a class of small deviation theorems for functionals of random fields on a homogeneous tree by constructing a non negative martingale on a homogeneous tree a class of small deviation theorems for functionals of random fields the strong law of large numbers for the frequencies of occurrence of states and ordered couple of states for random fields and the asymptotic equipartition property aep for finite random fields are established as corollary the strong law of large numbers and the aep for markov chains indexed by a cayley tree is obtained some known results are generalized in this paper

regression based specification tests for the multinomial logit model abstract diagnostic tests for omitted variables or functional misspecification in the multinomial logit mnl model can be performed conveniently by testing the significance of auxiliary regressions of residuals on included and excluded variables in particular lagrange multiplier lm and hausman mcfadden hm tests of the independence from irrelevant alternatives iia property of the mnl model can be carried out by the regression method using suitably defined excluded variables using this method it is straightforward to test jointly against several sources of misspecification and to diagnose the structure of deviations from the mnl model

assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

characterizing the robustness and susceptibility of steady state dynamics in post buckled structures to stochastic perturbations abstract recent reports exemplify both the potential and the concerns encountered in implementing post buckled structures in diverse applications by numerical and experimental methods characterizations have provided useful insights on the dynamic sensitivities of such bi or multistable structures subjected to either harmonic or stochastic excitations yet the more realistic scenario of combined harmonic and stochastic loading has been not been closely examined so that such sensitivities might be fully illuminated to provide a more complete understanding on the robustness and susceptibility of multistable structures to dynamic state transitions this research establishes new analytical and experimental methods to quantify the likelihood of triggering transitions among dynamic regimes of an archetypal post buckled structure as a result of combined harmonic and stochastic loading it is discovered that persistent periodic snap through dynamics are rapidly disabled by additional noise excitation when the harmonic excitation contribution occurs at frequencies close to the linearized resonance the extra noise may also drastically compromise the integrity of small amplitude periodic responses that occur at frequencies around one half of the linearized resonance particular relative proportions of the noise standard deviation and harmonic excitation amplitude are uncovered that most readily compromise the robustness of a given steady state dynamic regime the analytical method also complements prior developments focused on stochastic resonance by uncovering the broader perspective of dynamic sensitivities of post buckled structures under arbitrary combinations of harmonic and random driving loads

non parametric testing of discrete panel data models abstract the stochastic structures of the homogeneous multinomial process the heterogeneous multinomial process the markov chain and the heterogeneous markov chain are analyzed within a discrete panel data framework a general theoretical and computationally tractible framework to test the stochastic structures is proposed our testing framework is non parametric in nature and can incorporate the presence of time varying exogenous variables and can be applied to the general polychotomous response cases asymptotically optimal tests can be easily implemented the lm tests for the stochastic structures are simply to test certain orthogonality conditions with residuals

inconsistent treatment estimates from mis specified logistic regression analyses of randomized trials when the difference between treatments in a clinical trial is estimated by a difference in means then it is well known that randomization ensures unbiassed estimation even if no account is taken of important baseline covariates however when the treatment effect is assessed by other summaries for example by an odds ratio if the outcome is binary then bias can arise if some covariates are omitted regardless of the use of randomization for treatment allocation or the size of the trial we present accurate closed form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression we compare this approximation with ones in the literature and derive more convenient forms for some of these existing results the expressions give insight into the form of the bias which simulations show is usable for distributions other than the normal the key result applies even when there are additional binary covariates in the model

smoothing spline anova for multivariate bernoulli observations with application to ophthalmology data we combine a smoothing spline analysis of variance ss anova model and a log linear model to build a partly flexible model for multivariate bernoulli data the joint distribution conditioning on the predictor variables is estimated the log odds ratio is used to measure the association between outcome variables a numerical scheme based on the block one step successive over relaxation sor newton ralphson algorithm is proposed to obtain an approximate solution for the variational problem we extend the generalized approximate cross validation gacv and the randomized gacv for choosing smoothing parameters to the case of multivariate bernoulli responses the randomized version is fast and stable to compute and is used to adaptively select smoothing parameters in each block onestep sor iteration approximate bayesian confidence intervals are obtained for the flexible estimates of the conditional logit functions simulation studies are conducted to check the performance of the proposed method using the com

stochastic averaging based on generalized harmonic functions for energy harvesting systems abstract a stochastic averaging method is proposed for nonlinear vibration energy harvesters subject to gaussian white noise excitation the generalized harmonic transformation scheme is applied to decouple the electromechanical equations and then obtained an equivalent nonlinear system which is uncoupled to an electric circuit the frequency function is given through the equivalent potential energy which is independent of the total energy the stochastic averaging method is developed by using the generalized harmonic functions the averaged ito equations are derived via the proposed procedure and the fokker planck kolmogorov fpk equations of the decoupled system are established the exact stationary solution of the averaged fpk equation is used to determine the probability densities of the amplitude and the power of the stationary response the procedure is applied to three different type duffing vibration energy harvesters under gaussian white excitations the effects of the system parameters on the mean square voltage and the output power are examined it is demonstrated that quadratic nonlinearity only and quadratic combined with properly cubic nonlinearities can increase the mean square voltage and the output power respectively the approximate analytical outcomes are qualitatively and quantitatively supported by the monte carlo simulations

measures of conditional linear dependence and feedback between time series abstract measures of linear dependence and feedback for two multiple time series conditional on a third are defined the measure of conditional linear dependence is the sum of linear feedback from the first to the second conditional on the third linear feedback from the second to the first conditional on the third and instantaneous linear feedback between the first and second series conditional on the third the measures are non negative and may be expressed in terms of measures of unconditional feedback between various combinations of the three series the measures of conditional linear feedback can be additively decomposed by frequency estimates of these measures are straightforward to compute and their distribution can be routinely approximated by bootstrap methods an empirical example involving real output money and interest rates is presented

a simple frailty model for family studies with covariates a simple easily analysed frailty model based on logistic regression and employing only binary frailties is developed and analysed methods for testing for frailty and estimates of frailty parameters and covariate effects are presented the effects of ignoring or mis specifying frailty are examined in detail and shown to downwardly bias the estimates of covariate effects in a variety of situations even when frailty is overestimated when the true frailty is large it can be difficult to estimate accurately because of the flatness of the likelihood however it is shown that this does not have a large influence on the estimates of the effects of the observed covariates methods for dealing with multiple frailties for example sibships and spouse pairs are also developed the results are illustrated on a large data set examining the risk factors associated with palmar keratoses

correspondence analysis with an extension towards nominal time series abstract correspondence analysis is a technique for studying the relationship between two nominal variables which uses mainly simultaneous graphical displays it has been generalized to more than two variables under the name of multiple correspondence analysis qualitative harmonic analysis is an other extension towards individual time series where one observes the evolution of a nominal variable through a finite period of time the present paper is based essentially on the concept of multidimensional scaling by means of barycentric representation

simulated maximum likelihood estimation of dynamic discrete choice statistical models some monte carlo results this article reports monte carlo results on the simulated maximum likelihood estimation of discrete dynamic panel models introduced by james heckman 1981a the simulated maximum likelihood method is numerically stable even for long panels regression models and polya and renewal models can be better estimated than markov models with a moderate number of simulation draws most of these complex models can be adequately estimated for panels with length up to 30 polya and renewal models can be accurately estimated for panels up to 50 periods estimates of markov models can be sensitive to misspecified initial states but polya renewal and habit persistence models may not

on the existence and uniqueness of maximum likelihood estimates in the rasch model necessary and sufficient conditions for the existence and uniqueness of a solution of the so called unconditional uml and the conditional cml maximum likelihood estimation equations in the dichotomous rasch model are given the basic critical condition is essentially the same for uml and cml estimation for complete data matricesa it is formulated both as a structural property ofa and in terms of the sufficient marginal sums in case of incomplete data the condition is equivalent to complete connectedness of a certain directed graph it is shown how to apply the results in practical uses of the rasch model

strong deviation theorems for functionals of the nonnegative continuous random variables abstract by using the approach of laplace transform we establish the strong deviation theorems represented by inequalities and described by asymptotic average log likelihood ratio for functionals of the nonnegative continuous random variables as corollaries we obtain several strong laws of large numbers for the random variable functionals the results of this paper extend and improve the corresponding results of some current literatures

models and methods for the analysis of correlation coefficients abstract the normal distribution plays a very prominant role in statistics and in multivariate analysis the multinormal model is even more dominant than in the classical univariate or bivariate situations in this paper we show that the assumption of continuous multinormal observations can be relaxed in various ways for continuous multivariate analysis most of the existing large sample theory can be applied without assuming multivariate normality we also develop several discrete multinormal models the first one is the classical pearson model which results from discreticizing multinormal variables the second one is inspired by correspondence analysis and the third one by loglinear analysis the models are presented in terms of correlation coefficients and applied to the spearman model of factor analyses using an example from political science

anomalous diffusion in nonlinear oscillators with multiplicative noise the time asymptotic behavior of undamped nonlinear oscillators with a random frequency is investigated analytically and numerically we find that averaged quantities of physical interest such as the oscillator s mechanical energy root mean square position and velocity grow algebraically with time the scaling exponents and associated generalized diffusion constants are calculated when the oscillator s potential energy grows as a power of its position u x approximately x 2n for x infinity correlated noise yields anomalous diffusion exponents equal to half the value found for white noise

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

a time series analysis of binary data abstract binary data d 1 d 2 dn are assumed to be generated by an underlying real valued strictly stationary process xk and a response function f for a given monotone nondecreasing function f from r to 0 1 dk takes on 1 with probability f xk and 0 with probability 1 f xk where xk xk it is shown that all strictly stationary binary processes are characterized by such a procedure several approximations to the n dimensional joint probabilities of dk are developed when xk is a gaussian first order autoregressive process model building procedures and methods by which to estimate parameters of a given model are discussed the predictor of d n 1 that minimizes probability of error among all randomized rules is determined and for certain cases a bound for this probability is found

transforming contingency tables abstract we present a general theorem on transforming contingency tables and several applications where the transformation technique has allowed us to take advantage of the iterative proportional fitting procedure and has resulted in simple and useful procedures a further advantage of this technique is that it is sometimes possible to recognize closed form estimates in the transformed problem while they would be overlooked in the original setting we shall view the estimation problem as one of minimizing the kullback leibler information distance between two probability mass functions and will roughly follow the notation of csiszar 1976 although we have adopted the information distance point of veiw the duality between maximum likelihood estimation and minimum information estimation see e g darroch and ratcliff 1972 implies that the results of this paper can just as well be interpreted from the maximum likelihood point of view

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

strong law of large numbers and shannon mcmillan theorem for markov chain fields on trees we study the strong law of large numbers and the shannon mcmillan theorem for markov chain fields on trees first we prove the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for markov chain fields on trees then we prove the shannon mcmillan theorem with almost everywhere a e convergence for markov chain fields on trees we prove the results on a bethe tree and then just state the analogous results on a rooted cayley tree in the proof a new technique for establishing the strong limit theorem in probability theory is applied

estimating logistic regression parameters for bivariate binary data summary consider bivariate binary data with possibly different covariates for each marginal binary observation suppose that the correlation between paired observations is a nuisance and the interest lies in estimating logistic regression parameters associated with the covariates we consider the estimator obtained by using the independence estimating equation with corrected variance this estimator can be very efficient and robust compared with maximum likelihood or the estimator of liang and zeger some comments are made concerning higher dimensional multivariate data

response of uni modal duffing type harvesters to random forced excitations the common linear energy harvesters have an inherent shortcoming in their operation concept because they operate efficiently only when the excitation frequency is very close to the fundamental frequency of the harvester to extend the harvester s bandwidth some recent solutions call for utilizing energy harvesters with stiffness type nonlinearities from a steady state perspective this hardening nonlinearity can extend the coupling between the excitation and the harvester to a wider range of frequencies in this effort we investigate the response of such harvesters to gaussian white and colored excitations for gaussian white excitations we solve the fokker plank kolmogorov equation for the exact joint probability density function of the response we show that the expected value of the output power is not even a function of the nonlinearity as such under white gaussian excitations nonlinearities in the stiffness do not provide any enhancement over the typical linear harvesters furthermore we demonstrate that nonlinearities in the damping or inertia should be sought to enhance the output power we also use the van kampen expansion to analyze the response to colored excitations of different bandwidths and center frequencies again we show that regardless of the bandwidth or the center frequency the expected value of the power is always less than that associated with a linear harvester

multivariate methods for quantitative and qualitative data abstract in this paper several multivariate analysis methods are analyzed by means of the errors in variables model two specifications viz the principal relations and the principal factors model for the set of unobserved latent variables are introduced and shown to be complementary for particular choices of the error covariance matrix the general model reduces to several well known multivariate techniques including ordinary least squares principal components orthogonal regression and canonical correlations the same apparatus is used to arrive at a set of multivariate techniques in case the data is qualitative instead of quantitative the relationship with optimal scaling techniques for qualitative data is shown an empirical example is given of a regression involving a dependent latent variable having two ordered categorical indicator variables

a class of logistic regression models for multivariate binary time series abstract a logistic model for multivariate binary time series is proposed first we establish the equivalence between a log linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others the logistic formulation is used to describe a markov chain for each series which implies a markov model for the vector of time series a pseudolikelihood estimation procedure is presented the methods are illustrated with data on psychosomatic and psychological diagnoses for families in a health maintenance plan

loglinear models and categorical data analysis with psychometric and econometric applications revision abstract the past decade has seen the publication of a large number of books and papers on the analysis of multi way contingency tables using loglinear and logic models the present article presents a summary of the statistical theory that underlies much of this work and provides some linkage to models and methods of special interest to psychometricians and econometricians the discussion includes a review of recent and current research on the computation of maximum likelihood estimates for loglinear and logit models especially for large multi way contingency tables

prediction functions for categorical panel data prediction of categorical responses in panel studies is considered prediction functions based on general conditional log linear models are investigated for statistical properties both from a population perspective and a sampling perspective problems such as existence and uniqueness of optimal prediction functions are addressed and basic properties of measures of prediction quality are examined estimation consistency and asymptotic normality are studied for the proposed parameter estimates and measures of prediction quality

conditional log linear models for analyzing categorical panel data abstract conditional log linear models are developed for panel data and used to predict sequences of categorical responses the class of models considered includes conventional markov models and independence models as well as distance models in which all previous responses and present and past values of covariates are used to predict the current response the approach taken in this article has some advantages over the marginal modeling approach that has become popular for longitudinal studies quality of prediction is measured by using a logarithmic penalty function given a model conditional probabilities of responses consistent with the model are selected to provide the smallest expected penalty this minimum expected penalty provides a measure of the predictive power of a model models are compared through their predictive power as measured by the proportional reduction in expected penalty ways of incorporating the number of parameters of the competing models are discussed this emphasis on predicti

two random effects models for multivariate binary data we consider two regression models for multivariate binary data in the case that the marginal success probabilities are unequal the first model is based on an additive random effect operating on the probability scale the second model assumes a discrete random effect operates on the logit scale consequently the interpretation of the regression parameters differs for the two models their use is illustrated by application to some dental data

analysis of the power flow in nonlinear oscillators driven by random excitation using the first wiener kernel abstract random excitation of mechanical systems occurs in a wide variety of structures and in some applications calculation of the power dissipated by such a system will be of interest in this paper using the wiener series a general methodology is developed for calculating the power dissipated by a general nonlinear multi degree of freedom oscillatory system excited by random gaussian base motion of any spectrum the wiener series method is most commonly applied to systems with white noise inputs but can be extended to encompass a general non white input from the extended series a simple expression for the power dissipated can be derived in terms of the first term or kernel of the series and the spectrum of the input calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel namely that the integral over its frequency domain representation is proportional to the oscillating mass is derived the resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration the results are validated both numerically and experimentally using a base excited cantilever beam with a nonlinear restoring force produced by magnets

bounds on the vibrational energy that can be harvested from random base motion abstract this paper is concerned with the development of upper bounds on the energy harvesting performance of a general multi degree of freedom nonlinear electromechanical system that is subjected to random base motion and secondary applied periodic forces the secondary forces are applied with the aim of enhancing the energy harvested from the base motion and they may constitute direct excitation or they may produce parametric terms in the equations of motion it is shown that when the base motion has white noise acceleration then the power input by the base is always s 0 m 2 where s0 is the single sided spectral density of the acceleration and m is the mass of the system this implies that although the secondary forces may enhance the energy harvested by causing a larger fraction of the power input from the base to be harvested rather than dissipated there is an upper limit on the power that can be harvested attention is then turned to narrow band excitation and it is found that in the absence of secondary forces a bound can be derived for a single degree of freedom system with linear damping and arbitrary nonlinear stiffness the upper bound on the power input by the base is m max s 2 where s is the single sided base acceleration spectrum the validity of this result for more general systems is found to be related to the properties of the first wiener kernel and this issue is explored analytically and by numerical simulation

the strong ergodic theorem for densities generalized shannon mcmillan breiman theorem let xi x2 be a stationary process with probability densities f x1 x2 xn with respect to lebesgue measure or with respect to a markov measure with a stationary transition measure it is shown that the sequence of relative entropy densities 1 n log f xi x2 x0 converges almost surely this long conjectured result extends the l convergence obtained by moy perez and kieffer and generalizes the shannon mcmillanbreiman theorem to nondiscrete processes the heart of the proof is a new martingale inequality which shows that logarithms of densities are l dominated

multivariate contingency tables and the analysis of exchangeability there are settings in the social and health sciences where it is natural to question whether a collection of discrete random variables is exchangeable in this paper the inter relationships between parameter symmetry parameter invariance and exchangeable discrete random variables are investigated within the log linear models framework we demonstrate how log linear models can be used to formulate and test hypotheses of various forms of exchangeability and to characterize departures from exchangeability conditions under which the observed cross classification collapses into a lower dimensional cross classification while preserving the essential probability structure of the higher dimensional cross classification and the model structure of this lower dimensional cross classification are presented the development is sufficiently general to allow for subsetting the variables into classes which is important for some applications for example in studying the spatial clustering of periodontal disease there is interest in studying differences among disease patterns between the upper and lower arches in terms of parameter symmetry parameter invariance and exchangeability cross sectional periodontal disease data from a study of pima indians residing in the gila river indian community are used to illustrate how log linear models may be used to examine for exchangeability and for specific departures from exchangeability

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

transduction of a bistable inductive generator driven by white and exponentially correlated gaussian noise abstract in this theoretical study the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated both white and ornstein uhlenbeck type excitations are considered in the white noise limit the stationary fokker plank kolmagorov equation is solved for the exact joint probability density function pdf of the response the pdf is then used to obtain analytical expressions for the response statistics it is shown that the expected value of the generator s output power is independent of the potential shape leading to the conclusion that under white noise excitations bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single well potential in the case of ornstein uhlenbeck exponentially correlated noise an approximate expression for the mean power of the generator which depends on the potential shape the generator s design parameters and the noise bandwidth and intensity is obtained it is shown that there exists an optimal potential shape which maximizes the output power this optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied

the asymptotic stability of a noisy non linear oscillator abstract the purpose of this work is to obtain an approximation for the top lyapunov exponent the exponential growth rate of the response of a single well kramers oscillator driven by either a multiplicative or an additive white noise process to this end we consider the equations of motion as dissipative and noisy perturbations of a two dimensional hamiltonian system a perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation we show analytically that the top lyapunov exponent is positive and for small values of noise intensity e and dissipation e the exponent grows in proportion with e1 3

correspondence analysis used complementary to loglinear analysis loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables in this paper we will show that there are cases in which these two techniques can be used complementary to each other more specifically we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices each following a specific loglinear model therefore in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models a generalization of correspondence analysis recently proposed by escofier will also be discussed with this decomposition which includes classical correspondence analysis as a special case it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis in this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models

a markov regression model for nutritive sucking data we explore the relationship between nutritive sucking behavior and physiological status of premature infants conventional statistical methods are no longer adequate in this context due to the highly complex structure of nutritive sucking data we describe sucking pattern by a binary time series and propose a markov regression model that relates the transition probabilities of the markov chain to time dependent covariates through a logistic linkage function the model is fit to data collected at the hospital of the university of pennsylvania the results are compared with those obtained from traditional data analysis

bayesian analyses of longitudinal binary data using markov regression models of unknown order we present non homogenous markov regression models of unknown order as a means to assess the duration of autoregressive dependence in longitudinal binary data we describe a subject s transition probability evolving over time using logistic regression models for his or her past outcomes and covariates when the initial values of the binary process are unknown they are treated as latent variables the unknown initial values model parameters and the order of transitions are then estimated using a bayesian variable selection approach via gibbs sampling as a comparison with our approach we also implement the deviance information criterion dic for the determination of the order of transitions an example addresses the progression of substance use in a community sample of n 242 american indian children who were interviewed annually four times an extension of the markov model to account for subject to subject heterogeneity is also discussed copyright 2001 john wiley sons ltd

a parametric model for cluster correlated categorical data summary a fully parametric copula model for symmetric dependent clustered categorical data is discussed the model accommodates any marginal regression models of interest and admits a broad range of within cluster association the form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes the model contains an association parameter that is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence two examples are given to illustrate the methods

stationary solution for the color driven duffing oscillator adiabatic methods may be used to find approximate reduced stationary distributions for the linearly damped duffing oscillator driven by correlated noise of finite bandwidth here we show that a stationary distribution may be obtained which explains the insensitivity of the system to variations in damping coefficient and noise color as observed in numerical simulations exact analytic results are obtained for parabolic potentials for comparison

