nested generalized linear mixed models an orthodox best linear unbiased predictor approach summary we introduce a new class of generalized linear mixed models based on the tweedie exponential dispersion model distributions accommodating a wide range of discrete continuous and mixed data using the best linear unbiased predictor of random effects we obtain an optimal estimating function for the regression parameters in the sense of godambe allowing an efficient common fitting algorithm for the whole class although allowing full parametric inference our main results depend only on the first and second moment assumptions of unobserved random effects in addition we obtain consistent estimators for both regression and dispersion parameters we illustrate the method by analysing the epilepsy data and cake baking data along with simulations and asymptotic justifications this shows the usefulness of the method for analysis of clustered non normal data

inverse gaussian and its inverse process as the subordinators of fractional brownian motion in this paper we study the fractional brownian motion fbm time changed by the inverse gaussian ig process and its inverse called the inverse to the inverse gaussian iig process some properties of the time changed processes are similar to those of the classical fbm such as long range dependence however one can also observe different characteristics that are not satisfied by the fbm we study the distributional properties of both subordinators namely ig and iig processes and also that of the fbm time changed by these subordinators we establish also the connections between the subordinated processes considered and the continuous time random walk model for the application part we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters the effectiveness of these methods is checked for simulated trajectories

random effects cox models a poisson modelling approach summary we propose a poisson modelling approach to nested random effects cox proportional hazards models an important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects the orthodox best linear unbiased predictor approach to random effects poisson modelling techniques enables us to justify appropriate consistency and optimality the explicit expressions for the random effects given by our approach facilitate incorporation of a relatively large number of random effects the use of the proposed methods is illustrated through the reanalysis of data from a large scale cohort study of particulate air pollution and mortality previously reported by pope et al 1995

estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

estimated estimating equations semiparametric inference for clustered and longitudinal data summary we introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions this estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi likelihood regression where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link and variance covariance is an unknown smooth function of the marginal means we propose to estimate the nonparametric link and variance covariance functions via smoothing methods whereas the regression parameters are obtained via the estimated estimating equations these are score equations that contain nonparametric function estimates the proposed estimated estimating equations approach is motivated by its flexibility and easy implementation moreover if data follow a generalized linear mixed model with either a specified or an unspecified distribution of random effects and link function the model proposed emerges as the corresponding marginal population average version and can be used to obtain inference for the fixed effects in the underlying generalized linear mixed model without the need to specify any other components of this generalized linear mixed model among marginal models the estimated estimating equations approach provides a flexible alternative to modelling with generalized estimating equations applications of estimated estimating equations include diagnostics and link selection the asymptotic distribution of the proposed estimators for the model parameters is derived enabling statistical inference practical illustrations include poisson modelling of repeated epileptic seizure counts and simulations for clustered binomial responses

generalized linear models with random effects salamander mating revisited in recent years much effort has been devoted to extending regression methodology to non gaussian data where responses are not independent these methods for dependent responses are suitable for data from longitudinal studies or nested designs however use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution in this paper we cast the problem in a bayesian framework and use a monte carlo method the gibbs sampler to avoid current computational limitations the flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall

witt rings and brauer groups under multiquadratic extensions ii let f be a field of characteristic not 2 and suppose m is a multiquadratic extension of f that is m f is a finite abelian extension of exponent 2 so that m f for some finite subgroup g e f f where f 0 in studying brauer groups and products of quaternion algebras the second author was led to consider the homology groups n m f of a certain complex gm f associated to the extension m f this complex appears in 11 3 1 301 and in 1 1 below the purpose of the present work is to investigate the first homology group n m f and to exhibit its close connections with quadratic form theory the higher homology groups are examined in 11 301 the field f is said to have property pi n if n m f 1 for every multiquadratic extension m f with m f q 2 properties p l and p 2 always hold but there are examples 29 of fields f for which p 3 fails these examples are generalized in section 5

finding domains of invertibility for smooth functions by means of attraction basins abstract the problem of finding a large domain in r n where a locally invertible smooth function is one to one had been approached in different ways none of them exhaustive the present paper considers an auxiliary ordinary differential equation built upon c 1 which has an asymptotically stable equilibrium at the point around which we invert on the basin of attraction of this point the function is proved to be one to one a sufficient condition for injectivity on a compact ball b is derived the condition involves the values of and its jacobian matrix d on the boundary b this criterion of invertibility is easily generalized to more general domains

