steps were performed to evaluate the estimation tolerance a summation of the precedent time step coordinates with the average deviation metric is used iteratively to estimate the joint coordinates of the stick figure in the subsequent time step to develop the entire motion model finally the developed motion estimation mathematical model was compared to the actual motion phases for classification efficiencies using the bayes lazy function meta misc rules and trees classifiers our findings revealed the feasibility of using 2d stick model matching estimation for human motion classification analysis

testing for threshold effects in regression models in this article we develop a general method for testing threshold effects in regression models using sup likelihood ratio lr type statistics although the sup lr type test statistic has been considered in the literature our method for establishing the asymptotic null distribution is new and nonstandard the standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function the article provides an alternative novel method that can be used to establish the asymptotic null distribution even when the usual quadratic approximation is intractable we illustrate the usefulness of our approach in the examples of the maximum score estimation maximum likelihood estimation quantile regression and maximum rank correlation estimation we establish consistency and local power properties of the test we provide some simulation results and also an empirical application to tipping in racial segregation this ar

a nonparametric polynomial identification algorithm for the hammerstein system almost all existing hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable to overcome this defect in this paper a new nonparametric polynomial identification algorithm for the hammerstein system is proposed which extends the idea in the author s previous work 1993 1994 on the hammerstein system identification to a more general and practical case where no functional value of the system nonlinearity is known a priori convergence and convergence rates in both uniform and global senses are established and simulation studies demonstrate the effectiveness and advantage of the new algorithm

correspondence comments on identification of hammerstein nonlinear armax systems this note points out some errors in the proof of the main result of ding and chen 2005 identification of hammerstein nonlinear armax systems automatica 41 9 1479 1489 and mentions the well known results that have solved the problem discussed in theorem 1 of the above paper by ding and chen

decoupling the linear and nonlinear parts in hammerstein model identification the main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in hammerstein model identification therefore identification of the linear part for a hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

stochastic adaptive prediction and model reference control guo and chen 1991 have recently shown how to establish the self optimality and mean square stability of a self tuning regulator the idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering control and identification in adaptive filtering we examine both indirect and noninterlaced direct schemes for prediction using both least squares and gradient parameter estimation algorithms in addition to analyzing similar direct adaptive control algorithms we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection we also establish that the parameters converge to the null space of a certain matrix from this one may deduce the convergence of several adaptive controllers

stochastic approximation in nonparametric identification of hammerstein systems derived from the idea of stochastic approximation recursive algorithms to identify a hammerstein system are presented two of them recover the characteristic of the nonlinear memoryless subsystem while the third one estimates the impulse response of the linear dynamic part the a priori information about both subsystems is nonparametric consistency in quadratic mean is shown and the convergence rate is examined results of numerical simulation are also presented

segmented regression with errors in predictors semi parametric and parametric methods we consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors with a focus on linear and logistic regression in epidemiologic studies segmented regression models often occur as threshold models where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold furthermore in occupational and environmental studies the exposure typically cannot be measured exactly ignoring this measurement error leads to asymptotically biased estimators of the threshold it is shown that this asymptotic bias is different from that observed for estimating standard generalized linear model parameters in the presence of measurement error being both larger and in different directions than expected in most cases considered the threshold is asymptotically underestimated two standard general methods for correcting for this bias are considered regression calibration and simulation extrapolation simex in ordinary logistic and linear regression these procedures behave similarly but in the threshold segmented regression model they operate quite differently the regression calibration estimator usually has more bias but less variance than the simex estimator regression calibration and simex are typically thought of as functional methods also known as semi parametric methods because they make no assumptions about the distribution of the unobservable covariate x the contrasting structural parametric maximum likelihood estimate assumes a parametric distributional form for x in ordinary linear regression there is typically little difference between structural and functional methods one of the major surprising findings of our study is that in threshold regression the functional and structural methods differ substantially in their performance in one of our simulations approximately consistent functional estimates can be as much as 25 times more variable than the maximum likelihood estimate for a properly specified parametric model structural parametric modelling ought not be a neglected tool in measurement error models an example involving dust concentration and bronchitis in a mechanical engineering plant in munich is used to illustrate the results 1997 by john wiley sons ltd

transition models for change point estimation in logistic regression although a wide variety of change point models are available for continuous outcomes few models are available for dichotomous outcomes this paper introduces transition methods for logistic regression models in which the dose response relationship follows two different straight lines which may intersect or may present a jump at an unknown change point in these models the logit includes a differentiable transition function that provides parametric control of the sharpness of the transition at the change point allowing for abrupt changes or more gradual transitions between the two different linear trends as well as for estimation of the location of the change point linear linear logistic models are particular cases of the proposed transition models we present a modified iteratively reweighted least squares algorithm to estimate model parameters and we provide inference procedures including a test for the existence of the change point these transition models are explored in a simulation study and they are used to evaluate the existence of a change point in the association between plasma glucose after an oral glucose tolerance test and mortality using data from the mortality follow up of the second national health and nutrition examination survey

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

brief identification of linear systems with hard input nonlinearities of known structure this paper studies identification of systems with input nonlinearities of known structure for input nonlinearities parameterized by one parameter a deterministic approach is proposed based on the idea of separable least squares the identification problem is shown to be equivalent to an one dimensional minimization problem the method is very effective for several common static and nonstatic input nonlinearities for a general input nonlinearity a correlation analysis based identification algorithm is presented which is shown to be convergent

semiparametric estimation of a binary response model with a change point due to a covariate threshold this paper is concerned with semiparametric estimation of a threshold binary response model the estimation method considered in the paper is semiparametric since the parameters for a regression function are finite dimensional while allowing for heteroskedasticity of unknown form in particular the paper considers manski 1975 1985 s maximum score estimator the model in this paper is irregular because of a change point due to an unknown threshold in a covariate this irregularity coupled with the discontinuity of the objective function of the maximum score estimator complicates the analysis of the asymptotic behavior of the estimator sufficient conditions for the identification of parameters are given and the consistency of the estimator is obtained it is shown that the estimator of the threshold parameter is n consistent and the estimator of the remaining regression parameters is cube root n consistent furthermore we obtain the asymptotic distribution of the estimators it turns out that a suitably normalized estimator of the regression parameters converges weakly to the distribution to which it would converge weakly if the true threshold value were known and likewise for the threshold estimator

kernel based representation for 2d 3d motion trajectory retrieval and classification this paper proposes a novel kernel space representation for motion trajectories contrasted to most trajectory representation methods in the literature our method is more generic in the sense that it can be applied to either 2d or 3d trajectories in the proposed method a trajectory is firstly projected by the kernel principal component analysis kpca which can be considered as an implicit mapping to a much higher dimensional feature space the high dimensionality can effectively improve the accuracy in recognizing motion trajectories then nonparametric discriminant analysis nda is used to extract the most discriminative features from the kpca feature space the synergistic effect of kpca and nda leads to better class separability and makes the proposed trajectory representation a more powerful discriminator the experimental validation of the proposed method is conducted on the australian sign language asl data set the results show that our method performs significantly better in both trajectory classification and retrieval than the state of the art techniques

frequency domain identification of wiener models this paper proposes a frequency domain algorithm for wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity the convergence of the algorithm is established in the presence of white noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

on identification of the controlled plants described by the hammerstein system a new polynomial identification method for the hammerstein system is proposed the method employs the results of nonparametric statistics and best approximation theory obtaining a polynomial form estimate of the nonlinearity in the system except continuity no conditions are imposed on the nonlinearity the uniform as well as global convergence of the method is established the rates of convergence in both cases are derived under mild conditions on the smoothness of the nonlinearity the method is especially suitable for identifying the controlled plants with the description of hammerstein systems

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

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

on the convergence of an iterative algorithm used for hammerstein system identification an analytical counterexample to the general convergence of an interative algorithm used for identification of hammerstein systems is given numerical illustration is also included

parametric identification of hammerstein systems with consistency results using stochastic inputs the extended least squares algorithm is applied to identify the hammerstein system where the nonlinear static function f is expressed as a linear combination of basic functions with unknown coefficients strong consistency of the estimates is established and their convergent rates are obtained as well

parameter bounds for discrete time hammerstein models with bounded output errors in this note we present a two stage procedure for deriving parameters bounds in hammerstein models when the output measurement errors are bounded first using steady state input output data parameters of the nonlinear part are tightly bounded then for a given input transient sequence we evaluate tight bounds on the unmeasurable inner signal which together with noisy output measurements are used for bounding the parameters of the linear dynamic block

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

recursive identification of hammerstein systems with discontinuous nonlinearities containing dead zones this note deals with the recursive parameter identification of hammerstein systems with discontinuous nonlinearities i e two segment piecewise linear with dead zones and preloads a special form of the hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables the proposed method is illustrated by examples

extended least squares and their applications to adaptive control and prediction in linear systems herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature the argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators making use of these properties of the adaptive predictors simple modifications of the astrom wittenmark self tuning regulator are proposed and shown to be asymptotically optimal

compensation of the rls algorithm for output nonlinearities it is shown how the recursive least squares rls algorithm can be modified to compensate for a priori known errors of linearity in the output measurement a novel signal model is used for this purpose only the nonlinear effects are modeled by an output error model and much of the output measurements are used directly in the regression vector the main benefit with this approach is that the advantages of the rls like quick initial convergence for infinite impulse response models can be retained for small linearity errors at the same time the output nonlinearity is allowed to be noninvertible this can be important to treat for example small deadzones and also to avoid the amplification of additive measurement disturbances such amplification can result from inversion of the output nonlinearity simulations illustrate the performance of the algorithm

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

a statistical method for assessing a threshold in epidemiological studies i describe a method for estimating and testing a threshold value in epidemiological studies a threshold effect indicates an association between a risk factor and a defined outcome above the threshold value but none below it an important field of application is occupational medicine where for a lot of chemical compounds and other agents which are non carcinogenic health hazards so called threshold limit values or tlvs are specified the method is presented within the framework of the logistic regression model which is widely used in the analysis of the relationship between some explanatory variables and a dependent dichotomous outcome in most available programs for this and also for other models the concept of a threshold is disregarded the method for assessing a threshold consists of an estimation procedure using the maximum likelihood technique and a test procedure based on the likelihood ratio statistic r following under the null hypothesis no threshold a quasi one sided chi 2 distribution with one degree of freedom this use of this distribution is supported by a simulation study the method is applied to data from an epidemiological study of the relationship between occupational dust exposure and chronic bronchitic reactions the results are confirmed by bootstrap resampling

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed