testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

positive dependence in markov chains abstract a general notion of positive dependence among successive observations in a finite state stationary process is studied with particular attention to the case of a stationary ergodic markov chain this dependence condition can be expressed as a positivity condition on the joint probability matrices of pairs of observations some useful conditions equivalent to positive dependence are obtained for reversible chains but shown not to be equivalent for nonreversible chains

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

the mutual independence hypothesis for categorical data in complex sampling schemes summary this paper is concerned with the analysis of contingency tables which are constructed using categorical data from a complex sampling scheme for the mutual independence hypothesis we extend tavare s 1983 results on two dimensional contingency tables to higher dimensions in particular with respect to pearson s statistic for testing the independence of two variables we strengthen the robustness result proven by tavare thus making it applicable more widely this paper is concerned with the analysis of contingency tables which are constructed using categorical data from a complex sampling scheme i e from data containing some form of between observation dependence which renders the multinomial sampling scheme invalid throughout we are interested in how departures from multinomial sampling affect pearson s statistic x2 which is appropriate for multinomial data in the literature to date two distinct approaches to the problem of categorical data from complex sampling schemes have been discussed first holt scott ewings 1980 demonstrate that for survey data analyses based on x2 can be extremely misleading and propose the one moment adjustment of x2 related references are rao scott 1981 1984 and bedrick 1983 secondly altham 1976 cohen 1976 and brier 1980 model inherent clustering in the sample they show that to avoid invalid analyses some adjustment of x2 is then necessary more recently tavare altham 1983 and tavare 1983 have considered two dimensional contingency tables which are constructed from data generated by markov chains analytic results for the null asymptotic distribution of x2 are obtained and once more it is shown that some adjustment of x2 will usually be necessary however tavare 1983 also obtains a very interesting robustness result let y1 and y2 be independent variables where y1 is an independent trials process and y2 is an arbitrary irreducible first order markov chain then the null asymptotic distribution of x2 for testing the independence of y1 and y2 is x2 on the appropriate degrees of freedom in other words no adjustment of x2 is necessary of the literature cited above the present

using wavelet packet denoising and anfis networks based on cosfla optimization for electrical resistivity imaging inversion abstract electrical resistivity imaging eri inversion is a complicated non linear inversion problem which is high dimensional and non convex using traditional neural networks to solve the eri inversion problem has an over fitting phenomenon and easily falls into local minima moreover the artificial neural network ann model is a black box its relationships between the inputs and outputs are not easy to interpret in order to solve these problems a wavelet packet denoising wpd procedure and an improved adaptive neuro fuzzy inference system anfis based on cauchy oscillation shuffled frog leaping algorithm cosfla are proposed in this paper the wavelet packet denoising methodology is based on soft thresholding and shannon entropy using a db10 wavelet which is applied to remove the noise component from the measured apparent resistivity data meanwhile cosfla is introduced for updating the premise parameters of the anfis to improve the learning ability and prediction accuracy of the algorithm the development of the proposed method and the total inversion process are also presented the inversion of the synthetic and field examples are provided to demonstrate the feasibility and validity of the proposed method additionally the introduced method is transparent and its if then rules are easy to understand and interpret

goodness of fit tests for stationary distributions of markov chains based on rao s divergence abstract goodness of fit tests based on rao s divergence between observed and theoretical frequencies for stationary distributions of markov chains are considered the asymptotic distribution of these tests under uniform hypothesis is obtained a power comparison of the proposed tests is carried out in the case of binary markov data

exact goodness of fit tests for markov chains goodness of fit tests are useful in assessing whether a statistical model is consistent with available data however the usual asymptotics often fail either because of the paucity of the data or because a nonstandard test statistic is of interest in this article we describe exact goodness of fit tests for first and higher order markov chains with particular attention given to time reversible ones the tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple monte carlo sampling or by markov chain monte carlo they apply both to single and to multiple sequences and allow a free choice of test statistic three examples are given the first concerns multiple sequences of dry and wet january days for the years 1948 1983 at snoqualmie falls washington state and suggests that standard analysis may be misleading the second one is for a four state dna sequence and lends support to the original conclusion that a second order markov chain provides an adequate fit to the data the last one is six state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first order reversible markov chain at 6 picosecond time steps

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

smoothness of the density for solutions to gaussian rough differential equations we consider stochastic differential equations driven by a multi dimensional gaussian process under the assumption that the vector fields satisfy hormander s bracket condition we demonstrate that the solution admits a smooth density for any strictly positive time t provided the driving noise satisfies certain non degeneracy assumptions our analysis relies on an interplay of rough path theory malliavin calculus and the theory of gaussian processes our result applies to a broad range of examples including fractional brownian motion with hurst parameter greater than 1 4 the ornstein uhlenbeck process and the brownian bridge returning after time t

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

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

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

modified tests of independence in 2 x 2 tables with spatial data in this paper we suggest two modified chi squared tests of independence in 2 x 2 tables when the data are spatially autocorrelated for this purpose we first derive the asymptotic distribution of standard test statistics based on the sample cross product ratio under mild conditions on the nature of spatial dependence the performance of the tests is assessed by means of a monte carlo experiment in a lattice case from simulation results the need to adjust standard test statistics is apparent when spatial autocorrelation is present in both variables an illustrative application to ecological data is also given

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

on probability laws of solutions to differential systems driven by a fractional brownian motion this article investigates several properties related to densities of solutions xt t 0 1 xt t 0 1 to differential equations driven by a fractional brownian motion with hurst parameter h 1 4h 1 4 we first determine conditions for strict positivity of the density of xtxt then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition finally still in the elliptic case we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of newtonian capacities

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

a new method for the automatic interpretation of schlumberger and wenner sounding curves a fast iterative method for the automatic interpretation of schlumberger and wenner sounding curves is based on obtaining interpreted depths and resistivities from shifted electrode spacings and adjusted apparent resistivities respectively the method is fully automatic it does not require an initial guess of the number of layers their thicknesses or their resistivities and it does not require extrapolation of incomplete sounding curves the number of layers in the interpreted model equals the number of digitized points on the sounding curve the resulting multilayer model is always well behaved with no thin layers of unusually high or unusually low resistivities for noisy data interpretation is done in two sets of iterations two passes anomalous layers created because of noise in the first pass are eliminated in the second pass such layers are eliminated by considering the best fitting curve from the first pass to be a smoothed version of the observed curve and automatically reinterpreting i

serial dependence in contingency tables summary a simple and useful representation is given for the asymptotic behaviour of the pearson x2 test of independence in two way contingency tables this is used to analyse the statistic when the data are generated by markov chains a robustness result showing when the markov dependence has no effect on the usual limiting x2 distribution is also given

an approach for on line extraction of fuzzy rules using a self organising fuzzy neural network this paper presents a hybrid neural network called the self organising fuzzy neural network sofnn to extract fuzzy rules from the training data the first hidden layer of this network consists of ellipsoidal basis function ebf neurons every ebf neuron in the sofnn has both a centre vector and a width vector neurons are organised by the network itself the methods of the structure and parameter learning based on new adding and pruning techniques and a recursive learning algorithm are simple and effective with a high accuracy and a compact structure simulations show that the sofnn has the capability to encode fuzzy rules in the resulting network

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

serial dependence of observations leading to contingency tables and corrections to chi squared statistics summary the asymptotic behaviour of the pearson goodness of fit test and of the test of independence in 2 x 2 tables is examined when the data are generated by markov dependent sequences the results allow simple quantification of the effects of such serial dependence on some standard test statistics some key wrords hi squared tests contingency tables dependence goodness of fit markov chains reversibilitv 1 introi uction in this paper we discuss the asymptotic behaviour of some standard test statistics in the presence of markov dependence in a sequence of observations in particular we examine the standard pearson x2 goodness of fit test and the 2 x 2 contingency table test for independence

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

least squares deconvolution of apparent resistivity pseudosections a fast technique for the inversion of data from resistivity tomography surveys has been developed this technique is based on the smoothness constrained least squares method and it produces a 2 d subsurface model that is free of distortions in the apparent resistivity pseudosection caused by the electrode array geometry used a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically tests with a variety of models and data from field surveys show that this technique is insensitive to random noise provided a sufficiently large damping factor is used and that it can resolve structures that cause overlapping anomalies in the pseudosection on a 33 mhz 80486dx microcomputer it takes about 5 s to process a single data set

a version of hormander s theorem for the fractional brownian motion it is shown that the law of an sde driven by fractional brownian motion with hurst parameter greater than 1 2 has a smooth density with respect to lebesgue measure provided that the driving vector fields satisfy hormander s condition the main new ingredient of the proof is an extension of norris lemma to this situation

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

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

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

malliavin differentiability of solutions of rough differential equations abstract in this paper we study rough differential equations driven by gaussian rough paths from the viewpoint of malliavin calculus under mild assumptions on coefficient vector fields and underlying gaussian processes we prove that solutions at a fixed time are smooth in the sense of malliavin calculus examples of gaussian processes include fractional brownian motion with hurst parameter larger than 1 4

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