time changed ornstein uhlenbeck process the ornstein uhlenbeck process is one of the most popular systems used for financial data description however this process has also been examined in the context of many other phenomena in this paper we consider the so called time changed ornstein uhlenbeck process in which time is replaced by an inverse subordinator of general infinite divisible distribution time changed processes nowadays play an important role in various fields of mathematical physics chemistry and biology as well as in finance in this paper we examine the main characteristics of the time changed ornstein uhlenbeck process such as the covariance function moreover we also prove the formula for a generalized fractional fokker planck equation that describes the one dimensional probability density function of the analyzed system for three cases of subordinators we show the special forms of obtained general formulas furthermore we mention how to simulate the trajectory of the ornstein uhlenbeck process delayed by a general inverse subordinator

galois groups of maximal p extensions let p be an odd prime and f a field of characteristic different from p containing a primitive pth root of unity assume that the galois group g of the maximal p extension of f has a finite normal series with abelian factor groups then the commutator subgroup of g is abelian moreover g has a normal abelian subgroup with pro cyclic factor group if in addition f contains a primitive p 2 th root of unity then g has generators x y i i i with relations y i y j y j y i and xy i x 1 y i q 1 where q 0 or q p n for some n 1

stochastic solution of space time fractional diffusion equations classical and anomalous diffusion equations employ integer derivatives fractional derivatives and other pseudodifferential operators in space in this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are mittag leffler type this leads to explicit solutions for space time fractional diffusion equations with multiscaling space fractional derivatives and additional insight into the meaning of these equations

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

a new construction of noncrossed product algebras new examples of noncrossed product division algebras are obtained using methods different from all previous noncrossed product constructions the examples are division algebras over intersections of henselian valued fields and they have schur index and exponent p for any prime number p and any integers m n 2 n 3if 2 the basic tools used in the construction are valuation theory and galois cohomology no generic methods are applied and there is no p i theory along the way local global principles are proved for central simple algebras over intersections of p henselian valued fields the first examples of central simple division algebras which are not crossed products were obtained by amitsur in am in 1972 amitsur thereby settled a question that had been one of the outstanding open problems in the theory of algebras for at least thirty years his examples were the generic division algebras ud q n of index n over q the rational numbers for any natural number n such that p2 n p an odd prime or 8 all subsequent constructions of noncrossed products in ss 83 883 r r an ti have heretofore been based on amitsur s specialization argument and they are all generic division algebras or extensions of generic division algebras the centers of these noncrossed product algebras are not known nor are the brauer groups nor the absolute galois groups of the centers we present here a new method of constructing noncrossed product algebras in our approach the noncrossed product is realized as the underlying division algebra d of a tensor product of suitably chosen cyclic algebras over a field f l n l2 where each l is a pth root henselian valued field we prove local global principles relating the splitting fields of d to those of d f lt i 1 2 it is shown that the part of the brauer group of f is completely determined by that of ll and l2 computations for central simple f algebras thus become very tractable for exam ple we not only show that d is not a crossed product but also calculate exactly how large r must be so that the matrix ring mr d is a crossed product and how large s must be so that ms d is a tensor product of cyclic algebras indeed the structure of the brauer group of f is so nice that we were somewhat surprised that noncrossed products could possibly exist over f

strong approximation of stochastic differential equations driven by a time changed brownian motion with time space dependent coefficients abstract the rate of strong convergence is investigated for an approximation scheme for a class of stochastic differential equations driven by a time changed brownian motion where the random time changes e t t 0 considered include the inverses of stable and tempered stable subordinators as well as their mixtures unlike those in the work of jum and kobayashi 2016 the coefficients of the stochastic differential equations discussed in this paper depend on the regular time variable t rather than the time change e t this alteration makes it difficult to apply the method used in that paper to overcome this difficulty we utilize a gronwall type inequality involving a stochastic driver to control the moment of the error process moreover in order to guarantee that an ultimately derived error bound is finite we establish a useful criterion for the existence of exponential moments of powers of the random time change

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

a characterization of c fields via galois groups abstract it is known that those fields f which are of class c in the sense of r ware can be characterized by their witt ring structure as well as by the behavior of their binary quadratic forms and the structure of their galois 2 extensions in this paper we show that c fields which have at least 8 square classes are characterized by the absence of a certain group dc of order 16 as a galois group over them moreover we show that the level of such a field is determined by the presence or absence of the cyclic group of order 4 and the dihedral group of order 8 as galois groups over it these results provide an interesting continuation of the work of ware in the appendix we give an explicit construction of field extensions with galois group dc

geometric brownian motion with tempered stable waiting times one of the earliest system that was used to asset prices description is black scholes model it is based on geometric brownian motion and was used as a tool for pricing various financial instruments however when it comes to data description geometric brownian motion is not capable to capture many properties of present financial markets one can name here for instance periods of constant values therefore we propose an alternative approach based on subordinated tempered stable geometric brownian motion which is a combination of the popular geometric brownian motion and inverse tempered stable subordinator in this paper we introduce the mentioned process and present its main properties we propose also the estimation procedure and calibrate the analyzed system to real data

stochastic solution of fractional fokker planck equations with space time dependent coefficients abstract this paper develops solutions of fractional fokker planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non gaussian levy processes with space time dependent drift diffusion and jump coefficients thus significantly extends magdziarz and zorawik s result in 14 fractional fokker planck equation describing subdiffusion is solved by our result in full generality from perspective of stochastic representation

on the structure of pythagorean fields abstract in this paper we study in detail the relationship between fans and valuations first uncovered by brocker see 2 our techniques are somewhat different as our valuations are constructed by brute force from the properties of the fields involved this approach has the advantage in that the valuation theory it yields can be directly related to the structure theory for spaces of orderings as developed by murray marshall see 11 14 we also discuss several applications which include results in k theory

solvable absolute galois groups are metabelian we show that solvable absolute galois groups have an abelian normal subgroup such that the quotient is the direct product of two finite cyclic and a torsion free procyclic group in particular solvable absolute galois groups are metabelian moreover any field with solvable absolute galois group g admits a non trivial henselian valuation unless each sylow subgroup of g is either procyclic or isomorphic to z2 z 2z a complete classification of solvable absolute galois groups up to isomorphism is given

preconditioned iterative methods for space time fractional advection diffusion equations in this paper we propose practical numerical methods for solving a class of initial boundary value problems of space time fractional advection diffusion equations first we propose an implicit method based on two sided grunwald formulae and discuss its stability and consistency then we develop the preconditioned generalized minimal residual preconditioned gmres method and preconditioned conjugate gradient normal residual preconditioned cgnr method with easily constructed preconditioners importantly because resulting systems are toeplitz like fast fourier transform can be applied to significantly reduce the computational cost we perform numerical experiments to demonstrate the efficiency of our preconditioners even in cases with variable coefficients

the graded witt ring and galois cohomology ii a primary problem in the theory of quadratic forms over a field f of characteristic different from two is to prove that the rings hq f and gwf are isomorphic here hqf h gal fq f z 2z where fq is the quadratic closure of f and gwf is the graded witt nrng associated to the fundamental ideal of even dimensional forms in the witt ring wf of f in this paper we assume we are given a field extension k of f such that wk is close to wf or hq k is close to hq f a method is developed to obtain information about these graded rings over f and its 2 extensions from information about the corresponding graded ring of k this relative theory extends and includes the previously developed absolute case where k fq applications are also given to show that hq f and gwf are isomorphic for a collection of fields anrsing naturally from the theory of abstract witt rings

rigid elements valuations and realization of witt rings to the theory over the residue class field of the valuation this theorem generalizes to any 2 henselian valuation cf kl sect 12 21 let v be the valuation let a e k f o 1 be such that v a is not divisible by two the key idea behind the proof is that the quadratic form 1 a only represents elements in u a such an element a is called

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

small area inference for binary variables in the national health interview survey abstract the national health interview survey is designed to produce precise estimates of finite population parameters for the entire united states but not for small geographical areas or subpopulations our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months to include all sources of variation in the model we carry out a bayesian hierarchical analysis for the desired finite population quantities first for each cluster county a separate logistic regression relates the individual s probability of a doctor visit to his or her characteristics second a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level we describe the numerical methods needed to obtain the desired posterior moments then we compare estimates produced using the exact numerical method with approximations finally we compare the hierarchical bayes estimates to empirical bayes estimates and to stand

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

powers of totally positive subgroups of fields abstract for a formally real field f a totally positive co torsion subgroup s of f and m 1 we prove that s m s m this extends a result of becker we prove several refinements of this fact related to higher pythagoras numbers real holomorphy rings and sums with mixed powers

demuskin fields with valuations we study the arithmetic structure of fields f of characteristic neq p containing a primitive pth root of unity for which the maximal pro p galois group of f is a finitely generated demuskin group

witt rings and almost free pro 2 groups let f be a field of characteristic not 2 wf the witt ring of quadratic forms over f if the maximal ideal consisting of even dimensional forms and i f its square let g 2 gal f 2 f where f 2 is the maximal 2 extension quadratic closure of f in this note we prove a decomposition theorem for wf in the case that z f is torsion free and use it to obtain a new proof of a theorem of ershov on the structure of almost free pro a groups e theorem 41 in what follows w f denotes the torsion subgroup of wf and wredf wf w f is the reduced witt ring the set of orderings on f will be denoted by x and will be given the harrison topology with subbasis consisting of the sets h a e x 1 0 a f is called a sap field if every open and closed clopen subset of x is equal to some h a if r r are abstract witt rings then r x r denotes their product in the category of witt rings ml all unexplained notations and terminology about quadratic forms and witt rings can be found in l and m for elementary facts about profinite groups the reader is referred to ri following kijima and nishi kn the field f is called quasi pythugorean if z f is torsion free i e u f d 2 equivalently if the kaplansky radical of f consists of all nonzero sums of two squares ell corollary 2 91 compare el2 classification theorem 23 examples of these fields include formally real generalized hilbert fields k pseudo real closed fields p and fields satisfying the strong hasse principle h4 every totally indefinite quadratic form of dimension 4 over f is isotropic i e ii f 2 a formally real field satisfies h if and only if it is a quasi pythagorean sap field elp in ko koziol gives a criterion characterizing the class of quasi pythagorean algebraic extensions of q such fields necessarily satisfy h the best known examples of fields satisfying h are formally real

a generalization of marshall s equivalence relation for p prime and for a field f containing a root of unity of order p we generalize marshall s equivalence relation on orderings to arbitrary subgroups of f of index p the equivalence classes then correspond to free pro p factors of the maximal pro p galois group of f we generalize to this setting results of jacob on the maximal pro 2 galois group of a pythagorean field

diffusion and relaxation controlled by tempered α stable processes we derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha stable processes the tempering results in the existence of all moments of operational time the subordination by the inverse tempered alpha stable process provides diffusion relaxation that occupies an intermediate place between subdiffusion cole cole law and normal diffusion exponential law here we obtain explicitly the fokker planck equation and the cole davidson relaxation function this model includes subdiffusion as a particular case

demuskin groups galois modules and the elementary type conjecture abstract let p be a prime and f p the maximal p extension of a field f containing a primitive pth root of unity we give a new characterization of demuskin groups among galois groups gal f p f when p 2 and assuming the elementary type conjecture when p 2 as well this characterization is in terms of the structure as galois modules of the galois cohomology of index p subgroups of gal f p f

langevin formulation of a subdiffusive continuous time random walk in physical time systems living in complex nonequilibrated environments often exhibit subdiffusion characterized by a sublinear power law scaling of the mean square displacement one of the most common models to describe such subdiffusive dynamics is the continuous time random walk ctrw stochastic trajectories of a ctrw can be described in terms of the subordination of a normal diffusive process by an inverse levy stable process here we propose an equivalent langevin formulation of a force free ctrw without subordination by introducing a different type of non gaussian noise we are able to express the ctrw dynamics in terms of a single langevin equation in physical time with additive noise we derive the full multipoint statistics of this noise and compare it with the scaled brownian motion sbm an alternative stochastic model describing subdiffusive dynamics interestingly these two noises are identical up to the second order correlation functions but different in the higher order statistics we extend our formalism to general waiting time distributions and force fields and compare our results with those of the sbm in the presence of external forces our proposed noise generates a different class of stochastic processes resembling a ctrw but with forces acting at all times

fractional brownian motion time changed by gamma and inverse gamma process abstract many real time series exhibit behavior adequate to long range dependent data additionally very often these time series have constant time periods and also have characteristics similar to gaussian processes although they are not gaussian therefore there is need to consider new classes of systems to model these kinds of empirical behavior motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena both of them are constructed as the superposition of fractional brownian motion fbm and other process in the first case the internal process which plays role of the time is the gamma process while in the second case the internal process is its inverse we present in detail their main properties paying main attention to the long range dependence property moreover we show how to simulate these processes and estimate their parameters we propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process this method is very useful in description of rounded data like waiting times of subordinated processes delayed by inverse subordinators by using the monte carlo method we show the effectiveness of proposed estimation procedures finally we present the applications of proposed models to real time series

a recursive description of pro p galois groups abstract in this note we study a modified version of the elementary type conjecture for pro p galois groups to be precise let g p f be the galois group of the maximal galois p extension of a field f containing a primitive p th root of unity under some natural assumptions concerning valuation rings of f and also orderings of f when p 2 we prove that g p f can be obtained from suitable closed subgroups using a finite number of free pro p products and semidirect products

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

comment on fractional fokker planck equation with space and time dependent drift and diffusion the purpose of this paper is to correct errors presented recently in the paper lv et al j stat phys 149 619 628 2012 where the authors analyzed fractional fokker planck equation ffpe with space time dependent drift f x t f x f t and diffusion d x t d x tilde d t coefficients in the factorized form we show an important drawback in the derivation of the stochastic representation of ffpe presented in the aforementioned paper which makes the whole proof wrong moreover we present a correct proof of their result in even more general case when both drift and diffusion can have any not necessarily factorized form

consistent estimators in generalized linear mixed models abstract a simple method based on simulated moments is proposed for estimating the fixed effects and variance components in a generalized linear mixed model glmm it is shown that the method is not only computationally attractive but also leads to consistent estimators on the other hand simulation shows that the method can be quite inefficient

fokker planck type equations associated with fractional brownian motion controlled by infinitely divisible processes abstract in this paper we study the anomalous diffusion process driven by fractional brownian motion delayed by general infinitely divisible subordinator we show the analyzed process is the stochastic representation of the fokker planck type equation that describes the probability density function of an introduced model moreover we study main characteristics of the examined process the first two moments that allow us in special cases for classification of it as a system with accelerating subdiffusion property

calibration of the subdiffusive arithmetic brownian motion with tempered stable waiting times in the classical analysis many models used to real data description are based on the standard brownian diffusion type processes however some real data exhibit characteristic periods of constant values in such cases the popular systems seem not to be applicable therefore we propose an alternative approach based on the combination of the popular brownian motion with drift called also the arithmetic brownian motion and tempered stable subordinator the probability density function of the proposed model can be described by a fokker planck type equation and therefore it has many similar properties as the popular brownian motion with drift in this paper we propose the estimation procedure for the considered tempered stable subdiffusive arithmetic brownian motion and calibrate the analyzed process to the real financial data

asymptotically unbiased estimation in generalized linear models with random effects summary obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model in this paper we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent the method is motivated by iterative bias correction and can be applied in principle to any parametric model a simulation based approach of implementing the method is described and the relationship of the method proposed with other sampling based methods is discussed results from a small scale simulation study show that the method proposed can lead to estimates which are nearly unbiased even for the variance components while the standard errors are only slightly inflated a new analysis of the famous salamander mating data is described which reveals previously undetected between animal variation among the male salamanders and results in better prediction of mating outcomes

explicit form of the first passage time density for accelerating subdiffusion the first passage time fpt statistics play a central role in different fields apart of description of the underlying system state and its evolution it is essential to investigate the time at which this state reaches a certain area for the first time in this paper we study the fpt problem for recently developed models of an accelerating subdiffusion which extends incorporating various short and long time scalings of the mean square displacement msd popular models of subdiffusion based on fractional order differential equations we derive the laplace transform of the fpt density function in the case of constant bias for a force depending linearly on the position we provide a full analytical formula for the fpt density in terms of generalized mittag leffler functions and the hermite polynomials we also provide a numerical evidence that fpt properties are strictly connected with msd scalings of the accelerating subdiffusion

a method of simulated moments for estimation of discrete response models without numerical integration this paper proposes a simple modification of a conventional method of moments estimator for a discrete response model replacing response probabilities that require numerical integration with estimators obtained by monte carlo simulation this method of simulated moments msm does not require precise estimates of these probabilities for consistency and asymptotic normality relying instead on the law of large numbers operating across observations to control simulation error and hence can use simulations of practical size the method is useful for models such as high dimensional multinomial probit mnp where computation has restricted applications

option pricing in subdiffusive bachelier model the earliest model of stock prices based on brownian diffusion is the bachelier model in this paper we propose an extension of the bachelier model which reflects the subdiffusive nature of the underlying asset dynamics the subdiffusive property is manifested by the random infinitely divisible periods of time during which the asset price does not change we introduce a subdiffusive arithmetic brownian motion as a model of stock prices with such characteristics the structure of this process agrees with two stage scenario underlying the anomalous diffusion mechanism in which trapping random events are superimposed on the langevin dynamics we find the corresponding fractional fokker planck equation governing the probability density function of the introduced process we construct the corresponding martingale measure and show that the model is incomplete we derive the formulas for european put and call option prices we describe explicit algorithms and present some monte carlo simulations for the particular cases of stable and tempered stable distributions of waiting times

pricing european option under the time changed mixed brownian fractional brownian model abstract this paper deals with the problem of discrete time option pricing by a mixed brownian fractional subdiffusive black scholes model under the assumption that the price of the underlying stock follows a time changed mixed brownian fractional brownian motion we derive a pricing formula for the european call option in a discrete time setting

equivalence of subordinated processes with tempered alpha stable waiting times and fractional fokker planck equations in space and time dependent fields in this paper we introduce a subordinated stochastic process controlled by tempered alpha stable waiting times and prove the equivalence of this process and the fractional fokker planck equation with space and time dependent diffusion coefficients in the influence of an external space and time dependent force

the kummerian property and maximal pro p galois groups abstract for a prime number p we give a new restriction on pro p groups g which are realizable as the maximal pro p galois group g f p for a field f containing a root of unity of order p this restriction arises from kummer theory and the structure of the maximal p radical extension of f we study it in the abstract context of pro p groups g with a continuous homomorphism g 1 p z p and characterize it cohomologically and in terms of 1 cocycles on g this is used to produce new examples of pro p groups which do not occur as maximal pro p galois groups of fields as above

from continuous time random walks to the fractional fokker planck equation we generalize the continuous time random walk ctrw to include the effect of space dependent jump probabilities when the mean waiting time diverges we derive a fractional fokker planck equation ffpe this equation describes anomalous diffusion in an external force field and close to thermal equilibrium we discuss the domain of validity of the fractional kinetic equation for the force free case we compare between the ctrw solution and that of the ffpe

finite element approximation of optimal control problems governed by time fractional diffusion equation in this paper galerkin finite element approximation of optimal control problems governed by time fractional diffusion equations is investigated piecewise linear polynomials are used to approximate the state and adjoint state while the control is discretized by variational discretization method a priori error estimates for the semi discrete approximations of the state adjoint state and control are derived furthermore we also discuss the fully discrete scheme for the control problems a finite difference method developed in lin and xu 2007 is used to discretize the time fractional derivative fully discrete first order optimality condition is developed based on first discretize then optimize approach the stability and truncation error of the fully discrete scheme are analyzed numerical example is given to illustrate the theoretical findings

black scholes formula in subdiffusive regime in the classical approach the price of an asset is described by the celebrated black scholes model in this paper we consider a generalization of this model which captures the subdiffusive characteristics of financial markets we introduce a subdiffusive geometric brownian motion as a model of asset prices exhibiting subdiffusive dynamics we find the corresponding fractional fokker planck equation governing the dynamics of the probability density function of the introduced process we prove that the considered model is arbitrage free and incomplete we find the corresponding subdiffusive black scholes formula for the fair prices of european options and show how these prices can be evaluated using monte carlo methods we compare the obtained results with the classical ones

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

generalized mittag leffler relaxation clustering jump continuous time random walk approach a stochastic generalization of renormalization group transformation for continuous time random walk processes is proposed the renormalization consists in replacing the jump events from a randomly sized cluster by a single renormalized i e overall jump the clustering of the jumps followed by the corresponding transformation of the interjump time intervals yields a new class of coupled continuous time random walks which applied to modeling of relaxation lead to the general power law properties usually fitted with the empirical havriliak negami function

reml estimation with exact covariance in the logistic mixed model residual maximum likelihood reml estimation is adapted to certain logistic mixed models for which representation of the unconditional mean as a linear function of the fixed effects is possible only the first two moments of the unconditional distribution need be evaluated and except for the form of the covariance the maximization algorithm carries over directly from linear models the exact unconditional covariance is computed from the logistic normal mixture for input into the algorithm residual log likelihood plots provide a means of inference for the dispersion components the taylor series approximation to this covariance besides exhibiting insufficient accuracy fails to be positive definite for large values of the dispersion components as a consequence reml loglikelihood plots based on this approximate covariance attribute misleadingly high precision to the dispersion component estimates the method is presented in the context of a salamander mating experiment in which random effects corresponding to male and female animals occur in a crossed design analyses of these data by several methods are compared

langevin picture of subdiffusion with infinitely divisible waiting times in this paper we study a langevin approach to modeling of subdiffusion in the presence of time dependent external forces we construct a subordinated langevin process whose probability density function solves the subdiffusive fractional fokker planck equation we generalize the results known for the levy stable waiting times to the case of infinitely divisible waiting time distributions our approach provides a complete mathematical description of subdiffusion with time dependent forces moreover it allows to study the trajectories of the constructed process both analytically and numerically via monte carlo methodology

robust estimation in generalised linear mixed models summary we propose robust methods for estimation of parameters of interest in an extended generalised linear mixed model in which only the conditional means of the responses given the random effects are specified a first step estimator 0 of the vector 0 of parameters is obtained by solving a system of estimating equations it is shown that 9 is consistent if furthermore the conditional variances are correctly specified a second step estimator 0 can be obtained by solving a system of optimal estimating equations whose coefficients a are estimated by 0 it is shown that 0 maintains the asymptotic optimality simulations a also indicate solid improvement of 0 over 0 two examples involving real data analysis are considered the methods are developed under a more general framework so that they may be applied to more general estimation problems

langevin picture of levy walks and their extensions in this paper we derive langevin picture of levy walks applying recent advances in the theory of coupled continuous time random walks we find a limiting process of the properly scaled levy walk next we introduce extensions of levy walks in which jump sizes are some functions of waiting times we prove that under proper scaling conditions such generalized levy walks converge in distribution to the appropriate limiting processes we also derive the corresponding fractional diffusion equations and investigate behavior of the mean square displacements of the limiting processes showing that different coupling functions lead to various types of anomalous diffusion

fence methods for mixed model selection many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure asymptotic properties for these types of procedures in settings like linear regression and arma time series have been studied but these do not naturally extend to nonstandard situations such as mixed effects models where simple definition of the sample size is not meaningful this paper introduces a new class of strategies known as fence methods for mixed model selection which includes linear and generalized linear mixed models the idea involves a procedure to isolate a subgroup of what are known as correct models of which the optimal model is a member this is accomplished by constructing a statistical fence or barrier to carefully eliminate incorrect models once the fence is constructed the optimal model is selected from among those within the fence according to a criterion which can be made flexible in addition we propose two variations of the fence the first is a stepwise procedure to handle situations of many predictors the second is an adaptive approach for choosing a tuning constant we give sufficient conditions for consistency of fence and its variations a desirable property for a good model selection procedure the methods are illustrated through simulation studies and real data analysis

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

the kernel unipotent conjecture and the vanishing of massey products for odd rigid fields abstract a major difficult problem in galois theory is the characterization of profinite groups which are realizable as absolute galois groups of fields recently the kernel n unipotent conjecture and the vanishing n massey conjecture for n 3 were formulated these conjectures evolved in the last forty years as a byproduct of the application of topological methods to galois cohomology we show that both of these conjectures are true for odd rigid fields this is the first case of a significant family of fields where both of the conjectures are verified besides fields whose galois groups of p maximal extensions are free pro p groups we also prove the kernel unipotent conjecture for demushkin groups of rank 2 and establish various filtration results for free pro p groups provide examples of pro p groups which do not have the kernel n unipotent property compare various zassenhaus filtrations with the descending p central series and establish new type of automatic galois realization

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due

compatible valuations and generalized milnor k theory given a field and a subgroup of there is a minimal group for which there exists an compatible valuation whose units are contained in assuming that has finite index in and contains for prime we describe in computable theoretic terms