fractional kinetic equations and universal decoupling of a memory function in mesoscale region it is proved that kinetic equations containing non integer integrals and derivatives appear in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region in other words it means that after a proper statistical average the microscopic dynamics is converted into a collective motion in the mesoscopic regime a fractal medium containing weakly and strongly correlated relaxation units has been considered it is shown that in most cases the original of the memory function recovers the riemann liouville integral for a strongly correlated fractal medium a generalization of the riemann liouville integral is obtained for the fractal branched processes one can derive the stretched exponential law of relaxation that is widely used for description of relaxation phenomena in disordered media it is shown that the generalized stretched exponential function describes the averaged collective motion in the fractal branched complex systems it is confirmed that the generalized stretched exponential law can be definitely applicable for description of a set of spontaneous evoked postsynaptic signals in the living matter the application of these fractional kinetic equations for the description of the dielectric relaxation phenomena is also discussed these kinetic equations and their generalizations can be applicable for the description of different relaxation or diffusion processes in the intermediate mesoscale region

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

log periodic oscillations for biased diffusion on random lattice abstract random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log periodic oscillations in the effective exponent versus time a scaling argument accounts for the numerical results in the limit of large biases and small dilution and shows the importance of the interplay of these two ingredients in the generation of the log periodicity these results show that log periodicity is the dominant effect compared to previous predictions of and reports on anomalous diffusion

complex fractal dimensions describe the hierarchical structure of diffusion limited aggregate clusters we analyze large diffusion limited aggregates and uncover a ital discrete scaling invariance in their inner structure which can be quantified by the introduction of a set of ital complex fractal dimensions we provide a theoretical framework and prediction of their values based on renormalization group theory and a previous wavelet analysis copyright ital 1996 the american physical society

stock market and motion of a variable mass spring we establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock market dynamics within an economic model based on simple temporal demand and supply functions e canessa j phys a 33 2000 3637 the total system energy et is shown to be proportional to a decreasing time dependent spring constant kt this model allows to derive log periodicity cos log t tc on commodity prices and oscillations surplus and shortages in the level of stocks we also made an attempt to connect these results to the tsallis statistics parameter q based on a possible force entropy correlation e canessa physica a 341 2004 165 and find that the tsallis second entropic term i 1wpiq q 1 relates to the square of the demand or supply function

fluctuation noise spectroscopy and a universal fitting function of amplitudes of random sequences abstract a universal fitting function has been recognized that makes use of the eigen coordinates method physica a 285 2000 547 to accurately describe the distribution of ordered amplitudes within random sequences taken from a diversity of sources it is shown that sequences with a discrete structure can be described in terms of specific distributions of relative frequencies with respect to the number of quantum levels an investigation of these quantum distributions leads to an increase in both sensitivity and selectivity when attempting the statistical detection of various predominant factors of the hidden signals the physical meaning of this new function is discussed and a proposal is made as the basis of a new fluctuation noise spectroscopy in which the recognized function can be used for the detection of small signals and or the forerunners of strong signals that are hidden within the random sequences analyzed

methods of density estimation on the grassmann manifold abstract the grassmann manifold gk m k consists of k dimensional hyperplanes in r m and is equivalent to the manifold pk m k of all m m orthogonal projection matrices idempotent of rank k this paper develops a method of semiparametric density estimation on the manifold pk m k designed to nonparametrically correct a parametric model by its linear function to obtain better density estimators than the ordinary kernel density estimator we suggest two procedures to estimate the correction factors comparing with the ordinary kernel density estimator for small smoothing parameter matrix and or for large sample size n the suggested semiparametric density estimator is seen to have approximately the same variance to the order of approximation used but a smaller bias a one to one transformation of pk m k into r k m k is of use in the asymptotic investigation the general discussion is applied and examined for special kernel function discrepancy measures for matrices on pk m k and starting parametric model

log periodic oscillations for diffusion on self similar finitely ramified structures under certain circumstances the time behavior of a random walk is modulated by logarithmic periodic oscillations using heuristic arguments we give a simple explanation of the origin of this modulation for diffusion on a substrate with two properties self similarity and finite ramification order on these media the time dependence of the mean square displacement shows log periodic modulations around a leading power law which can be understood on the basis of a hierarchical set of diffusion constants both the random walk exponent and the period of oscillations are analytically obtained for a pair of examples one is fractal and the other is nonfractal and confirmed by monte carlo simulations the last example shows that the anomalous diffusion can arise from substrates without holes of all sizes

random walk on percolation under an external field random walk on percolation under an external field has been investigated by using statistical analysis and monte carlo simulation the mean square displacement r2 as a function of time t was obtained there exist some steps in the log r2 logt plot the defect in the percolation plays the part of the trap for the walker each step corresponds to a type of trap the height of the steps indicates the mean square displacement before the walker enters the trap and the width of the step expresses the trapping time spent in the trap the calculated height and width by the probability theory are in agreement with simulation results quite well

a semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error summary a common objective in longitudinal studies is to characterise the relationship between a failure time process and time independent and time dependent covariates timedependent covariates are generally available as longitudinal data collected periodically during the course of the study we assume that these data follow a linear mixed effects model with normal measurement error and that the hazard of failure depends both on the underlying random effects describing the covariate process and other time independent covariates through a proportional hazards relationship a routine assumption is that the random effects are normally distributed however this need not hold in practice within this framework we develop a simple method for estimating the proportional hazards model parameters that requires no assumption on the distribution of the random effects large sample properties are discussed and finite sample performance is assessed and compared to competing methods via simulation

a hierarchical model of financial crashes abstract we follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics the term critical refers to regimes of cooperative behavior such as magnetism at the curie temperature and liquid gas transitions and is characterized by the singular mathematical behavior of relevant observables to illustrate the concept of criticality we present a simple hierarchical model of traders exhibiting crowd behavior and show that it has a well defined critical point whose mathematical signature is a power law dependence of the price modulated by log periodic structures as recently found in market data by several independent groups

a serially correlated gamma frailty model for longitudinal count data a poisson gamma model is introduced to account for between subjects heterogeneity and within subjects serial correlation occurring in longitudinal count data the model extends the usual time constant shared frailty approach to allow time varying serially correlated gamma frailty whilst retaining standard marginal assumptions a composite likelihood approach to estimation and testing for serial correlation is proposed the work is motivated by a clinical trial on patient controlled analgesia where the number of analgesic doses taken by hospital patients in successive time intervals following abdominal surgery is recorded

conductivity exponent and backbone dimension in 2 d percolation abstract we present high statistics simulations for 2 d percolation clusters in the bus bar geometry at the critical point for site and for bond percolation we measured their backbone sizes and electrical conductivities for all sets of measurements we find large corrections to scaling most of which do not seem to be described by single powers using single power terms for the corrections to scaling of the backbone masses we would obtain fractal dimensions which are different for site and bond percolation while the correct result is d b 1 6432 0 0008 for both for the conductivity the corrections to scaling are strongly non monotonic for bond percolation the exponent t t is measured as 0 9826 0 0008 in disagreement with the alexander orbach and other conjectures

density estimation on the spaces of symmetric and rectangular matrices abstract this paper develops the theory of density estimation on the space s m of all m m symmetric matrices and on the space r m p of all m p rectangular matrices we consider the two methods kernel density estimation and density estimation by orthogonal series and illustrate them with examples for the normal kernel density functions and for the hermite orthonormal bases with symmetric and rectangular matrix arguments on s m and r m p respectively the problem of estimating unknown joint density functions of multiple random matrices is also discussed

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

generalized noncentral hermite and laguerre polynomials in multiple matrices abstract we are concerned with the generalized noncentral hermite and laguerre polynomials in multiple matrices we define the generalized hermite polynomials h mn k r o y q a r in q m n rectangular matrix arguments y1 yq y q and r m m constant matrices a1 ar a r q r associated with the joint distribution of q independent m n rectangular matrix variate standard normal distributions and present various properties of theirs the discussion of the generalized hermite polynomials h m k r o x q a r in q m m symmetric matrix arguments x1 xq x q associated with the joint distribution of q independent m m symmetric matrix variate normal distributions introduced by chikuse is further facilitated the generalized noncentral hermite polynomials are defined as h mn k r o y n q a r and h m k r o x m q a r for q m n rectangular and m m symmetric matrices n q and m q respectively extending results of chikuse and davis to the noncentral case we define and discuss the generalized noncentral laguerre polynomials l u q k r o x q a r q in q m m noncentrality matrices 1 q q associated with the joint distribution of q independent noncentral wishart distributions many unsolved problems can now be resolved by introducing these noncentral polynomials in multiple matrices specifically both the differential and integral versions of the generalized multivariate rodrigues formulae are obtained for all of these polynomials they are of great use in multivariate distribution theory a simple example of applications is presented

regression analysis under non standard situations a pairwise pseudolikelihood approach regression analysis is one of the most used statistical methods for data analysis there are however many situations in which one cannot base inference solely on f y x the conditional probability density function for the response variable y given x the covariates examples include missing data where the missingness is non ignorable sampling surveys in which subjects are selected on the basis of the y values and meta analysis where published studies are subject to selection bias the conventional approaches require the correct specification of the missingness mechanism sampling probability and probability for being published respectively in this paper we propose an alternative estimating procedure for based on an idea originated by kalbfleisch the novelty of this method is that no assumption on the missingness probability mechanisms etc mentioned above is required to be specified asymptotic efficiency calculations and simulation studies were conducted to compare the method proposed with the two existing methods the conditional likelihood and the weighted estimating function approaches

a linear mixed effects model with heterogeneity in the random effects population abstract this article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed effects model it shows that if the distribution of random effects is a finite mixture of normal distributions then the random effects may be badly estimated if normality is assumed and the current methods for inspecting the appropriateness of the model assumptions are not sound further it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then compare the fitted model with the gaussian model all of this is illustrated on two practical examples

the speed of biased random walk on percolation clusters we consider biased random walk on supercritical percolation clusters in 2 we show that the random walk is transient and that there are two speed regimes if the bias is large enough the random walk has speed zero while if the bias is small enough the speed of the random walk is positive

data based optimal smoothing of orthogonal series density estimates let f be a density possessing some smoothness properties and let x 1 cdots x n be independent observations from f some desirable properties of orthogonal series density estimates f n m lambda of f of the form f n m lambda t sum n nu 1 frac hat f nu 1 lambda nu 2m phi nu t where phi nu is an orthonormal sequence and hat f nu 1 n sum n j 1 phi nu x j is an estimate of f nu int phi nu t f t dt are discussed the parameter lambda plays the role of a bandwidth or smoothing parameter and m controls a shape factor the major novel result of this note is a simple method for estimating lambda and m from the data in an objective manner to minimize integrated mean square error the results extend to multivariate estimates

oscillations in the tsallis income distribution abstract oscillations in the complementary cumulative distribution function ccdf of individual income data have been found in the data of various countries studied by different authors at different time periods but the dynamical origins of this behavior are currently unknown although these datasets can be fitted by different functions at different income ranges the tsallis distribution has recently been found capable of fitting the whole distribution by means of only two parameters this procedure showed clearly such oscillatory feature in the entire income range feature but made it particularly visible at the tail of the distribution although log periodic functions fitted to the data are capable of describing this behavior a different approach to naturally disclose such oscillatory characteristics is to allow the tsallis q parameter to become complex in this paper we use this idea in order to describe the behavior of the ccdf of the brazilian personal income recently studied empirically by soares et al 2016 typical elements of periodic motion such as amplitude and angular frequency coupled to this income analysis were obtained by means of this approach a highly non linear function for the ccdf was obtained through this methodology and a numerical test showed it capable of recovering the main oscillatory feature of the original ccdf of the personal income data of brazil

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

random effects logistic regression analysis with auxiliary covariates summary we study a semiparametric estimation method for the random effects logistic regression when there is auxiliary covariate information about the main exposure variable we extend the semiparametric estimator of pepe and fleming 1991 journal of the american statistical association86 108 113 to the random effects model using the best linear unbiased prediction approach of henderson 1975 biometrics31 423 448 the method can be used to handle the missing covariate or mismeasured covariate data problems in a variety of real applications simulation study results show that the proposed method outperforms the existing methods we analyzed a data set from the collaborative perinatal project using the proposed method and found that the use of ddt increases the risk of preterm births among us children

log periodic critical amplitudes a perturbative approach log periodic amplitudes appear in the critical behavior of a large class of systems in particular when a discrete scale invariance is present here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial in this case the log periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

a hybrid pairwise likelihood method a modification to the pairwise likelihood method is proposed which aims to improve the estimation of the marginal distribution parameters this is achieved by replacing the pairwise likelihood score equations for estimating such parameters by the optimal linear combinations of the marginal score functions a further advantage of the proposed estimator of marginal parameters over pairwise likelihood is that it is robust to misspecification of the bivariate distributions as long as the univariate marginal distributions are correctly specified while alternating logistic regression can be seen as a special case of the proposed method it is shown that an existing generalization of alternating logistic regression applicable to ordinal data is not the same as and is inferior to the proposed method because it replaces certain conditional densities by pseudodensities that assume working independence the fitting of the multivariate negative binomial distribution is another scenario involving intractable likelihood that calls for the use of pairwise likelihood methods and the superiority of the modified method is demonstrated in a simulation study two examples based on the analyses of salamander mating and patient controlled analgesia data demonstrate the usefulness of the proposed method the possibility of combining optimally the pairwise rather than marginal scores is also considered and its difficulty and potential are discussed

stable limit laws for randomly biased walks on supercritical trees we consider a random walk on a supercritical galton watson tree with leaves where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree the biases are chosen independently on distinct edges each one according to a given law that satisfies a logarithmic nonlattice condition we determine the condition under which the walk is sub ballistic and in the sub ballistic regime we find a formula for the exponent 0 1 such that the distance x n moved by the walk in time n is of the order of n we prove a stable limiting law for walker distance at late time proving that the rescaled walk n x n converges in distribution to an explicitly identified function of the stable law of index this paper is a counterpart to ben arous et al ann probab 40 2012 280 338 in which it is proved that in the model where the biases on edges are taken to be a given constant there is a logarithmic periodicity effect that prevents the existence of a stable limit law for scaled walker displacement it is randomization of edge biases that is responsible for the emergence of the stable limit in the present article while also introducing further correlations into the model in comparison with the constant bias case the derivation requires the development of a detailed understanding of trap geometry and the interplay between traps and backbone the paper may be considered as a sequel to ben arous and hammond comm pure appl math 65 2012 1481 1527 since it makes use of a result on the regular tail of the total conductance of a randomly biased subcritical galton watson tree

approximate models for bacteria leaching through porous media to study leaching of bacteria through complex soils the researcher has to employ numerical methods as the known theoretical methods available are too restricted direct simulation of diffusion faces the problem of absence of statistical stability as the diffusion times vary dramatically between different realisations and soil samples we propose an approximation to the original leaching problem which is fast to simulate and is shown to give reliable approximation to the exit times in the whole range of parameter values including the problematic values that exhibit extreme behaviour in addition we have shown that a completely different type of pore structure such as produced by tunnels through the soil does not greatly affect diffusive properties when we are not close to the percolation threshold

the quantified histograms detection of the hidden unsteadiness abstract for a given level of digitization a number of relative frequencies presented by a histogram constructed for a short sample defined as a segment of a random series related in a certain way to both the length of the sampling l and the number of decompositions k may form a set of some levels possessing a discrete spectrum this spectrum can be defined as a quantified histogram qh the structure of parameters of a certain qh can be analyzed via both the number of quantum levels nql and the proper collection of relative frequencies on every level these parameters form kind of specific fingerprints which characterizes statistical properties of the segment of random series treated in this way qhs allow us to introduce the concept of a standard noise sn which can be used as a noise ruler to compare random series of distinct nature this standard noise turns out to be very useful in the detection of both a hidden unsteadiness and superweak signals existing in random series in the capacity of an example of the application of this new method a comparison of statistically sensible distinctions between noises accompanying either earthquakes or technogenic explosions is given distinctions thus obtained called earthquake forerunner can be used for earthquakes forecasting

randomly biased walks on subcritical trees as a model of trapping by biased motion in random structure we study the time taken for a biased random walk to return to the root of a subcritical galton watson tree we do so for trees in which these biases are randomly chosen independently for distinct edges according to a law that satisfies a logarithmic non lattice condition the mean return time of the walk is in essence given by the total conductance of the tree we determine the asymptotic decay of this total conductance finding it to have a pure power law decay in the case of the conductance associated to a single vertex at maximal depth in the tree this asymptotic decay may be analysed by the classical defective renewal theorem due to the non lattice edge bias assumption however the derivation of the decay for total conductance requires computing an additional constant multiple outside the power law that allows for the contribution of all vertices close to the base of the tree this computation entails a detailed study of a convenient decomposition of the tree under conditioning on the tree having high total conductance as such our principal conclusion may be viewed as a development of renewal theory in the context of random environments for randomly biased random walk on a supercritical galton watson tree with positive extinction probability our main results may be regarded as a description of the slowdown mechanism caused by the presence of subcritical trees adjacent to the backbone that may act as traps that detain the walker indeed this conclusion is exploited in 18 to obtain a stable limiting law for walker displacement in such a tree

minimum hellinger distance estimation for k component poisson mixture with random effects the k component poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations however the residual maximum likelihood estimation reml of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination in the literature the minimum hellinger distance mhd estimation has been investigated to obtain robust estimation for finite poisson mixtures this article aims to develop a robust mhd estimation approach for k component poisson mixtures with normally distributed random effects by applying the gaussian quadrature technique to approximate the integrals involved in the marginal distribution the marginal probability function of the k component poisson mixture with random effects can be approximated by the summation of a set of finite poisson mixtures simulation study shows that the mhd estimates perform satisfactorily for data without outlying observation s and outperform the reml estimates when data are contaminated application to a data set of recurrent urinary tract infections uti with random institution effects demonstrates the practical use of the robust mhd estimation method

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

on the anisotropic walk on the supercritical percolation cluster we investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on d d 2 in particular we show that for small anisotropy the walk behaves in a ballistic fashion whereas for strong anisotropy the walk is sub diffusive for arbitrary anisotropy we also prove the directional transience of the walk and construct a renewal structure

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

bootstrapping clustered data summary various bootstraps have been proposed for bootstrapping clustered data from one way arrays the simulation results in the literature suggest that some of these methods work quite well in practice the theoretical results are limited and more mixed in their conclusions for example mccullagh reached negative conclusions about the use of non parametric bootstraps for one way arrays the purpose of this paper is to extend our understanding of the issues by discussing the effect of different ways of modelling clustered data the criteria for successful bootstraps used in the literature and extending the theory from functions of the sample mean to include functions of the between and within sums of squares and non parametric bootstraps to include model based bootstraps we determine that the consistency of variance estimates for a bootstrap method depends on the choice of model with the residual bootstrap giving consistency under the transformation model whereas the cluster bootstrap gives consistent estimates under both the transformation and the random effect model in addition we note that the criteria based on the distribution of the bootstrap observations are not really useful in assessing consistency

semiparametric estimation in generalized linear mixed models with auxiliary covariates a pairwise likelihood approach auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects this article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data we propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation based inference procedure by treating both the error structure and random effects as nuisance parameters this method is robust against misspecification of either error structure or random effects distribution and allows for dependence between random effects and covariates we show that the resulting estimators are consistent and asymptotically normal extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method we illustrate the method with two real data examples

