de finetti s coherence and statistical inference on donne la definition d une inference coherente en conformite avec une theorie des probabilites conditionnelles derivee du principe de coherence de de finetti et on effectue une comparaison critique d une telle definition avec celle proposee par heath lane et sudderth

bayesian hypothesis testing in latent variable models hypothesis testing using bayes factors bfs is known not to be well defined under the improper prior in the context of latent variable models an additional problem with bfs is that they are difficult to compute in this paper a new bayesian method based on the decision theory and the em algorithm is introduced to test a point hypothesis in latent variable models the new statistic is a by product of the bayesian mcmc output and hence easy to compute it is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function in addition it is easy to interpret the method is illustrated using a one factor asset pricing model and a stochastic volatility model with jumps

asymptotic normality of the maximum likelihood estimator for general hidden markov models hidden markov models hmms have during the last decade become a widespread tool for modeling sequences of dependent random variables inference for such models is usually based on the maximum likelihood estimator mle and consistency of the mle for general hmms was recently proved by leroux in this paper we show that under mild conditions the mle is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the fisher information

rao blackwellization of particle markov chain monte carlo methods using forward filtering backward sampling smoothing in state space models amounts to computing the conditional distribution of the latent state trajectory given observations or expectations of functionals of the state trajectory with respect to this distribution in recent years there has been an increased interest in monte carlo based methods often involving particle filters for approximate smoothing in nonlinear and or non gaussian state space models one such method is to approximate filter distributions using a particle filter and then to simulate using backward kernels a state trajectory backwards on the set of particles we show that by simulating multiple realizations of the particle filter and adding a metropolis hastings step one obtains a markov chain monte carlo scheme whose stationary distribution is the exact smoothing distribution this procedure expands upon a similar one recently proposed by andrieu doucet holenstein and whiteley we also show that simulating multiple trajectories from each realization of the particle filter can be beneficial from a perspective of variance versus computation time and illustrate this idea using two examples

a new look at fresnel field computation using the jacobi bessel series many useful applications exist for the efficient computation of fresnel and near zone fields of large antennas even small antennas in beam waveguide systems must be evaluated in the fresnel zone far zone fields computed from measured near zone measurements can be verified by both the measurement and the computation of the fresnel zone fields the authors start with the premise that the far field has been computed by a jacobi bessel series these results are used then to determine the higher order terms of a barrar kay 1 r p expansion of the fields the leading term of the 1 r p series is the far zone field classically the higher order terms are found by repetitive differentiation a laborious and often inaccurate procedure particularly since the 1 r p series is slowly convergent as d 2 r d is the diameter of antenna source the approach of the authors via the jacobi bessel 1 r p series determines the higher order terms by simple algebraic recursion the only restriction on the method is that it be used within the range of validity of the fresnel small angle fsa approximation however since the fresnel approximation is a second order approximation in terms of d r the range of validity is quite large this is demonstrated in detail the method is applicable to reflector as well as aperture field sources

limit theorems in hidden markov models in this paper under mild assumptions we derive a law of large numbers a central limit theorem with an error estimate an almost sure invariance principle and a variant of the chernoff bound in finite state hidden markov models these limit theorems are of interest in certain areas of information theory and statistics particularly we apply the limit theorems to derive the rate of convergence of the maximum likelihood estimator in finite state hidden markov models

the bernstein von mises theorem and nonregular models we study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the true solution occurs on the boundary of the parameter space we show that in this case the bayesian inference is consistent and that the posterior distribution has not only gaussian components as in the case of regular models the bernstein von mises theorem but also has gamma distribution components that depend on the behaviour of the prior distribution on the boundary and have a faster rate of convergence we also show a remarkable property of bayesian inference that for some models there appears to be no bound on efficiency of estimating the unknown parameter if it is on the boundary of the parameter space we illustrate the results on a problem from emission tomography

numerical evaluation of one dimensional diffraction integrals an efficient technique is described for performing one dimensional 1 d integrals of oscillatory complex functions such as might arise in the numerical solution of diffraction problems the upper integration limit may be infinite provided that the phase of the integrand varies rapidly beyond some point the integration is done in segments chosen so that both the phase and amplitude may be approximated as cubic polynomials on each segment with a small cubic term for phase and continued to infinity from the last segment three methods are given for integrating at each step 1 an asymptotic series method 2 an almost quadratic phase method and 3 an almost linear phase method criteria are given for choosing among the methods an example calculation verifies the method in the special case of wave diffraction over two knife edges

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

asymptotic normality of the maximum likelihood estimator in state space models state space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way inference in such models has been studied by bickel ritov and ryden who consider hidden markov models which are special kinds of state space models and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions in this paper we generalize the results of bickel ritov and ryden to state space models where the latent process is a continuous state markov chain satisfying regularity conditions which are fulfilled if the latent process takes values in a compact space

the stability of conditional markov processes and markov chains in random environments we consider a discrete time hidden markov model where the signal is a stationary markov chain when conditioned on the observations the signal is a markov chain in a random environment under the conditional measure it is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate this permits a delicate exchange of the intersection and supremum of fields which is key for the stability of the nonlinear filter and partially resolves a long standing gap in the proof of a result of kunita j multivariate anal 1 1971 365 393 a similar result is obtained also in the continuous time setting the proofs are based on an ergodic theorem for markov chains in random environments in a general state space

asymptotic expansions for sums of weakly dependent random vectors it is shown that formal edgeworth expansions are valid for sums of weakly dependent random vectors the error of approximation has ordero n s 2 2 if the strong mixing coefficients in iii are decreasing at an exponential rate the above conditions can easily be checked and are often satisfied when the sequence of random vectors is a gaussian or a markov or an autoregressive process explicit formulas are given for the distribution of finite fourier transforms of a strictly stationary time series

sure wins separating probabilities and the representation of linear functionals abstract we discuss conditions under which a convex cone k r admits a finitely additive probability m such that sup k k m k 0 based on these we characterise those linear functionals that are representable as finitely additive expectations a version of riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions

efficient computation of the far field of parabolic reflectors by pseudo sampling algorithm the newly developed pseudo sampling representation is applied for computing the far field of an offset parabolic reflector with a cluster feed illumination a new comb type fast fourier transform fft algorithm is used in a computer program both precision and computational time are analyzed demonstrating the excellent performance of the method

refinements in asymptotic expansions for sums of weakly dependent random vectors let s0 denote the nth normalized partial sum of a sequence of mean zero weakly dependent random vectors this paper gives asymptotic expansions for ef sn under weaker moment conditions than those of g6tze and hipp 1983 it is also shown that an expansion for ef sn with an error term o n s 2 2 is valid without any cramer type condition if f has partial derivatives of order s 1 only this settles a conjecture of g6tze and hipp in their 1983 paper

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

a semiparametric stochastic volatility model abstract in this paper the correlation structure in the classical leverage stochastic volatility sv model is generalized based on a linear spline in the new model the correlation between the return and volatility innovations is time varying and depends nonparametrically on the type of news arrived to the market theoretical properties of the proposed model are examined the model estimation and comparison are conducted by bayesian methods the performance of the estimates are examined in simulations the new model is fitted to daily and weekly us data and compared with the classical sv and garch models in terms of their in sample and out of sample performances empirical results suggest evidence in favor of the proposed model in particular the new model finds strong evidence of time varying leverage effect in individual stocks when the classical model fails to identify the leverage effect

the strong ergodic theorem for densities generalized shannon mcmillan breiman theorem let xi x2 be a stationary process with probability densities f x1 x2 xn with respect to lebesgue measure or with respect to a markov measure with a stationary transition measure it is shown that the sequence of relative entropy densities 1 n log f xi x2 x0 converges almost surely this long conjectured result extends the l convergence obtained by moy perez and kieffer and generalizes the shannon mcmillanbreiman theorem to nondiscrete processes the heart of the proof is a new martingale inequality which shows that logarithms of densities are l dominated

inference in arch and garch models with heavy tailed errors arch and garch models directly address the dependency of conditional second moments and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present these include financial time series which can be particularly heavy tailed however little is known about properties of arch or garch models in the heavy tailed setting and no methods are available for approximating the distributions of parameter estimators there in this paper we show that for heavy tailed errors the asymptotic distributions of quasi maximum likelihood parameter estimators in arch and garch models are nonnormal and are particularly difficult to estimate directly using standard parametric methods standard bootstrap methods also fail to produce consistent estimators to overcome these problems we develop percentile t subsample bootstrap approximations to estimator distributions studentizing is employed to approximate scale and the subsample bootstrap is used to estimate shape the good performance of this approach is demonstrated both theoretically and numerically

complex polynomial phase integration a previously published integration algorithm applicable to the numerical computation of integrals with rapidly oscillating integrands is generalized the previous algorithm involved quadratic approximation of the phase function which was assumed to be real the present generalization concerns approximation of a complex phase function by a polynomial of arbitrary degree as before the integrand is then written without approximation as a slowly varying function multiplied by the polynomial phase exponential and the slowly varying factor is approximated by a finite sum of chebyshev polynomials the integral is thus expressed as a sum of constituent integrals which are computed recursively via lu decomposition applied to a system of linear equations with a banded coefficients matrix examples are presented comparing various degree phase approximants

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

a liapounov bound for solutions of the poisson equation in this paper we consider psi irreducible markov processes evolving in discrete or continuous time on a general state space we develop a liapounov function criterion that permits one to obtain explicit bounds on the solution to the poisson equation and in particular obtain conditions under which the solution is square integrable these results are applied to obtain sufficient conditions that guarantee the validity of a functional central limit theorem for the markov process as a second consequence of the bounds obtained a perturbation theory for markov processes is developed which gives conditions under which both the solution to the poisson equation and the invariant probability for the process are continuous functions of its transition kernel the techniques are illustrated with applications to queueing theory and autoregressive processes

quadratic phase integration using a chebyshev expansion an integration algorithm is described which is particularly effective in the numerical treatment of integrands having rapidly varying phase and slowly varying amplitude the algorithm involves approximating the phase function by a quadratic polynomial and rewriting the integrand without approximation as a slowly varying function multiplied by this quadratic phase exponential the slowly varying function is then approximated by chebyshev expansion and the desired integral is thus expressed as a sum of constituent integrals with integrands containing a chebyshev polynomial multiplied by the quadratic phase factor these constituent integrals are computed by means of lu decomposition applied to a system of linear equations with a banded coefficients matrix example results are presented indicating that a substantial reduction in computation time may be realized by means of this approach

correction to a new integration algorithm and its application to the analysis of symmetrical cassegrain microwave antennas an efficient numerical algorithm for physical optics po analysis of reflectors is presented cylindrical symmetry of the reflector is not essential but is assumed for purposes of illustration and this leads to the use of fourier representation in the azimuthal variable the algorithm is based on quadratic approximation of the phase and polynomial approximation of the remaining portion of the integrand the necessary integrals are generated recursively and they involve the fresnel integral additional efficiency is achieved by means of an interpolation scheme therein one interpolates all but the rapidly varying edge diffraction contribution to the integral and then adds the explicitly calculated edge contribution at each far field point a few illustrative examples are included

the theorem of halmos and savage under finite additivity abstract we prove an extension to the finitely additive setting of the theorem of halmos and savage from this we deduce extensions of classical results of drewnowski and of yan as well as a new characterization of weak compactness in the space of finitely additive set functions

sprt and cusum in hidden markov models in this paper we study the problems of sequential probability ratio tests for parameterized hidden markov models we investigate in some detail the performance of the tests and derive corrected brownian approximations for error probabilities and expected sample sizes asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden markov chain data is established next we consider the cumulative sum cusum procedure for change point detection in this model based on the renewal property of the stopping rule cusum can be regarded as a repeated one sided sequential probability ratio test asymptotic optimality of the cusum procedure is proved in the sense of lorden 1971 motivated by the sequential analysis in hidden markov models wald s likelihood ratio identity and wald s equation for products of markov random matrices are also given we apply these results to several types of hidden markov models i i d hidden markov models switch gaussian regression and switch gaussian autoregression which are commonly used in digital communications speech recognition bioinformatics and economics

consistency of the maximum likelihood estimator for general hidden markov models consider a parametrized family of general hidden markov models where both the observed and unobserved components take values in a complete separable metric space we prove that the maximum likelihood estimator mle of the parameter is strongly consistent under a rather minimal set of assumptions as special cases of our main result we obtain consistency in a large class of nonlinear state space models as well as general results on linear gaussian state space models and finite state models a novel aspect of our approach is an information theoretic technique for proving identifiability which does not require an explicit representation for the relative entropy rate our method of proof could therefore form a foundation for the investigation of mle consistency in more general dependent and non markovian time series also of independent interest is a general concentration inequality for v uniformly ergodic markov chains

self normalized cramer type moderate deviations under dependence we establish a cramer type moderate deviation result for self normalized sums of weakly dependent random variables where the moment requirement is much weaker than the non self normalized counterpart the range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes we consider three types of self normalization the equal block scheme the big block small block scheme and the interlacing scheme simulation study shows that the latter can have a better finite sample performance our result is applied to multiple testing and construction of simultaneous confidence intervals for ultra high dimensional time series mean vectors

asymptotic operating characteristics of an optimal change point detection in hidden markov models let 0 1 1 be observations from the hidden markov model with probability distribution p 0 and let 1 be observations from the hidden markov model with probability distribution p 1 the parameters 0 and 1 are given while the change point is unknown the problem is to raise an alarm as soon as possible after the distribution changes from p 0 to p 1 but to avoid false alarms specifically we seek a stopping rule n which allows us to observe the s sequentially such that e n is large and subject to this constraint sup k e k n k n k is as small as possible here e k denotes expectation under the change point k and e denotes expectation under the hypothesis of no change whatever in this paper we investigate the performance of the shiryayev roberts pollak srp rule for change point detection in the dynamic system of hidden markov models by making use of markov chain representation for the likelihood function the structure of asymptotically minimax policy and of the bayes rule and sequential hypothesis testing theory for markov random walks we show that the srp procedure is asymptotically minimax in the sense of pollak ann statist 13 1985 206 227 next we present a second order asymptotic approximation for the expected stopping time of such a stopping scheme when w 1 motivated by the sequential analysis in hidden markov models a nonlinear renewal theory for markov random walks is also given

filtered likelihood for point processes abstract point processes are widely used in finance and economics to model the timing of defaults market transactions unemployment spells births and a range of other events we develop and analyze likelihood estimators for the parameters of a marked point process and incompletely observed explanatory factors that influence the arrival intensity and mark distribution we establish an approximation to the likelihood and analyze the convergence and large sample properties of the associated estimators numerical results illustrate the behavior of our estimators

reflector antenna fields an exact aperture like approach a new computational approach is presented which allows fast analysis of radiation from large reflector antennas for an aperture a fourier transform ft relationship does exist between far field and aperture distribution accordingly the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe shannon whittaker theorem applied at nyquist rate the finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a ft in order to overcome this difficulty a new pseudosampling expansion which explicitly takes into account the extra factor is developed for parabolic reflector the sampling functions are related to the fresnel integrals and the far field can be exactly reconstructed in terms of aperture far field samples which can be computed using the fast fourier transform fft numerical computations and error analysis show the excellent performance of the method which can be generalized to deal with arbitrary reflector surfaces and near field evaluation

efficient likelihood estimation in state space models motivated by studying asymptotic properties of the maximum likelihood estimator mle in stochastic volatility sv models in this paper we investigate likelihood estimation in state space models we first prove under some regularity conditions there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the fisher information as its variance with an extra assumption that the likelihood equation has a unique root for each n then there is a consistent sequence of estimators of the unknown parameters if in addition the supremum of the log likelihood function is integrable the mle exists and is strongly consistent edge worth expansion of the approximate solution of likelihood equation is also established several examples including markov switching models arma models g arch models and stochastic volatility sv models are given for illustration

simplified technique for evaluating the radiation integrals a simplified numerical method is described for computing the radiation integral of a reflector antenna which is associated with either the aperture field method afm or the induced current method icm the method involves linear approximation of the phase function and absorption of the approximation error into amplitude function then the integrand is rewritten as a slowly varying function multiplied by the phase exponential the slowly varying function is expanded in terms of a polynomial for the radial direction and trigonometric functions for the circumferential direction expansion coefficients are determined by matching at points on the aperture the matching points are chosen in a manner similar to that of a two dimensional numerical integration scheme