a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset

two step estimation of functional linear models with applications to longitudinal data functional linear models are useful in longitudinal data analysis they include many classical and recently proposed statistical models for longitudinal data and other functional data recently smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance to overcome these drawbacks in this paper a simple and powerful two step alternative is proposed in particular the implementation of the proposed approach via local polynomial smoothing is discussed methods for estimating standard deviations of estimated coefficient functions are also proposed some asymptotic results for the local polynomial estimators are established two longitudinal data sets one of which involves time dependent covariates are used to demonstrate the approach proposed simulation studies show that our two step approach improves the kernel method proposed by hoover and co workers in several aspects such as accuracy computational time and visual appeal of the estimators

effect of noise on the dynamics of a complex map at the period tripling accumulation point as shown recently o b isaeva et al phys rev e 64 055201 2001 the phenomena intrinsic to dynamics of complex analytic maps under appropriate conditions may occur in physical systems we study scaling regularities associated with the effect of additive noise upon the period tripling bifurcation cascade generalizing the renormalization group approach of crutchfield et al phys rev lett 46 933 1981 and shraiman et al phys rev lett 46 935 1981 originally developed for the period doubling transition to chaos in the presence of noise the universal constant determining the rescaling rule for the intensity of the noise in period tripling is found to be gamma 12 206 640 9 em leader numerical evidence of the expected scaling is demonstrated

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

on the formulation of wald tests of nonlinear restrictions this paper utilizes asymptotic expansions of the edgeworth type to investigate alternative forms of the wald test of nonlinear restrictions some formulae for the asymptotic expansion of the distribution of the wald statistic are provided for a general case that should include most econometric applications when specialized to the simple cases that have been studied recently in the literature these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors it is further shown how the corrections delivered by edgeworth expansions may be used to find transformations of the restrictions which accelerate convergence to the asymptotic distribution

a variety of period doubling universality classes in multi parameter analysis of transition to chaos abstract in multi parameter analysis of the onset of chaos non feigenbaum period doubling behavior may occur at some special paths in the parameter space there are two possibilities i the dynamics at the onset of chaos remains essentially one dimensional but the one dimensional map is distorted in such a way that leaves feigenbaum s universality class ii a new mode comes to the threshold of instability and increases the effective dimension of the dynamics we submit a list of one dimensional and two dimensional maps which represent distinct classes of the period doubling universality discuss the properties of the associated types of critical behavior at the border of chaos and demonstrate pictures of the universal parameter space arrangement near the critical points

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

properties of synchronization in the systems of non identical coupled van der pol and van der pol duffing oscillators broadband synchronization the particular properties of dynamics are discussed for dissipatively coupled van der pol oscillators non identical in values of parameters controlling the hopf bifurcation possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system features of the bifurcation picture are discussed for different values of the control parameters and for the case of additional duffing type nonlinearity analysis of the slow flow equations is presented

on the differential geometry of the wald test with nonlinear restrictions in this paper we exploit the tools of differential geometry to provide a clear explanation for the finite sample lack of invariance of the wald statistic to algebraically equivalent reformulations of the null hypothesis

multiparameter critical situations universality and scaling in two dimensional period doubling maps we review critical situations linked with period doubling transition to chaos which require using at least two dimensional maps as models representing the universality classes each of them corresponds to a saddle solution of the two dimensional generalization of feigenbaum cvitanovic equation and is characterized by a set of distinct universal constants analogous to feigenbaum s and one type of criticality designated h was discovered by several authors in 80 th in the context of period doubling in conservative dynamics but occurs as well in dissipative dynamics as a phenomenon of codimension 2 second is bicritical behavior which takes place in systems allowing decomposition onto two dissipative period doubling subsystems each of which is brought by parameter tuning onto a threshold of chaos types of criticality designated as fq and c occur in non invertible two dimensional maps we present and discuss a number of realistic systems manifesting those types of critical behavior and point out some relevant conditions of their potential observation in physical systems in particular we indicate a possibility for realization of the h type criticality without vanishing dissipation but with its compensation in a self oscillatory system next we present a number of examples coupled henon like maps coupled driven oscillators coupled chaotic self oscillators which manifest bicritical behavior for fq type we indicate possibility to arrange it in non symmetric systems of coupled period doubling subsystems e g in henon like maps and in chua s circuits for c type we present examples of its appearance in a driven rossler oscillator at the period doubling accumulation on the edge of syncronization tongue and in a model map with the neimark sacker bifurcation

empirical likelihood based inference in generalized random coefficient autoregressive model with conditional moment restrictions abstract this paper concentrates on the parameter estimating strategy for the generalized random coefficient autoregressive grca model in the presence of the auxiliary information we propose a weighted least squares estimate for the model parameters and empirical likelihood el based weights are obtained through using these auxiliary information the asymptotic distribution of our proposed estimator is normal distribution and the asymptotic variance is reduced compared to the least square ls estimator therefore our method yields more efficient estimates we also carry out some simulation experiments to assess the performance of the suggested estimator and illustrate the usefulness of this method through the analysis of a real time series data sets

bifurcation structure of the c type period doubling transition abstract the period doubling transition to chaos along the edge of an arnold tongue is known to display unusual organization and scaling behavior kuznetsov et al 2005 7 it is also known that forced period doubling systems may be associated with the appearance of so called period doubled tori arneodo et al 1983 15 using the rossler system as an example we present a detailed analysis of the bifurcation structure associated with the forcing of a three dimensional period doubling system we explain how this structure is related to the recently discovered phenomenon of multi layered tori and discuss different bifurcation scenarios that transform a resonance torus into a period doubled ergodic torus similar bifurcation phenomena have recently been observed in a biologically relevant model of kidney blood flow regulation in response to fluctuations in arterial pressure

time varying additive models for longitudinal data the additive model is an effective dimension reduction approach that also provides flexibility in modeling the relation between a response variable and key covariates the literature is largely developed to scalar response and vector covariates in this article more complex data are of interest where both the response and the covariates are functions we propose a functional additive model together with a new backfitting algorithm to estimate the unknown regression functions whose components are time dependent additive functions of the covariates such functional data may not be completely observed since measurements may only be collected intermittently at discrete time points we develop a unified platform and an efficient approach that can cover both dense and sparse functional data and the needed theory for statistical inference we also establish the oracle properties of the proposed estimators of the component functions

uniform convergence rates for nonparametric regression and principal component analysis in functional longitudinal data we consider nonparametric estimation of the mean and covariance functions for functional longitudinal data strong uniform convergence rates are developed for estimators that are local linear smoothers our results are obtained in a unified framework in which the number of observations within each curve cluster can be of any rate relative to the sample size we show that the convergence rates for the procedures depend on both the number of sample curves and the number of observations on each curve for sparse functional data these rates are equivalent to the optimal rates in nonparametric regression for dense functional data root n rates of convergence can be achieved with proper choices of bandwidths we further derive almost sure rates of convergence for principal component analysis using the estimated covariance function the results are illustrated with simulation studies

some skew linear groups associated with lie algebras of characteristic zero let f be a field l a lie f algebra of finite dimension d and u the universal enveloping algebra of l then u is a noetherian domain 3 p 1661 let d denote its division ring of quotients suppose charf 0 lichtman in s 63 considers some group theoretic properties of gl n d and its subgroups in this note we pursue this investigation a little further for fuller statements of both lichtman s results and our own see section 2 below here we merely summarize a few of the more interesting points suppose g is a finitely generated subgroup of gl n d we show for all but a finite number of primes q that g has a normal subgroup of finite index that is residually a finite q group in particular of course g is residually finite further it follows that g is torsion free by finite and hence if g is periodic then g is finite thus s a periodic subgroup p of gl n d is locally finite we also show that such a p is isomorphic to a subgroup of gl n c and hence that s the group p has an abelian normal subgroup with index finite and bounded in terms of n only suppose g is a subgroup of gl n d containing no free subgroup of rank two then the structure of go is described by theorem a of 6 we give an alternative approach yielding some improvement of the bounds involved as a consequence we produce a sharper bound for the derived length of a soluble subgroup of gl n d assume again that g is a finitely generated subgroup of gl n d an easy result is that if every finite image of g is soluble then g is soluble in order to proceed much further with elucidating the structure of g along the lines suggested by the theory of linear groups we would need something like the nilpotence of g given that the finite images of g are nilpotent unfortunately the unipotent elements present problems this is frequently the case where imperfect ground fields are involved to see that is the situation here refer to section 1 below we have only been able to prove under considerably weaker hypotheses that g is nilpotent modulo 155 0021 8693 89 93 00

an empirical likelihood goodness of fit test for time series summary standard goodness of fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model when a parametric regression model is compared with a nonparametric model goodness of fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework we employ the empirical likelihood for an mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model the technique is based on a comparison with kernel smoothing estimators the empirical likelihood formulation of the test has two attractive features one is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood s ability to studentize internally the other is that the asymptotic distribution of the test statistic is free of unknown parameters avoiding plug in estimation we apply the test to a discretized diffusion model which has recently been considered in financial market analysis

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

nonlinear hypotheses inequality restrictions and non nested hypotheses exact simultaneous tests in linear regressions in the context of the classical linear model the problem of comparing two arbitrary hypotheses on the regression coefficients is considered problems involving nonlinear hypotheses inequality restrictions or non nested hypotheses are included as special cases exact bounds on the null distribution of likelihood ratio statistics are derived the bounds are based on the central fisher distribution and are very easy to use in an important special case a bounds test similar to the durbin watson test is proposed multiple testing problems are also studied the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows one to combine any number of tests this result extends to nonlinear hypotheses a well known result given by scheffe for linear hypotheses a method of building bounds induced tests is also suggested

universal properties of the transition from quasi periodicity to chaos in dissipative systems abstract an exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi periodic regime is held at a fixed irrational value our approach is a natural extension of k a m theory to strong coupling most of our analysis is for analytic circle maps we have found a strong coupling fixed point where invertibility is lost which describes the universal features of the transition to chaos we find numerically that any two such critical maps with the same winding number are c 1 conjugate it follows that the low frequency peaks in an experimental spectrum are universal and we determine how their envelope scales with frequency when the winding number has a periodic continued fraction our renormalization transform has a fixed point and spectra are self similar in addition for a set of non periodic winding numbers with full measure our renormalization transformation yields an ergodic trajectory in a sub space of all critical maps physically one finds singular and universal spectra that do not scale

on bartlett correction of empirical likelihood in the presence of nuisance parameters summary lazar mykland 1999 showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be bartlett correctable this paper shows that bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest we establish in the broad framework of estimating functions that the empirical likelihood is still bartlett correctable if the nuisance parameter is profiled out given the value of the parameter of interest

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

properties of principal component methods for functional and longitudinal data analysis the use of principal component methods to analyze functional data is appropriate in a wide range of different settings in studies of functional data analysis it has often been assumed that a sample of random functions is observed precisely in the continuum and without noise while this has been the traditional setting for functional data analysis in the context of longitudinal data analysis a random function typically represents a patient or subject who is observed at only a small number of randomly distributed points with nonnegligible measurement error nevertheless essentially the same methods can be used in both these cases as well as in the vast number of settings that lie between them how is performance affected by the sampling plan in this paper we answer that question we show that if there is a sample of n functions or subjects then estimation of eigenvalues is a semiparametric problem with root n consistent estimators even if only a few observations are made of each function and if each observation is encumbered by noise however estimation of eigenfunctions becomes a nonparametric problem when observations are sparse the optimal convergence rates in this case are those which pertain to more familiar function estimation settings we also describe the effects of sampling at regularly spaced points as opposed to random points in particular it is shown that there are often advantages in sampling randomly however even in the case of noisy data there is a threshold sampling rate depending on the number of functions treated above which the rate of sampling either randomly or regularly has negligible impact on estimator performance no matter whether eigenfunctions or eigenvectors are being estimated

unified empirical likelihood ratio tests for functional concurrent linear models and the phase transition from sparse to dense functional data summary we consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points we propose test procedures based on the empirical likelihood with bias corrected estimating equations to conduct both pointwise and simultaneous inferences the asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses where sparse and dense functional data are considered in a unified framework we find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data specifically the tests proposed can detect alternatives of n order when the number of repeated measurements per curve is of an order larger than n 0 with n being the number of curves the transition points 0 for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem simulation studies and real data analyses are conducted to demonstrate the methods proposed

coupled van der pol duffing oscillators phase dynamics and structure of synchronization tongues abstract synchronization in the system of coupled non identical non isochronous van der pol duffing oscillators with inertial and dissipative coupling is discussed generalized adler s equation is obtained and investigated in the presence of all relevant factors affecting the synchronization non isochronism of the oscillators their non identity coupling of the dissipative and inertial types characteristic symmetries are revealed for the adler s equation responsible for equivalence of some of the factors numerical study of the parameters space of the initial differential equations is carried out using the method of charts of dynamic regimes in the parameter planes results obtained by both these approaches are compared and discussed

functional linear regression analysis for longitudinal data we propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data where both the predictor and response are functions of a covariate such as time predictor and response processes have smooth random trajectories and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects in longitudinal studies the number of repeated measurements per subject is often small and may be modeled as a discrete random number and accordingly only a finite and asymptotically nonincreasing number of measurements are available for each subject or experimental unit we propose a functional regression approach for this situation using functional principal component analysis where we estimate the functional principal component scores through conditional expectations this allows the prediction of an unobserved response trajectory from sparse measurements of a predictor trajectory the resulting technique is flexible and allows for different patterns regarding the timing of the measurements obtained for predictor and response trajectories asymptotic properties for a sample of n subjects are investigated under mild conditions as n oo and we obtain consistent estimation for the regression function besides convergence results for the components of functional linear regression such as the regression parameter function we construct asymptotic pointwise confidence bands for the predicted trajectories a functional coefficient of determination as a measure of the variance explained by the functional regression model is introduced extending the standard r 2 to the functional case the proposed methods are illustrated with a simulation study longitudinal primary biliary liver cirrhosis data and an analysis of the longitudinal relationship between blood pressure and body mass index

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

empirical likelihood for a varying coefficient model with longitudinal data in this article local empirical likelihood based inference for a varying coefficient model with longitudinal data is investigated first we show that the naive empirical likelihood ratio is asymptotically standard chi squared when undersmoothing is employed the ratio is self scale invariant and the plug in estimate of the limiting variance is not needed second to enhance the performance of the ratio mean corrected and residual adjusted empirical likelihood ratios are recommended the merit of these two bias corrections is that without undersmoothing both also have standard chi squared limits third a maximum empirical likelihood estimator mele of the time varying coefficient is defined the asymptotic equivalence to the weighted least squares estimator wlse is provided and the asymptotic normality is shown by the empirical likelihood ratios and the normal approximation of the mele wlse the confidence regions of the time varying coefficients are constructed fourth when some components are o

unified inference for sparse and dense longitudinal models in longitudinal data analysis statistical inference for sparse data and dense data could be substantially different for kernel smoothing estimate of the mean function the convergence rates and limiting variance functions are different under the two scenarios the latter phenomenon poses challenges for statistical inference as a subjective choice between the sparse and dense cases may lead to wrong conclusions we develop self normalization based methods that can adapt to the sparse and dense cases in a unified framework simulations show that the proposed methods outperform some existing methods

the complete set of hamiltonian intermittency scaling behaviors renormalization group equations describing the phenomenon of intermittency in hamiltonian systems are presented all solutions satisfying certain physical constraints are obtained they are the complete set of simple singularities further considerations lead to precise predictions for scaling behavior at the onset of intermittency

anova for longitudinal data with missing values we carry out anova comparisons of multiple treatments for longitudinal studies with missing values the treatment effects are modeled semiparametrically via a partially linear regression which is flexible in quantifying the time effects of treatments the empirical likelihood is employed to formulate model robust nonparametric anova tests for treatment effects with respect to covariates the nonparametric time effect functions and interactions between covariates and time the proposed tests can be readily modified for a variety of data and model combinations that encompasses parametric semiparametric and nonparametric regression models cross sectional and longitudinal data and with or without missing values

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

effect of noise on the critical golden mean quasiperiodic dynamics in the circle map abstract scaling regularities are examined associated with effect of additive noise on a critical circle map at the golden mean rotation number we present an improved numerical estimate for the scaling constant of hamm and graham phys rev a46 1992 6323 responsible for the effect of noise 2 3061852653 decrease of the noise amplitude by this number ensures possibility to distinguish one more level of fractal like structure associated with increase of characteristic time scale by the golden mean factor 5 1 2 numeric results demonstrating evidence of the expected scaling are presented e g portraits of the noisy attractors devil s staircase plots lyapunov charts on the parameter plane in different scales

on empirical likelihood statistical functions abstract we consider the empirical likelihood method for estimation of distribution and quantile functions where side information is incorporated through moment conditions we systematically study the asymptotic properties of the estimators such as the uniform strong laws of large numbers and weak convergence over classes of functions two monte carlo examples are also given to illustrate the practical utility of the method

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

birth of a new class of period doubling scaling behavior as a result of bifurcation in the renormalization equation it is found that a fixed point of the renormalization group equation corresponding to a system of a unimodal map with extremum of power and a map summarizing values of a function of the dynamical variable of the first subsystem undergoes a bifurcation in the course of increase of it occurs at c 1 984396 and results in a birth of the period 2 stationary solution of the rg equation at 2 this period 2 solution corresponds to the universal period doubling behavior discovered earlier and denoted as the c type criticality kuznetsov and sataev in phys lett a 162 236 242 1992 by combination of analytical methods and numerical computations we obtain and analyze an asymptotic expansion of the period 2 solution in powers of c the developed approach resembles the e expansion in the phase transition theory in which a trivial stationary point of the rg transformation undergoes a bifurcation that gives rise to a new fixed point responsible for the critical behavior with nontrivial critical indices

asymptotic equivalence between the cox estimator and the general ml estimators of regression and survival parameters in the cox model the usual approach to estimating regression parameters in the cox regression model uses the partial likelihood if the covariates are not time dependent the model can be stated in terms of the survival function which allows one to derive a generalized likelihood containing both regression and survival curve parameters it is shown that in the absence of ties an estimator results which is asymptotically equivalent to the partial likelihood estimator a joint information matrix leads simply to standard errors for both regression and survival curve parameters which are asymptotically correct

constrained empirical likelihood confidence regions in nonignorable covariate missing data problems missing covariates in regression analysis are a pervasive problem in medical social and economic researches we study empirical likelihood confidence regions for unconstrained and constrained regression parameters in a nonignorable covariate missing data problem for an assumed conditional mean regression model we assume that some covariates are fully observed but other covariates are missing for some subjects by exploitation of a probability model of missingness and a working conditional score model from a semiparametric perspective we build a system of unbiased estimating equations where the number of equations exceeds the number of unknown parameters based on the proposed estimating equations we introduce unconstrained and constrained empirical likelihood ratio statistics to construct empirical likelihood confidence regions for the underlying regression parameters without and with constraints we establish the asymptotic distributions of the proposed empirical likelihood ratio statistics simulation results show that the proposed empirical likelihood methods have a better finite sample performance than other competitors in terms of coverage probability and interval length finally we apply the proposed empirical likelihood methods to the analysis of a data set from the us national health and nutrition examination survey

matrix rings and linear groups over a field of fractions of enveloping algebras and group rings i 1 1 let h be a lie algebra over a field k u h be its universal envelope it is well known that u h is a domain see 1 section v 31 and the theorem of cohn see 2 states that u h can be imbedded in a field when h is locally finite u h has even a field of fractions see 1 theorem v 3 61 the class of lie algebras whose universal envelope has a field of fractions is however much wider than the class of locally finite lie algebras it follows from proposition 4 1 of the article that it contains for instance all the locally soluble by locally finite algebras this gives a negative answer of the question in 2 page 528 let h satisfy any one of the following three conditions

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

principal modes of variation for processes with continuous sample curves analysis of a process with continuous sample curves can be carried out in a manner similar to principal components analysis of vector processes by appropriate definition of a best linear model in the continuous case we show that principal modes of variation consist of eigenfunctions of the process covariance function c s t procedures for estimation of these eigenfunctions from a finite sample of observed curves are given and results are compared with principal components analysis of the same data

statistical inferences for functional data with modem technology development functional data are being observed frequently in many scientific fields a popular method for analyzing such functional data is smoothing first then estimation that is statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another however little is known about this substitution effect on functional data analysis in this paper this problem is investigated when the local polynomial kernel lpk smoothing technique is used for individual function reconstructions we find that under some mild conditions the substitution effect can be ignored asymptotically based on this we construct lpk reconstruction based estimators for the mean covariance and noise variance functions of a functional data set and derive their asymptotics we also propose a gcv rule for selecting good bandwidths for the lpk reconstructions when the mean function also depends on some time independent covariates we consider a functional linear model where the mean function is linearly related to the covariates but the covariate effects are functions of time the lpk reconstruction based estimators for the covariate effects and the covariance function are also constructed and their asymptotics are derived moreover we propose a l 2 norm based global test statistic for a general hypothesis testing problem about the covariate effects and derive its asymptotic random expression the effect of the bandwidths selected by the proposed gcv rule on the accuracy of the lpk reconstructions and the mean function estimator is investigated via a simulation study the proposed methodologies are illustrated via an application to a real functional data set collected in climatology

two parameter analysis of the scaling behavior at the onset of chaos tricritical and pseudo tricritical points abstract we discuss the so called tricritical points at the border of the period doubling transition to chaos and examine to what extent the associated universality applies to 2d dissipative maps as a concrete example the ikeda map is studied together with its 1d analog for the approximate 1d map the tricritical points appear as the terminal points of feigenbaum s critical curves in the parameter plane for the 2d map the same type of critical behavior does not occur in a rigorous sense it may be observed as a kind of intermediate asymptotics however when one considers a finite number of period doublings we refer to the associated points in the parameter plane as pseudo tricritical for the ikeda map we present estimates of the number of period doublings after which the departure from the tricritical universality becomes essential

trajectory scaling function for bifurcations in area preserving maps on the plane abstract the trajectory scaling function for area preserving maps on the plane is found using a calculation of the unstable manifold for the renormalization group operator r t t2 1 with 0 0 internal self similarities of high order cycles and of power spectra are deduced

common functional principal components functional principal component analysis fpca based on the karhunen loeve decomposition has been successfully applied in many applications mainly for one sample problems in this paper we con sider common functional principal components for two sample prob lems our research is motivated not only by the theoretical challenge of this data situation but also by the actual question of dynamics of implied volatility iv functions for different maturities the log returns of ivs are samples of smooth random functions and the methods proposed here study the similarities of their stochastic be havior first we present a new method for estimation of functional principal components from discrete noisy data next we present the two sample inference for fpca and develop the two sample theory we propose bootstrap tests for testing the equality of eigenvalues eigenfunctions and mean functions of two functional samples illus trate the test properties by simulation study and apply the method to the iv analysis

on universality for area preserving maps of the plane abstract we present detailed evidence that one parameter families of area preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter we relate this behaviour to a fixed point equation of the form 1 and det d 1 r 2 r 2 in particular we argue that the scaling transformation r 2 r 2 is conjugate to the transformation 0 x y x y with 2 and in fact 2 we present some numerical evidence that 8 721 1 4 018 1 16 36 where is the asymptotic ratio of the differences of the parameter values corresponding to the successive periods 2k described above

renormalization group analysis of bifurcations in area preserving maps abstract two dimensional area preserving maps can be represented by a generating function the action high orders of successive period doubling bifurcations are studied by writing a renormalization group scheme for this action fixed points and eigenvalues of this scheme are found and interpreted

on the bootstrap and likelihood based confidence regions summary we describe a method for constructing likelihood based confidence regions for a vector parameter using the bootstrap and nonparametric density estimation the technique is illustrated by application to a numerical example and its theoretical properties are elucidated it is argued that likelihood based regions should not be approximated by ellipses if we are to have any hope of capturing first order departures from normality bootstrap algorithms for constructing simultaneous confidence intervals for the components of a vector parameter are also presented advantages of the percentile t method over the ordinary percentile method are demonstrated in a multivariate setting