partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

power stable aggregation functions we discuss and exemplify binary power stable aggregation functions on the interval 0 1 i e log ratio invariant aggregation functions for continuous power stable aggregation functions we introduce several methods of constructing dependence functions we also study dependence functions yielding symmetry idempotency and some other properties finally continuous associative power stable aggregation functions are completely characterized

misspecified structural change threshold and markov switching models sudden perturbations of a large amplitude occur frequently in macroeconomic and financial time series a usual practice is to test linearity against a permanent structural change however changes can also be captured by nonlinear stationary models such that threshold and markov switching models in this paper we show that tests designed for a threshold alternative have also power against parameter instability originating from structural change or markov switching models on the other hand it is shown that tests for structural change have no power if the data are generated by a markov switching or threshold model therefore it appears that testing the null of parameter stability against a threshold alternative is a robust way to detect parameter instability in economic and financial time series a monte carlo analysis based on several models studied in the literature illustrates how the tests perform in practice

invariant functionals on completely distributive lattices in this paper we are interested in functionals defined on completely distributive lattices and which are invariant under mappings preserving arbitrary joins and meets we prove that the class of nondecreasing invariant functionals coincides with the class of sugeno integrals associated with 0 1 valued capacities the so called term functionals thus extending previous results both to the infinitary case as well as to the realm of completely distributive lattices furthermore we show that in the case of functionals over complete chains the nondecreasing condition is redundant characterizations of the class of sugeno integrals as well as its superclass comprising all polynomial functionals are provided by showing that the axiomatizations given in terms of homogeneity of their restriction to finitary functionals still hold over completely distributive lattices we also present canonical normal form representations of polynomial functionals on completely distributive lattices which appear as the natural extensions to their finitary counterparts and as a by product we obtain an axiomatization of complete distributivity in the case of bounded lattices

shrinkage estimation for multivariate hidden markov models abstractmotivated from a changing market environment over time we consider high dimensional data such as financial returns generated by a hidden markov model that allows for switching between different regimes or states to get more stable estimates of the covariance matrices of the different states potentially driven by a number of observations that are small compared to the dimension we modify the expectation maximization em algorithm so that it yields the shrinkage estimators for the covariance matrices the final algorithm turns out to reproduce better estimates not only for the covariance matrices but also for the transition matrix it results into a more stable and reliable filter that allows for reconstructing the values of the hidden markov chain in addition to a simulation study performed in this article we also present a series of theoretical results that include dimensionality asymptotics and provide the motivation for certain techniques used in the algorithm supplementary materials fo

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

consistent and asymptotically normal parameter estimates for hidden markov models hidden markov models are today widespread for modeling of various phenomena it has recently been shown by leroux that the maximum likelihood estimate mle of the parameters of a such a model is consistent and local asymptotic normality has been proved by bickel and ritov in this paper we propose a new clans of estimates which are consistent asymptoti cally normal and almost as good an the mle

bayesian estimation of switching arma models abstract switching arma processes have recently appeared as an efficient modelling to nonlinear time series models because they can represent multiple or heterogeneous dynamics through simple components the levels of dependence between the observations are double at a first level the parameters of the model are selected by a markovian procedure at a second level the next observation is generated according to a standard time series model when the model involves a moving average structure the complexity of the resulting likelihood function is such that simulation techniques like those proposed by shephard 1994 biometrika 81 115 131 and billio and monfort 1998 journal of statistical planning and inference 68 65 103 are necessary to derive an inference on the parameters of the model we propose in this paper a bayesian approach with a non informative prior distribution developed in mengersen and robert 1996 bayesian statistics 5 oxford university press oxford pp 255 276 and robert and titterington 1998 statistics and computing 8 2 145 158 in the setup of mixtures of distributions and hidden markov models respectively the computation of the bayes estimates relies on mcmc techniques which iteratively simulate missing states innovations and parameters until convergence the performances of the method are illustrated on several simulated examples this work also extends the papers by chib and greenberg 1994 journal of econometrics 64 183 206 and chib 1996 journal of econometrics 75 1 79 97 which deal with arma and hidden markov models respectively

asymptotic properties of the maximum likelihood estimator in autoregressive models with markov regime an autoregressive process with markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable markov chain in this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden markov chain conditional on the observations

the self dual core and the anti self dual remainder of an aggregation operator in most decisional models based on pairwise comparison between alternatives the reciprocity of the individual preference representations expresses a natural assumption of rationality in those models self dual aggregation operators play a central role in so far as they preserve the reciprocity of the preference representations in the aggregation mechanism from individual to collective preferences in this paper we propose a simple method by which one can associate a self dual aggregation operator to any aggregation operator on the unit interval the resulting aggregation operator is said to be the self dual core of the original one and inherits most of its properties our method constitutes thus a new characterization of self duality with some technical advantages relatively to the traditional symmetric sums method due to silvert in our framework moreover every aggregation operator can be written as a sum of a self dual core and an anti self dual remainder which in some cases seems to give some indication on the dispersion of the variables in order to illustrate the method proposed we apply it to two important classes of continuous aggregation operators with the properties of idempotency symmetry and stability for translations the owa operators and the exponential quasiarithmetic means

analysis of time series subject to changes in regime abstract this paper introduces an em algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters with the shifts themselves modeled as the outcome of a discrete valued markov process the simplicity of the em algorithm permits potential application of the approach to large vector systems

stationarity of multivariate markov switching arma models in this article we consider multivariate arma models subject to markov switching in these models the parameters are allowed to depend on the state of an unobserved markov chain a natural idea when estimating these models is to impose local stationarity conditions i e stationarity within each regime in this article we show that the local stationarity of the observed process is neither sufficient nor necessary to obtain the global stationarity we derive stationarity conditions and we compute the autocovariance function of this nonlinear process interestingly it turns out that the autocovariance structure coincides with that of a standard arma some examples are proposed to illustrate the stationarity conditions using monte carlo simulations we investigate the consequences of accounting for the stationarity conditions in statistical inference

kernel aggregation functions on finite scales constructions from their marginals abstract the study of discrete aggregation functions those defined on a finite chain with some kind of smoothness has been extensively developed in last years many different kinds of aggregation functions have been characterized in this context in this paper discrete aggregation functions with the kernel property which implies the smoothness property are investigated some properties and characterizations as well as some construction methods for this kind of discrete aggregation functions are studied it is also investigated when the marginal functions of a discrete kernel aggregation function fully determine it

representation and construction of self dual aggregation operators abstract two different characterizations of self dual aggregation operators are available in the literature one based on c x y x x 1 y and one based on the arithmetic mean both approaches construct a self dual aggregation operator by combining an aggregation operator with its dual in this paper we fit these approaches into a more general framework and characterize n invariant aggregation operators with n an involutive negator various binary aggregation operators fulfilling some kind of symmetry w r t n and with a sufficiently large range can be used to combine an aggregation operator and its dual into an n invariant aggregation operator moreover using aggregation operators to construct n invariant aggregation operators seems rather restrictive it suffices to consider n ary operators fulfilling some weaker conditions special attention is drawn to the equivalence classes that arise as several of these n ary operators can yield the same n invariant aggregation operator

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

fuzzy measures and integrals we present fuzzy measures and fuzzy integrals as special poset homeomorphisms besides general fuzzy integrals regular fuzzy integrals are introduced and some of their properties are discussed state of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

on modular representations of bar q q arising from modular forms where g is the galois group gai i q and f is a finite field of characteristic i 3 suppose that p is modular of level n i e that it arises from a weight 2 newform of level dividing n and trivial nebentypus character then p is an odd representation the matrix p c where c is a complex conjugation in g has eigenvalues 1 1 since 1 and 1 are distinct in f p is absolutely irreducible and has a model over every subfield of f containing the set trace p we assume that f has been chosen so that it is generated by this set assume that p is a prime which exactly divides n we write p i n and restrict p to a decomposition group of g for the prime p view the restriction as a representation p p of gal t p qp we say that p is finite at p 34 or 35 w if there is a finite flat f vector space scheme h over zp for which the action of gal t p qp on the f vector space h 1 p gives pp i f p 9 is finite at p if and only if pp is unramified it is clear that p is finite at p whenever p is already modular of level n p in w of 34 cf 35 serre conjectured the converse i e that if p is finite then p is modular of level n p soon thereafter mazur 1 20 proved this conjecture in the case

smith theory and hecke operators abstract of the connections between the cohomology of arithmetic groups and representations of galois groups some are known and more are conjectured this paper proves one of these conjectures for certain monomial galois representations let p be a prime we show that the representation of the absolute galois group of q induced from an f p valued ray class character of the cyclotomic field q p is attached to a hecke eigenclass in the mod p cohomology of a torsion free congruence subgroup m of gl p 1 z the method involves constructing an action of the hecke algebra on the fundamental exact sequence of smith theory arising from the action by conjugation of an element of order p in gl p 1 z on m

characterization of invariant aggregation operators abstract following the ideas of bartlomiejczyk and drewniak minimal invariant subsets of 0 1 n are investigated an equivalence relation on these subsets is introduced consequently invariant aggregation operators are characterized by means of choquet integral based representation there are exactly 68 binary invariant aggregation operators 4 among them are also continuous further there are 6 self dual invariant binary aggregation operators a recurrent method of constructing invariant aggregation operators for n 2 is proposed restriction of invariant aggregation operators to finite scales is also discussed

the median and its extensions we review various representations of the median and related aggregation functions an advantage of the median is that it discards extreme values of the inputs and hence exhibits a better central tendency than the arithmetic mean however the value of the median depends on only one or two central inputs our aim is to design median like aggregation functions whose value depends on several central inputs such functions will preserve the stability of the median against extreme values but will take more inputs into account a method based on graduation curves is presented

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

calculating posterior distributions and modal estimates in markov mixture models abstract this paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved markov process a new full bayesian approach based on the method of gibbs sampling is developed calculations are simplified by data augmentation achieved by introducing a population index variable into the list of unknown parameters it is shown that the latent variables one for each observation can be simulated from their joint distribution given the data and the remaining parameters this result serves to accelerate the convergence of the gibbs sample modal estimates are also computed by stochastic versions of the em algorithm these provide an alternative to a full bayesian approach and to existing methods of locating the maximum likelihood estimate the ideas are applied in detail to poisson data mixtures of multivariate normal distributions and autoregressive time series