brownian motion with restoring drift micro canonical ensemble and the thermodynamic limit we take up the old problem of micro canonical conditioning in the context of diffusion starting with a potential the schrodinger operator with ground state is carried by a conjugation into the diffusion generator with invariant density the latter motion is made micro canonical by first conditioning the path to be periodic and then further conditioning on the empirical mean square or particle number the thermodynamics are then studied by taking while d remains fixed the problem in this form owes its inception to mckean vaninsky cite mv2 who obtained the following result for with they showed the same type of diffusion appears in the thermodynamic limit but with drift arising from the shifted potential being such that the limiting mean square equals d their method of proof predicts the same outcome for so long as d is smaller than the canonical mean square while if the matter was unresolved the purpose of this note is to show a type of phase transition takes place in this case the conditioning is overcome in the limit and one sees the original stationary diffusion on the line the proof employs an entropy inequality due to csiszar 1

a dependent data extension of wald s identity and its application to sequential test performance computation the development of an exponential transformation of measure not restricted to independent identically distributed data is presented for a class of semi markov processes known as markov additive ma process the ma measure transformation is applied to obtain a new form of the wald identity to demonstrate the utility of this extension to ma processes the application of sequential tests with markov data to error probability performance analysis is investigated in particular it is demonstrated how previous work dealing with robust error probability evaluation in the presence of uncertain serial dependency can be applied to sequential tests

an asymptotically least favorable chernoff bound for a large class of dependent data processes it is desired to determine the worst case asymptotic error probability performance of a given detector operating in an environment of uncertain data dependency a class of markov data process distributions is considered which satisfy a one shift dependency bound and agree with a specified univariate distribution within this dependency contamination class the distribution structure which minimizes the exponential rate of decrease of detection error probabilities is identified this is a uniform least favorability principle because the least favorable dependency structure is the same for all bounded memoryless detectors the error probability exponential rate criterion used is a device of large deviations theory the results agree well with previous results obtained using pitman s asymptotic relative efficiency are which is a more tractable small signal performance criterion in contrast to are large deviations theory is closely related to finite sample error probabilities via the finite sample chernoff bounds and other exponentially tight bounds and other approximations

dynamic programming approach to the optimal control of systems governed by goursat darboux equations the method of dynamic programming is extended to a class of two dimensional time problems the goursat darboux systems hyperbolic systems with initial boundary data on characteristics a formal derivation of a maximum principle of pontryagin s type is obtained by using the semi dynamic programming equations controlled goursat darboux systems have applications to the probiems of gas absorption and drying processes

dynamic programming and maximum principle for discrete goursat systems abstract we obtain the dynamic programming equations for discrete goursat systems we prove that they are necessary and sufficient for optimality and we prove formulas for the exact or approximate solution of these equations using dynamic programming arguments we obtain semi dynamic programming equations and then we prove a maximum principle of pontryagin s type

a large deviations perspective on the efficiency of multilevel splitting we analyze the performance of a multilevel splitting method for rare event simulation related to one recently proposed in the telecommunications literature this method splits promising paths into subpaths at intermediate levels to increase the number of observations of a rare event in our previous paper 1997 we gave sufficient conditions in specific classes of models for this method to be asymptotically optimal here we focus on necessary conditions in a general setting we show through a variety of results the importance of choosing the intermediate thresholds in a way consistent with the most likely path to a rare set both when the number of levels is fixed and when it increases with the rarity of the event in the latter case we give very general necessary conditions based on large deviations rate functions these indicate that even when the intermediate levels are chosen appropriately the method will frequently fail to be asymptotically optimal we illustrate the conditions with examples

structural analysis of subjective categorical data a general approach to the analysis of subjective categorical data is considered in which agreement matrices of two or more raters are directly expressed in terms of error and agreement parameters the method provides focused analyses of ratings from several raters for whom ratings have measurement error distributions that may induce bias in the evaluation of substantive questions of interest each rater s judgment process is modeled as a mixture of two components an error variable that is unique for the rater in question as well as an agreement variable that operationalizes the true values of the units of observation the statistical problems of identification estimation and testing of such measurement models are discussed