inverse cascade in a percolation model hierarchical description of time dependent scaling the dynamics of a two dimensional site percolation model on a square lattice is studied using the hierarchical approach introduced by gabrielov et al phys rev e 60 5293 1999 the key elements of the approach are the tree representation of clusters and their coalescence and the horton strahler scheme for cluster ranking accordingly the evolution of the percolation model is considered as a hierarchical inverse cascade of cluster aggregation a three exponent time dependent scaling for the cluster rank distribution is derived using the tokunaga branching constraint and classical results on percolation in terms of cluster masses deviations from the pure scaling are described an empirical constraint on the dynamics of a rank population is reported based on numerical simulations

properties of hermite and laguerre polynomials in matrix argument and their applications abstract this paper is concerned with the hermite polynomials in symmetric and rectangular matrix argument and the laguerre polynomials in symmetric matrix argument which are associated with the symmetric and rectangular matrix variate normal distributions and the wishart distribution respectively we derive the multivariate rodrigues formula a differential equation for each of the two kinds of hermite polynomials with respect to the associating p d f and the mutivariate differential operator i e the zonal polynomial in the matrix of differential operators which plays the role of the ordinary differential the multivariate rodrigues formulae are useful in asymptotic multivariate distribution theory for matrix variates we consider the general forms of the series edgeworth expansions for distributions of both symmetric and rectangular random matrices and then give an asymptotic edgeworth expansion for the distribution of a scale mixture matrix as a simple example as for the laguerre polynomials alternative forms of differential equations are derived we also present series expansions and recurrence relationships for the hermite and laguerre polynomials and some limit properties of the laguerre polynomials

evidence of intermittent cascades from discrete hierarchical dissipation in turbulence abstract we present the results of a search of log periodic corrections to scaling in the moments of the square of velocity increments taken as proxies of the energy dissipation rate in experiments at high reynolds number 2500 of three dimensional fully developed turbulence a simple dynamical representation of the richardson kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log periodic corrections to scaling associated with a discrete hierarchy to remedy this drawback we introduce a novel canonical averaging that we test extensively on synthetic examples constructed to mimic the interplay between a weak log periodic component and rather strong multiplicative and phase noises tests are also presented on 1 f5 3 random phase noise on the multifractal random walk model and on lattice and non lattice multifractal models our extensive tests confirm the remarkable observation of statistically significant log periodic corrections to scaling with a preferred scaling ratio for length scales compatible with the value 2 a strong confirmation of this result is provided by the identification of up to five harmonics of the fundamental log periodic undulations associated with up to five levels of the underlying hierarchical dynamical structure a natural interpretation of our results is that the richardson kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales

generalized hermite and laguerre polynomials in multiple symmetric matrix arguments and their applications abstract we investigate properties of the generalized hermite h m r x q b r and laguerre l u q r x q b r polynomials in q m m symmetric matrix arguments x 1 x q x q and r m m constant matrices b 1 b r b r and with q parameters u 1 u q u q q r and consider their applications in multivariate distribution theory the results extend those for the case of one symmetric matrix argument obtained by chikuse we derive the generalized multivariate rodrigues formula a differential equation for the polynomial h m r with respect to the associated joint multiple symmetric matrix variate normal p d f and the generalized multivariate differential operator i e the invariant polynomial in the multiple matrices of differential operators which plays the role of the ordinary differential the generalized multivariate rodrigues formula and the associated polynomials h m r are utilized to present the general form of the series edgeworth expansion for a distribution of multiple symmetric random matrices and then give a simple example alternative forms of differential equations are derived for the polynomial l u q r series expansions and recurrence relationships or some related results are obtained for the polynomials h m r and l u q r

stochastic theory of log periodic patterns we introduce an analytical model based on birth death clustering processes to help in understanding the empirical log periodic corrections to power law scaling and the finite time singularity as reported in several domains including rupture earthquakes world population and financial systems in our stochastic theory log periodicities are a consequence of transient clusters induced by an entropy like term that may reflect the amount of co operative information carried by the state of a large system of different species the clustering completion rates for the system are assumed to be given by a simple linear death process the singularity at t0 is derived in terms of birth death clustering coefficients

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations