fundamental limitations in passive time delay estimation part i narrow band systems time delay estimation of a noise like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar sonar applications a new method is presented to analyze the mean square error performance of delay estimation schemes based on a modified improved version of the ziv zakai lower bound zzlb this technique is shown to yield the tightest results on the attainable system performance for a wide range of signal to noise ratio snr conditions for delay estimation using narrow band ambiguity prone signals the fundamental result of this study is illustrated in fig 3 the entire domain of snr is divided into several disjoint segments indicating several distinct modes of operation if the available snr does not exceed snr 1 signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation as a result the attainable mean square error bar epsilon 2 is bounded only by the a priori parameter domain if snr 1 2 the modified zzlb coincides with the barankin bound in this regime differential delay observations are subject to ambiguities if snr snr 3 the modified zzlb coincides with the cramer rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved the transition from the ambiguity dominated mode of operation to the ambiguity free mode of operation starts at snr 2 and ends at snr 3 this is the threshold phenomenon in time delay estimation the various deflection points snr i and the various segments of the bound fig 3 are given as functions of such important system parameters as time bandwidth product wt signal bandwidth to center frequency ratio w 0 and the number of half wavelengths of the signal center frequency contained in the spacing between receivers with this information the composite bound illustrated in fig 3 provides the most complete characterization of the attainable system performance under any prespecified snr conditions

marginal longitudinal nonparametric regression locality and efficiency of spline and kernel methods we consider nonparametric regression in a longitudinal marginal model of generalized estimating equation gee type with a time varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large in such models the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations two methods of estimating the nonparametric function can be considered kernel methods and spline methods recently surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent that is working independence in the gee jargon as seen through equivalent kernel results in univariate independent data problems splines and kernels have similar behavior smoothing splines are equivalent to kernel regression with a s

modelling multivariate binary data with alternating logistic regressions marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables and the association between pairs of responses when the former is the scientific focus a first order generalized estimating equation method liang zeger 1986 is easy to implement and gives efficient estimates of regression coefficients although estimates of the association among the binary outcomes can be inefficient when the association model is a focus simultaneous modelling of the responses and all pairwise products prentice 1988 using second order estimating equations gives more efficient estimates of association parameters as well however this procedure can become computationally infeasible as the cluster size gets large this paper proposes an alternative approach alternating logistic regressions for simultaneously regressing the response on explanatory variables as well as modelling the association among responses in terms of pairwise odds ratios this algorithm iterates between a logistic regression using first order generalized estimating equations to estimate regression coefficients and a logistic regression of each response on others from the same cluster using an appropriate offset to update the odds ratio parameters for clusters of size n alternating logistic regression involves evaluation and inversion of matrices of order n2 rather than n4 as required for second order generalized estimating equations the alternating logistic regression estimates are shown to be reasonably efficient relative to solutions of second order equations in a few problems the new method is illustrated with an analysis of neuropsychological tests on patients with epileptic seizures

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

modelling of covariance structures in generalised estimating equations for longitudinal data summary when used for modelling longitudinal data generalised estimating equations specify a working structure for the within subject covariance matrices aiming to produce efficient parameter estimators however misspecification of the working covariance structure may lead to a large loss of efficiency of the estimators of the mean parameters in this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations the resulting estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed real data analysis and simulation studies show that the proposed approach yields efficient estimators for both the mean and covariance parameters

joint mean covariance models with applications to longitudinal data unconstrained parameterisation summary we provide unconstrained parameterisation for and model a covariance using covariates the cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix the entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors an extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity gabriel s antedependence models dempster s covariance selection models and the class of graphical models the likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data a graphical method similar to that based on the correlogram in time series is developed and used to identify parametric models for nonstationary covariances

robust estimation in generalized partial linear models for clustered data in this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models gplms for longitudinal data or clustered data in general we approximate the nonparametric function in the gplm by a regression spline and use bounded scores and leverage based weights in the estimating equation to achieve robustness against outliers we show that the regression spline approach avoids some of the intricacies associated with the profile kernel method and that robust estimation and inference can be carried out operationally as if a generalized linear model were used

unified lasso estimation by least squares approximation we propose a method of least squares approximation lsa for unified yet simple lasso estimation our general theoretical framework includes ordinary least squares generalized linear models quantile regression and many others as special cases specifically lsa can transfer many different types of lasso objective functions into their asymptotically equivalent least squares problems thereafter the standard asymptotic theory can be established and the lars algorithm can be applied in particular if the adaptive lasso penalty and a bayes information criterion type tuning parameter selector are used the resulting lsa estimator can be as efficient as the oracle extensive numerical studies confirm our theory

threshold region performance of maximum likelihood direction of arrival estimators this paper presents a performance analysis of the maximum likelihood ml estimator for finding the directions of arrival doas with a sensor array the asymptotic properties of this estimator are well known in this paper the performance under conditions of low signal to noise ratio snr and a small number of array snapshots is investigated it is well known that the ml estimator exhibits a threshold effect i e a rapid deterioration of estimation accuracy below a certain snr or number of snapshots this effect is caused by outliers and is not captured by standard techniques such as the crame spl acute r rao bound and asymptotic analysis in this paper approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ml estimator with high accuracy both the deterministic ml and stochastic ml estimators are treated for the single source and multisource estimation problems these approximations alleviate the need for time consuming computer simulations when evaluating the threshold region performance for the special case of a single stochastic source signal and a single snapshot it is shown that the ml estimator is not statistically efficient as snr spl rarr spl infin due to the effect of outliers

cholesky decompositions and estimation of a covariance matrix orthogonality of variance correlation parameters summary chen dunson 2003 have proposed a modified cholesky decomposition of the form e dll d for a covariance matrix where d is a diagonal matrix with entries proportional to the square roots of the diagonal entries of e and l is a unit lower triangular matrix solely determining its correlation matrix this total separation of variance and correlation is definitely a major advantage over the more traditional modified cholesky decomposition of the form ld2l pourahmadi 1999 we show that though the variance and correlation parameters of the former decomposition are separate they are not asymptotically orthogonal and that the estimation of the new parameters could be more demanding computationally we also provide statistical interpretation for the entries of l and d as certain moving average parameters and innovation variances and indicate how the existing likelihood procedures can be employed to estimate the new parameters

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

a moving average cholesky factor model in covariance modelling for longitudinal data we propose new regression models for parameterizing covariance structures in longitudinal data analysis using a novel cholesky factor the entries in this decomposition have a moving average and log innovation interpretation and are modelled as linear functions of covariates we propose efficient maximum likelihood estimates for joint mean covariance analysis based on this decomposition and derive the asymptotic distributions of the coefficient estimates furthermore we study a local search algorithm computationally more efficient than traditional all subset selection based on bic for model selection and show its model selection consistency thus a conjecture of pan mackenzie 2003 is verified we demonstrate the finite sample performance of the method via analysis of data on cd4 trajectories and through simulations

penalized generalized estimating equations for high dimensional longitudinal data analysis we consider the penalized generalized estimating equations gees for analyzing longitudinal data with high dimensional covariates which often arise in microarray experiments and large scale health studies existing high dimensional regression procedures often assume independent data and rely on the likelihood function construction of a feasible joint likelihood function for high dimensional longitudinal data is challenging particularly for correlated discrete outcome data the penalized gee procedure only requires specifying the first two marginal moments and a working correlation structure we establish the asymptotic theory in a high dimensional framework where the number of covariates p n increases as the number of clusters n increases and p n can reach the same order as n one important feature of the new procedure is that the consistency of model selection holds even if the working correlation structure is misspecified we evaluate the performance of the proposed method using monte carlo simulations and demonstrate its application using a yeast cell cycle gene expression data set

small sample adjustments in using the sandwich variance estimator in generalized estimating equations the generalized estimating equation gee approach is widely used in regression analyses with correlated response data under mild conditions the resulting regression coefficient estimator is consistent and asymptotically normal with its variance being consistently estimated by the so called sandwich estimator statistical inference is thus accomplished by using the asymptotic wald chi squared test however it has been noted in the literature that for small samples the sandwich estimator may not perform well and may lead to much inflated type i errors for the wald chi squared test here we propose using an approximate t or f test that takes account of the variability of the sandwich estimator the level of type i error of the proposed t or f test is guaranteed to be no larger than that of the wald chi squared test the satisfactory performance of the proposed new tests is confirmed in a simulation study our proposal also has some advantages when compared with other new approaches based on direct modifications of the sandwich estimator including the one that corrects the downward bias of the sandwich estimator in addition to hypothesis testing our result has a clear implication on constructing wald type confidence intervals or regions

on the adaptive elastic net with a diverging number of parameters we consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size when the dimension is high an ideal method should have the oracle property fan and li 2001 fan and peng 2004 which ensures the optimal large sample performance furthermore the high dimensionality often induces the collinearity problem which should be properly handled by the ideal method many existing variable selection methods fail to achieve both goals simultaneously in this paper we propose the adaptive elastic net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage under weak regularity conditions we establish the oracle property of the adaptive elastic net we show by simulations that the adaptive elastic net deals with the collinearity problem better than the other oracle like methods thus enjoying much improved finite sample performance

dispersing billiards with cusps slow decay of correlations dispersing billiards introduced by sinai are uniformly hyperbolic and have strong statistical properties exponential decay of correlations and various limit theorems however if the billiard table has cusps corner points with zero interior angles then its hyperbolicity is nonuniform and statistical properties deteriorate until now only heuristic and experimental results existed predicting the decay of correlations as mathcal o 1 n we present a first rigorous analysis of correlations for dispersing billiards with cusps

correlation decay and recurrence asymptotics for some robust nonuniformly hyperbolic maps we study a robust class of multidimensional non uniformly hyperbolic transformations considered by oliveira and viana ergod theory dyn syst 28 501 533 2008 for an open class of holder continuous potentials with small variation we show that the unique equilibrium state has exponential decay of correlations and that the distribution of hitting times is asymptotically exponential furthermore using that the equilibrium states satisfy a weak gibbs property we also prove log normal fluctuations of the return times around their average

model diagnostic tests for selecting informative correlation structure in correlated data in the generalized method of moments approach to longitudinal data analysis unbiased estimating functions can be constructed to incorporate both the marginal mean and the correlation structure of the data increasing the number of parameters in the correlation structure corresponds to increasing the number of estimating functions thus building a correlation model is equivalent to selecting estimating functions this paper proposes a chi squared test to choose informative unbiased estimating functions we show that this methodology is useful for identifying which source of correlation it is important to incorporate when there are multiple possible sources of correlation this method can also be applied to determine the optimal working correlation for the generalized estimating equation approach

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

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

on modelling mean covariance structures in longitudinal studies we exploit a reparameterisation of the marginal covariance matrix arising in longitudinal studies pourahmadi 1999 2000 to model jointly the mean and covariance structures in terms of three polynomial functions of time by reanalysing kenward s 1987 cattle data we compare model selection procedures based on regressogram estimation with these based on a global search of the model space using a bic based model selection criterion to identify the optimum degree triple of the three polynomials we show that the use of a saturated mean model is not optimal and explain why regressogram based model estimation may be misleading we also suggest a new computational method for finding the global optimum based on a criterion involving three pairwise saturated profile likelihoods

ergodic properties of invariant measures for piecewise monotonic transformations during the last decade a lot of research has been done on onedimensional dynamics different kinds of invariant measures for certain classes of piecewise monotonic transformations have been considered in most of these cases the perron frobenius operator plays an important role in this paper we try to unify these different examples which are discussed in detail below first we give a discription of the results proved in this paper

exact invariant measures how the strength of measure settles the intensity of chaos the aim of this paper is to show how to extract dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures on the one hand we provide an approach to deal with the inverse problem of finding nonlinear interval maps from a given invariant measure then we show how to identify ergodic properties by means of transitions along the phase space via exact measures on the other hand we discuss quantitatively how infinite measures imply maps having subexponential lyapunov instability weakly chaotic as opposed to finite measure ergodic maps which are fully chaotic in addition we provide general solutions of maps for which infinite invariant measures are exactly known throughout the interval a demand from this field finally we give a simple proof that infinite measure implies universal mittag leffler statistics of observables rather than narrow distributions typically observed in finite measure ergodic maps

analysis of longitudinal data with semiparametric estimation of covariance function improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data both involve estimation of the covariance function yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed a kernel estimator for estimating the nonparametric variance function is developed two methods for estimating parameters in the correlation structure a quasi likelihood approach and a minimum generalized variance method are proposed a semiparametric varying coefficient partially linear model for longitudinal data is introduced and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed sampling properties of the proposed estimation procedures are studied and asy

a note on automatic variable selection using smooth threshold estimating equations this paper develops smooth threshold estimating equations that can automatically eliminate irrelevant parameters by setting them as zero the resulting estimator enjoys the oracle property in the sense of fan li 2001 even in estimators for which the covariance assumption of wang leng 2007 is violated such as the buckley james estimator furthermore the estimator can be obtained without solving a convex optimization problem a bic type criterion for tuning parameter selection is also proposed it is shown that the criterion achieves consistent model selection a numerical study confirms the performance of the method

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

using second order generalized estimating equations to model heterogeneous intraclass correlation in cluster randomized trials in cluster randomized trials it is commonly assumed that the magnitude of the correlation among subjects within a cluster is constant across clusters however the correlation may in fact be heterogeneous and depend on cluster characteristics accurate modeling of the correlation has the potential to improve inference we use second order generalized estimating equations to model heterogeneous correlation in cluster randomized trials using simulation studies we show that accurate modeling of heterogeneous correlation can improve inference when the correlation is high or varies by cluster size we apply the methods to a cluster randomized trial of an intervention to promote breast cancer screening

some mathematical problems in the theory of quantum chaos abstract we discuss the general problem of distribution of spacings between levels in quantum problems for the quantum kicked rotator model we formulate the results on the poisson distribution for spacings some general remarks concerning the reasons for the appearance of this distribution are given

efficient semiparametric marginal estimation for longitudinal clustered data we consider marginal generalized semiparametric partially linear models for clustered data lin and carroll derived the semiparametric efficient score function for this problem in the multivariate gaussian case but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound here we propose such an estimator and generalize the work to marginal generalized partially linear models we investigate asymptotic relative efficiencies of the estimators that ignore the within cluster correlation structure either in nonparametric curve estimation or throughout we evaluate the finite sample performance of these estimators through simulations and illustrate it using a longitudinal cd4 cell count dataset both theoretical and numerical results indicate that properly taking into account the within subject correlation among the responses can substantially improve efficiency

time delay estimation via cross correlation in the presence of large estimation errors the estimate of the difference in time of arrival of a common random signal received at two sensors each of which also receives uncorrelated noise is examined for both small and large estimation errors it is shown that as the post integration signal to noise ratio decreases the correlator exhibits a thresholding effect that is the probability of a large error an anomalous estimate increases rapidly approximate theoretical results for the probability of an anomaly are presented and are verified experimentally the variance of the time delay estimate is examined for both a gated mode in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay and an ungated mode in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate the observed variance for both modes is compared with the theoretical variance based on a small error analysis for the gated modes the signal to noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion it is shown however that the expected variance for the ungated mode can depart from the small error theory at a higher signal to noise ratio than for the gated modes thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis

maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix the positive definiteness constraint is the most awkward stumbling block in modelling the covariance matrix pourahmadi s 1999 unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models the new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors in this paper the maximum likelihood estimators of the parameters of a generalised linear model for the covariance matrix their consistency and their asymptotic normality are studied when the observations are normally distributed these results along with the likelihood ratio test and penalised likelihood criteria such as bic for model and variable selection are illustrated using a real dataset

generalized empirical likelihood methods for analyzing longitudinal data efficient estimation of parameters is a major objective in analyzing longitudinal data we propose two generalized empirical likelihood based methods that take into consideration within subject correlations a nonparametric version of the wilks theorem for the limiting distributions of the empirical likelihood ratios is derived it is shown that one of the proposed methods is locally efficient among a class of within subject variance covariance matrices a simulation study is conducted to investigate the finite sample properties of the proposed methods and compares them with the block empirical likelihood method by you et al 2006 and the normal approximation with a correctly estimated variance covariance the results suggest that the proposed methods are generally more efficient than existing methods that ignore the correlation structure and are better in coverage compared to the normal approximation with correctly specified within subject correlation an application illustrating our methods and supporting the simulation study results is presented

robust estimating functions and bias correction for longitudinal data analysis robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions the widely used method of the generalized estimating equations can be robustified by replacing the standardized residuals with the m residuals if the pearson residuals are assumed to be unbiased from zero parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric we propose a distribution free method for correcting this bias our extensive numerical studies show that the proposed method can reduce the bias substantially examples are given for illustration

variances are not always nuisance parameters summary in classical problems e g comparing two populations fitting a regression surface etc variability is a nuisance parameter the term nuisance parameter is meant here in both the technical and the practical sense however there are many instances where understanding the structure of variability is just as central as understanding the mean structure the purpose of this article is to review a few of these problems i focus in particular on two issues a the determination of the validity of an assay and b the issue of the power for detecting health effects from nutrient intakes when the latter are measured by food frequency questionnaires i will also briefly mention the problems of variance structure in generalized linear mixed models robust parameter design in quality technology and the signal in microarrays in these and other problems treating variance structure as a nuisance instead of a central part of the modeling effort not only leads to inefficient estimation of means but also to misleading conclusions

poisson models and mean squared error for correlator estimator of time delay a method for modeling large errors in correlation based time delay estimation is developed in terms of level crossing probabilities the level crossing interpretation for peak ambiguity leads directly to an exact expression for the probability of large error involving the hazard function associated with the level crossing process two models for the distribution of the error over the level crossing time yield approximations to the mean square error mse that involve the low order

covariance structure regularization via frobenius norm discrepancy abstract in many practical problems the underlying structure of an estimated covariance matrix is usually blurred due to random noise particularly when the dimension of the matrix is high hence it is necessary to filter the random noise or regularize the available covariance matrix in certain senses so that the covariance structure becomes clear in this paper we propose a new method for regularizing the covariance structure of a given covariance matrix by choosing an optimal structure from an available class of covariance structures the regularization is made in terms of minimizing the discrepancy defined by frobenius norm between the given covariance matrix and the class of covariance structures a range of potential candidate structures including the order 1 moving average structure compound symmetry structure order 1 autoregressive structure order 1 autoregressive moving average structure are considered simulation studies show that the proposed new approach is reliable in regularization of covariance structures the proposed approach is also applied to real data analysis in signal processing showing the usefulness of the proposed approach in practice

semiparametric mean covariance regression analysis for longitudinal data efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure existing approaches usually focus on modeling the mean with specification of certain covariance structures which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs in this article we propose a data driven approach based on semiparametric regression models for the mean and the covariance simultaneously motivated by the modified cholesky decomposition a regression spline based approach using generalized estimating equations is developed to estimate the parameters in the mean and the covariance the resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed in addition the nonparametric functions in these two structures are estimated at their optimal rate of convergence simulation studies and a real data analysis show

breakdown properties of location m estimators in this article we consider the asymptotic behavior of three kinds of sample breakdown points it is shown that for the location m estimator with bounded objective function both the addition sample breakdown point and the simplified replacement sample breakdown point strongly converge to the gross error asymptotic breakdown point whereas the replacement sample breakdown point strongly converges to a smaller value in addition it is proved that under some regularity conditions these sample breakdown points are asymptotically normal the addition sample breakdown point has a smaller asymptotic variance than the simplified replacement sample breakdown point for the commonly used redescending m estimators of location numerical results indicate that among the three kinds of sample breakdown points the replacement sample breakdown point has the largest asymptotic variance

nonparametric estimation of covariance structure in longitudinal data summary in longitudinal studies the effect of various treatments over time is usually of prime interest however observations on the same subject are usually correlated and any analysis should account for the underlying covariance structure a nonparametric estimate of the covariance structure is useful either as a guide to the formulation of a parametric model or as the basis for formal inference without imposing parametric assumptions the sample covariance matrix provides such an estimate when the data consist of a short sequence of measurements at a common set of time points on each of many subjects but is impractical when the data are severely unbalanced or when the sequences of measurements on individual subjects are long relative to the number of subjects the variogram of residuals from a saturated model for the mean response has previously been suggested as a nonparametric estimator for covariance structure assuming stationarity in this paper we consider kernel weighted local linear regression smoothing of sample variogram ordinates and of squared residuals to provide a nonparametric estimator for the covariance structure without assuming stationarity the value of the estimator as a diagnostic tool is demonstrated in two applications one to a set of data concerning the blood pressure of newborn babies in an intensive care unit and the other to data on the time evolution of cd4 cell numbers in hiv seroconverters

modelling the random effects covariance matrix in longitudinal data a common class of models for longitudinal data are random effects mixed models in these models the random effects covariance matrix is typically assumed constant across subject however in many situations this matrix may differ by measured covariates in this paper we propose an approach to model the random effects covariance matrix by using a special cholesky decomposition of the matrix in particular we will allow the parameters that result from this decomposition to depend on subject specific covariates and also explore ways to parsimoniously model these parameters an advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix in addition the parameters resulting from this decomposition have a sensible interpretation we propose fully bayesian modelling for which a simple gibbs sampler can be implemented to sample from the posterior distribution of the parameters we illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects

a joint modelling approach for longitudinal studies in longitudinal studies it is of fundamental importance to understand the dynamics in the mean function variance function and correlations of the repeated or clustered measurements for modelling the covariance structure cholesky type decomposition based approaches have been demonstrated to be effective however parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure we propose a novel joint mean variance correlation modelling approach for longitudinal studies by applying hyperspherical co ordinates we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization the modelling framework proposed is parsimonious interpretable and flexible for analysing longitudinal data extensive data examples and simulations support the effectiveness of the approach proposed

statistics of close visits to the indifferent fixed point of an interval map we study a dynamical system defined by a map of the interval 0 1 which has 0 as an indifferent fixed point but is otherwise expanding we prove that the sequence of successive entrance times in a small neighborhood 0 a converges in law when suitably normalized to a homogeneous poisson point process

continuity of type i intermittency from a measure theoretical point of view we study a simple dynamical system which displays a so called type i intermittency bifurcation we determine the bowen ruelle measure e and prove that the expectation e g of any continuous functiong and the kolmogoroff sinai entropyh e are continuous functions of the bifurcation parameter therefore the transition is continuous from a measure theoretical point of view those results could be generalized to any similar dynamical system

modelling covariance structure in bivariate marginal models for longitudinal data summary it can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case due to the correlations arising between multiple responses the positive definiteness constraint and the high dimensionality are further obstacles in covariance modelling in this paper we develop a data based method by which the parametersinthecovariancematricesarereplacedbyunconstrainedandinterpretableparameterswith reduced dimensions the maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures

efficient semiparametric mean association estimation for longitudinal binary responses semiparametric methods for longitudinal data with association within subjects have recently received considerable attention however existing methods for semiparametric longitudinal binary regression modeling i mainly concern mean structures with association parameters treated as nuisance ii generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates and iii usually run into computation and estimation problems when the time points are irregularly and possibly subject specific in this article we propose a semiparametric logistic regression model which simultaneously takes into account both the mean and response association structures via conditional log odds ratio for multivariate longitudinal binary outcomes our main interest lies in efficient estimation of both the marginal and association parameters the estimators of the parameters are obtained via the profile kernel approach we evaluate the proposed methodology through simulation studies and apply it to a real dataset both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily copyright 2012 john wiley sons ltd

robust variable selection in semiparametric mean covariance regression for longitudinal data analysis this paper considers robust semiparametric smooth threshold generalized estimating equations for the analysis of longitudinal data based on the modified cholesky decomposition and b spline approximations the proposed method can automatically eliminate inactive predictors by setting the corresponding parameters to be zero and simultaneously estimate the mean regression coefficients generalized autoregressive coefficients and innovation variances in order to overcome the outliers in either the response or and the covariate domain we use a bounded score function and leverage based weights to achieve better robustness moreover the proposed estimators have desired large sample properties including consistency and oracle property finally monte carlo simulation studies are conducted to investigate the robustness and efficiency of the proposed method under different contaminations

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

statistics of return times a general framework and new applications in this paper we provide general estimates for the errors between the distribution of the first and more generally the k th return time suitably rescaled and the poisson law for measurable dynamical systems in the case that the system exhibits strong mixing properties these bounds are explicitly expressed in terms of the speed of mixing using these approximations the poisson law is finally proved to hold for a large class of non hyperbolic systems on the interval

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

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

analysis of longitudinal data with semiparametric varying coefficient mean covariance models abstract the efficient estimation of regression coefficients in the longitudinal data analysis requires a correct specification of the covariance structure existing approaches usually focus on modeling the mean with specification of certain covariance structures which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs in this article we propose a novel data driven approach based on semiparametric varying coefficient models to model the mean and the covariance simultaneously motivated by the modified cholesky decomposition an iterative estimation method is proposed consisting of an orthogonality based technique for parameters an adaptive jump preserving estimation method for varying coefficients a modification of local linear smoothing technique for the autoregressive coefficient function and a kernel smoothing technique for the variance function theoretical properties of the resulting estimators including uniform consistency and asymptotic normality are explicitly studied under certain mild conditions simulation studies are carried out to evaluate the efficacy of the proposed methods and an analysis of a real data example is provided for illustration

outlier probability of generalized chirpogram based estimators for multicomponent polynomial phase signals outliers are often encountered by estimators that have a nonlinear nature in this paper the probability of outliers is derived concerning the generalized chirpogram gc based estimators for polynomial phase signals pps to derive the approximate theoretical expressions we develop an approach that is based on the extrema theory of complex gaussian envelope and the asymptotic poisson model the semi aliasing effect of pps is also considered in order to predict the outliers more accurately then expressions of the probability of outliers are presented for several typical cases of pps including single tone and chirp signals and their two component versions the gc with the hamming windowing is also incorporated numerical examples of computer simulations are also provided to show the accuracy of the theoretical expressions

a profile likelihood approach for longitudinal data analysis summary inappropriate choice of working correlation structure in generalized estimating equations gee could lead to inefficient parameter estimation while impractical normality assumption in likelihood approach would limit its applicability in longitudinal data analysis in this article we propose a profile likelihood method for estimating parameters in longitudinal data analysis via maximizing the estimated likelihood the proposed method yields consistent and efficient estimates without specifications of the working correlation structure nor the underlying error distribution both theoretical and simulation results confirm the satisfactory performance of the proposed method we illustrate our methodology with a diastolic blood pressure data set