hitting probabilities and large deviations let fyngn2z be a sequence of random variables in r d and let a r d then pfyn 2 a for some ng is the hitting probability of the set a by the sequence fyng we consider the asymptotic behavior as m 1 o fpfyn 2 ma some ng pfhitting mag whenever 1 the probability law of yn n satises the large deviation principle and 2 the central tendency of yn n is directed away from the given set a for a particular function i w e showpfyn 2 ma some n ge m i a

optimal control of goursat darboux systems with discontinuous co state abstract we study an optimal control problem for goursat darboux systems over domains that are more general than rectangles with costs that include integral terms supported in the two dimensional domain as well as terms with singular one dimensional and zero dimensional support we prove that the co state satisfies a system of hamiltonian equations and a set of side conditions that involves jump discontinuities across a network of characteristic curves we present a method of solution of the hamiltonian equations and in the process of doing so we establish the unique solvability of these equations

on duality in problems of optimal control described by convex differential inclusions of goursat darboux type sufficient conditions of optimality are derived for convex and non convex problems with state constraints on the basis of the apparatus of locally conjugate mappings the duality theorem is formulated and the conditions under which the direct and dual problems are connected by the duality relation are searched for

moderate deviations for empirical measures of markov chains lower bounds we obtain upper bounds for moderate deviations of empirical measures of markov chains with general state space in the topology under the minimal assumption of geometric ergodicity the regeneration split chain method and a result on projective systems are employed in the proof

large deviation bounds for functionals of viterbi paths in a number of applications the underlying stochastic process is modeled as a finite state discrete time markov chain that cannot be observed directly and is represented by an auxiliary process the maximum a posteriori map estimator is widely used to estimate states of this hidden markov model through available observations the map path estimator based on a finite number of observations is calculated by the viterbi algorithm and is often referred to as the viterbi path it was recently shown in and see also and that under mild conditions the sequence of estimators of a given state converges almost surely to a limiting regenerative process as the number of observations approaches infinity this in particular implies a law of large numbers for some functionals of hidden states and finite viterbi paths the aim of this paper is to provide the corresponding large deviation estimates

branching random walk in random environment phase transitions for local and global growth rates let n be the infinite particle system on whose evolution is as follows at each unit of time each particle independently is replaced by a new generation the size of a new generation descending from a particle at sitex has distributionf x and each of its members independently jumps to sitex 1 with probability 1 h 2 h 0 1 the sequence f x is i i d with uniformly bounded second moment and is kept fixed during the evolution the initial configuration 0 is shift invariant and ergodic two quantities are considered

uniformly integrable operators and large deviations for markov processes abstract in this paper we introduce and investigate the notion of uniformly integrable operators on l p e its relations to classical compactness and hypercontractivity are exhibited several consequences of this notion are established such as perron frobenius type theorems independence on p of the spectral radius in l p p continuity of spectral radius and especially the existence of spectral gap in the irreducible case we also present some infinitesimal criteria ensuring the uniform integrability of a positive semigroup or of its resolvent for a essentially irreducible markov process we show that the uniform integrability in l p of some type of resolvent associated with the transition semigroup implies the large deviation principle of level 3 with some rate function given by a modified donsker varadhan entropy functional we also prove that the uniform integrability condition becomes even necessary in the symmetric case finally we present several applications of our results to feynman kac semigroups to the thermodynamical limits of grand ensembles and to non symmetric markov processes given by girsanov s formula