specification error in multinomial logit models analysis of the omitted variable bias abstract in this article we analyze the omitted variable bias problem in the multinomial logistic probability model sufficient as well as necessary conditions under which the omitted variable will not create asymptotically biased coefficient estimates for the included variables are derived conditional on the response variable if the omitted explanatory and the included explanatory variable are independent the bias will not occur bias will occur if the omitted relevant variable is independent with the included explanatory variable the coefficient of the included variable plays an important role in the direction of the bias

generalized langevin equations anomalous diffusion and probability distributions we study the motion of a particle governed by a generalized langevin equation we show that when no fluctuation dissipation relation holds the long time behavior of the particle may be from stationary to superdiffusive along with subdiffusive and diffusive when the random force is gaussian we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions s1063 651x 96 10706 6

some comments on rosner s multiple logistic model for clustered data rosner 1984 biometrics 41 1025 1035 proposed a binary regression model for analyzing binary response data gathered in clusters or groups this model is useful for understanding the degree of intracluster correlation among responses adjusted for the potential confounding effects of other covariates however estimates of the effects of covariates on the binary outcome obtained using rosner s model can be misleading for example we show that the covariate effects given by rosner s model do not correspond to those measured by either of the two standard approaches for correlated binary data we present an example that compares the regression coefficients arising from fits of rosner s model to other logistic models for clustered observations using data from a study of breast disease

multivariate methods for binary longitudinal data with heterogeneous correlation over time clustered binary data occur frequently in biostatistical work one particular application is in binary longitudinal data where several visits are available for the same individual several approaches have been proposed for the analysis of clustered binary data in rosner a polychotomous logistic regression model was proposed which is a generalization of the beta binomial distribution and allows for person and visit specific covariates while controlling for clustering effects one assumption of this model is that all pairs of visits within an individual are equally correlated which may be inappropriate if several visits are available over a long follow up period in this paper this approach is extended to allow for heterogeneous correlation over time the total time period is divided into subintervals and a beta binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals to include covariates an extension of the polychotomous logistic regression model is proposed which allows one to estimate effects of person subinterval and visit specific covariates while controlling for clustering using the beta binomial mixture model this model is applied to the analysis of respiratory symptom data in children collected over a 14 year period in east boston ma in relation to maternal and child smoking where the unit is the child and symptom history is divided into early adolescent and late adolescent symptom experience

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

positive lyapunov exponents in the kramers oscillator the maximum lyapunov exponent is computed numerically for the double well oscillator in a heat bath positive exponents are found in a wide range of friction coefficients in the low damping regime

latent trait models abstract latent trait models deal with a set of binary responces from an individual in a given population the aim of the statistical analysis is to estimate the value of an assumed latent parameter characteristic of the individual and to describe the variation of the latent parameters among individuals in the paper various approaches to such statistical analyses are discussed and the methods of analysis are illustrated with a set of consumer complaint behaviour data

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

multivariate methods for clustered binary data with multiple subclasses with application to binary longitudinal data clustered binary data occur frequently in biostatistical work several approaches have been proposed for the analysis of clustered binary data in rosner 1984 biometrics 40 1025 1035 a polychotomous logistic regression model was proposed that is a generalization of the beta binomial distribution and allows for unit and subunit specific covariates while controlling for clustering effects one assumption of this model is that all pairs of subunits within a cluster are equally correlated this is appropriate for ophthalmologic work where clusters are generally of size 2 but may be inappropriate for larger cluster sizes a beta binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses to include covariates an extension of the polychotomous logistic regression model is proposed which allows one to estimate effects of unit class and subunit specific covariates while controlling for clustering using the beta binomial mixture model this model is applied to the analysis of respiratory symptom data in children collected over a 14 year period in east boston massachusetts in relation to maternal and child smoking where the unit is the child and symptom history is divided into early adolescent and late adolescent symptom experience