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

nonparametric estimates of standard error the jackknife the bootstrap and other methods summary we discuss several nonparametric methods for attaching a standard error to a point estimate the jackknife the bootstrap half sampling subsampling balanced repeated replications the infinitesimal jackknife influence function techniques and the delta method the last three methods are shown to be identical all the methods derive from the same basic idea which is also the idea underlying the common parametric methods extended numerical comparisons are made for the special case of the correlation coefficient

optimal control of volterra integral equations in two independent variables we prove an extremality condition for optimal control problems for systems of integral equations of volterra type with two independent variables these systems generalize both the hyperbolic control problems in two independent variables and the optimal control of ordinary i e with one independent variable volterra integral equations

the optimal control problem in the processes described by the goursat problem for a hyperbolic equation in variable exponent sobolev spaces with dominating mixed derivatives in this paper a necessary and sufficient condition such as the pontryagin s maximum principle for an optimal control problem with distributed parameters is given by a hyperbolic equation of the second order with l p x coefficients the results can be used in the theory of optimal processes for distribution pontryagin maximum principle for various controlled processes described by hyperbolic equations of second order with discontinuous coefficients in variable exponent sobolev spaces with dominant mixed derivatives

markov additive processes i eigenvalue properties and limit theorems on etudie d un point de vue general les proprietes d existence et de regularite des valeurs propres et des fonctions propres de l operateur de feynman kac

saddlepoint approximations of the distribution of the person parameter in the two parameter logistic model large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic 2pl model in short tests however the assumption of normality can be grossly wrong as a consequence intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative methods belonging to the higher order theory more specifically saddlepoint approximations are a convenient way to deal with small sample problems confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter moreover an approximation to the exact distribution permits to compute median unbiased estimates mue that are as likely to overestimate as to underestimate the true person parameter additionally in small samples these mue are less mean biased than the often used maximum likelihood estimator

critical phenomena for sequence matching with scoring consider two independent sequences x 1 x n and y 1 y n suppose that x 1 x n are i i d x and y 1 y n are i i d y where x and y are distributions on finite alphabets x and y respectively a score f x x y r is assigned to each pair x i y j and the maximal nonaligned segment score is m n max 0 i j n 0 l 1 f x i l y j l our result is that m n log n x y a s with determined by a tractable variational formula moreover the pair empirical measure of x i l y j l during the segment where m n is achieved converges to a probability measure which is accessible by the same formula these results generalize to x i y j taking values in any polish space to intrasequence scores under shifts to long quality segments and to more than two sequences

assessing statistical accuracy in ability estimation a bootstrap approach given known item parameters the bootstrap method can be used to determine the statistical accuracy of ability estimates in item response theory through a monte carlo study the method is evaluated as a way of approximating the standard error and confidence limits for the maximum likelihood estimate of the ability parameter and compared to the use of the theoretical standard error and confidence limits developed by lord at least for short tests the bootstrap method yielded better estimates than the corresponding theoretical values

first passage time statistics for two channel diffusion we present rigorous results for the mean first passage time and first passage time statistics for two channel markov additive diffusion in a 3 dimensional spherical domain inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes which is shown to effect a non trivial first passage behaviour we also address the scenario of intermittent immobilisation in both cases we prove that despite the perfectly non recurrent motion of two channel markov additive diffusion in 3 dimensions the first passage statistics at long times do not display poisson like behaviour if none of the phases has a vanishing diffusion coefficient this stands in stark contrast to the standard one channel markov diffusion counterpart we also discuss the relevance of our results in the context of cellular signalling

approximation of partial sums of arbitrary i i d random variables and the precision of the usual exponential upper bound this paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary i i d random variables the introduction of a single truncation allows the usual exponential upper bound to apply usefully whenever the summands are arbitrary i i d random variables more specifically let n be a fixed natural number and let z z 1 z 2 z n be arbitrary i i d random variables we construct a function f z n derived from the probability of occurrence of one or more large summands plus an upper bound of exponential type such that for some constant c 0 independent of z n and a and all real a c f z 2 n a formula math zj na 2f z n a furthermore examples show that the upper and lower bounds are achievable

large deviations theory and efficient simulation of excessive backlogs in a gi gi m queue the problem of using importance sampling to estimate the average time to buffer overflow in a stable gi gi m queue is considered using the notion of busy cycles estimation of the expected time to buffer overflow is reduced to the problem of estimating p sub n p buffer overflow during a cycle where n is the buffer size the probability p sub n is a large deviations probability p sub n vanishes exponentially fast as n to infinity a rigorous analysis of the method is presented it is demonstrated that the exponentially twisted distribution of s parekh and j walrand 1989 has the following strong asymptotic optimality property within the nonparametric class of all gi gi importance sampling simulation distributions as n to infinity the computational cost of the optimal twisted distribution of large deviations theory grows less than exponentially fast and conversely all other gi gi simulation distributions incur a computational cost that grows with strictly positive exponential rate

unbiased estimators of ability parameters of their variance and of their parallel forms reliability given known item parameters unbiased estimators are derived i for an examinee s ability parameter and for his proportion correct true score ii for the variances of and across examinees in the group tested and iii for the parallel forms reliability of the maximum likelihood estimator hat theta

a note on the jackknife the bootstrap and the delta method estimators of bias and variance three methods for the nonparametric reduction of bias and estimation of variance are in common use the jackknife the delta method i e the method of statistical differentials and the bootstrap in recent work efron 1981 a b 1982 has compared these three methods numerically for the case of the sample correlation coefficient for present purposes we define the procedures as follows consider a statistic tn thought of as an estimator of an unknown parameter 0 we wish to study the possibility of bias reduction by estimating the bias and subtracting off the estimate and variance estimation for g tj considered as an estimator of g 0 throughout we assume that we observe x1 xn independent and identically distributed with common cumulative distribution function f let tn denote the abovementioned statistic computed based on x1 xn we assume tn to be symmetric in its arguments furthermore let t 1 denote the above mentioned statistic computed based upon the sample of size n 1 consisting of x1 xi1 xi 1 xn the jackknife estimator of the bias of g tn is then given as b n n 1 1 g t 1 g tn n and the jackknife variance estimator is just

some monotonicity properties of schur powers of matrices and related inequalities abstract a series of inequalities are developed relating the spectral radius a b of the schur product a b of two nonnegative matrices a and b with those of a a and b b yielding a b a a b b 1 2 as a corollary it is proved that the spectral radius of the schur powers r a r a r a a a r factors satisfies 1 r log r is decreasing while 1 r 1 log r is increasing the latter provided a is a stochastic matrix the entropy of a finite stationary markov chain is identified with d r dr r 1 a number of majorization comparisons for the spectral radius of schur powers is given

markov additive processes and perron frobenius eigenvalue inequalities we present a method for proving perron frobenius eigenvalue inequalities the method is to apply jensen s inequality to the change in a random evolution over a regenerative cycle of the underlying finite state markov chain one of the primary benefits of the method is that it readily gives necessary and sufficient conditions for strict inequality it also gives insights into some of the conjectures of j e cohen ney and nummelin s hypothesis 2 arises here as a condition for strict inequality and we explore its ramifications in detail for a special family of markov additive processes which we call fluid models this leads to a connection between hypothesis 2 and the condition p t p irreducible which arose in the work of cohen friedland kato and kelly

erdős renyi laws for gibbs measures can one detect a phase transition from a single large sample of a gibbs measure what information does one get on the other gibbs distributions with the same potential we approach these questions via erd s renyi laws in particular we prove almost sure limit theorems for sets of empirical distributions of sub samples of the given one for suitable sub samples size this set converges to the set of stationary gibbs measures moreover we formulate erd s renyi laws for general families of random variables with suitable large deviation principles

rate tilting for fast simulation of level phase processes abstract this paper study the efficient simulation methods for estimating some metrics that depend heavily on a certain rarely occurring event the process considered is the so called level phase process a markov process in which the level and the phase are two state variables furthermore changes of level and phase are induced by events which have rates that are independent of the level except at a boundary if a system typically stays at lower levels then reaching a high level n is a rare event thus direct simulation for the related metrics is very inefficient we change the events rates in a level phase process to accelerate simulation and find from simulation the so called hitting probability the probability of entering a rare event set this method is called rate tilting and in our approach a proper construct of rate tilting relates to a generalized eigenvalue problem involving the infinitesimal generator matrix of the process being considered we can show that the relative estimation error of the hitting probability resulting from the proposed simulation remains bounded as the level increases provided that the boundary set of the state space satisfies certain conditions if these conditions are met rate tilting will be advantageous