performance measures for single degree of freedom energy harvesters under stochastic excitation we develop performance criteria for the objective comparison of different classes of single degree of freedom oscillators under stochastic excitation for each family of oscillators these objective criteria take into account the maximum possible energy harvested for a given response level which is a quantity that is directly connected to the size of the harvesting configuration we prove that the derived criteria are invariant with respect to magnitude or temporal rescaling of the input spectrum and they depend only on the relative distribution of energy across different harmonics of the excitation we then compare three different classes of linear and nonlinear oscillators and using stochastic analysis methods we illustrate that in all cases of excitation spectra monochromatic broadband white noise the optimal performance of all designs cannot exceed the performance of the linear design subsequently we study the robustness of this optimal performance to small perturbations of the input spectrum and illustrate the advantages of nonlinear designs relative to linear ones

stationary energy probability density of oscillators driven by a random external force we derive rigorous analytical results for the stationary energy probability density function of linear and nonlinear oscillators driven by additive gaussian noise our study focuses on two cases i a harmonic oscillator subjected to gaussian colored noise with an arbitrary correlation function and ii nonlinear oscillators with a general potential driven by gaussian white noise we also derive analytical expressions for the stationary moments of the energy and investigate the partition of the mean energy between kinetic and potential energy to illustrate our general results we consider specifically the case of exponentially correlated noise for i and power law and bistable potentials for ii our theoretical results are substantiated by langevin simulations between the kinetic energy and the potential energy of the oscillator our studies focus on two cases first we consider a harmonically bound particle driven by general additive gaussian colored noise second we consider a particle in a general potential driven by gaussian white noise in both cases we develop a general theory and study specific illustrative examples the paper is organized as follows in sec ii we formulate the langevin equations for a particle with inertia in a general potential driven by an additive random force we also derive the general relation between the stationary energy pdf and the stationary pdf for the particle s position and velocity section iii is devoted to the motion of a particle in a harmonic potential driven by colored gaussian noise with an arbitrary correlation function the stationary energy pdf as well as the first and second moments of the energy is derived analytically we apply these results to the case of exponentially correlated gaussian noise and to gaussian white noise for these specific cases we also determine the partition of the energy between kinetic and potential energy we analyze the effect of the potential shape on the stationary energy pdf for oscillators driven by an additive gaussian white noise in sec iv w e apply our analytical results to two specific cases a general power law potential and a bistable potential the first type of oscillator without friction and with additive noise 36 and multiplicative noise 37 has recently been studied in the context of anomalous diffusion the second type the duffing oscillator has been investigated as an alternative to the linear oscillator for harvesting energy from external random sources 28 29 35 38 39

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

analyzing rectangular tables by joint and constrained multidimensional scaling abstract this paper selectively discusses multidimensional scaling methods addressing both theory and applications most of the discussion is focussed upon the analysis of rectangular tables the term joint mds is introduced for an analysis which gives a meaningful joint representation of the set of row and the set of column objects of such a table so that the dissimilarities either within sets or between sets are optimally approximated from this perspective it is possible to give an unified account of the relationships between classical multidimensional scaling principal components analysis and correspondence analysis by imposing constraints the general model can be structurally changed in a number of ways for example it can be made discrete that is in principle it subsumes subset models and quadratic assignment as special cases it can also be made more flexible in the sense that external information may be used in order to tune the analysis to specific hypotheses finally an elegant joint mds model called multidimensional unfolding is discussed as a technique unfolding unfortunately suffers from being extremely sensitive to ill conditioned data a new way of coping with this problem is indicated and an application is given in which the bootstrap technique succesfully establishes the stability of the results

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

an exact mcnemar test for paired binary markov chains a straightforward extension of the mcnemar test for paired binary data yields an exact test for the equality of the limiting marginal distributions for bivariate binary markov chains the exact distribution of the test statistics under the null hypothesis of equal marginals depends on the classical cell occupancy statistics for the bose einstein model exact p values are computed for the one sided test and the mean and variance of the test statistic are found the power of the markov mcnemar test is found to be close to the power of the classical mcnemar test for independent paired observations when the independence assumption holds the method is applied to the comparison of ribosomal dna sequences

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

consistent estimation in the rasch model based on nonparametric margins consider the class of two parameter marginal logistic rasch models for a test ofm true false items where the latent ability is assumed to be bounded using results of karlin and studen we show that this class of nonparametric marginal logistic nml models is equivalent to the class of marginal logistic models where the latent ability assumes at most m 2 2 values this equivalence has two implications first estimation for the nml model is accomplished by estimating the parameters of a discrete marginal logistic model second consistency for the maximum likelihood estimates of the nml model can be shown whenm is odd using the results of kiefer and wolfowitz an example is presented which demonstrates the estimation strategy and contrasts the nml model with a normal marginal logistic model