discounted dynamic programming with unbounded returns application to economic models in this paper we study discounted markov decision processes on an uncountable state space we allow a utility reward function to be unbounded both from above and below a new feature in our approach is an easily verifiable rate of growth condition introduced for a positive part of the utility function this assumption in turn enables us to prove the convergence of a value iteration algorithm to a solution to the bellman equation moreover by virtue of the optimality equation we show the existence of an optimal stationary policy

uniform fatou s lemma abstract fatou s lemma is a classic fact in real analysis stating that the limit inferior of integrals of functions is greater than or equal to the integral of the inferior limit this paper introduces a stronger inequality that holds uniformly for integrals on measurable subsets of a measurable space the necessary and sufficient condition under which this inequality holds for a sequence of finite measures converging in total variation is provided this statement is called the uniform fatou lemma and it holds under the minor assumption that all the integrals in the inequality are well defined the uniform fatou lemma improves the classic fatou lemma in the following directions the uniform fatou lemma states a more precise inequality it provides the necessary and sufficient condition and it deals with variable measures various corollaries of the uniform fatou lemma are formulated the examples in this paper demonstrate that a the uniform fatou lemma may indeed provide a more accurate inequality than the classic fatou lemma b the uniform fatou lemma does not hold if convergence of measures in total variation is relaxed to setwise convergence

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

nonstationary discrete time deterministic and stochastic control systems bounded and unbounded cases this paper is about nonstationary nonlinear discrete time deterministic and stochastic control systems with borel state and control spaces with either bounded or unbounded costs the control problem is to minimize an infinite horizon total cost performance index using dynamic programming arguments we show that under suitable assumptions the optimal cost functions satisfy optimality equations which in turn give a procedure to find optimal control policies we also prove the convergence of value iteration or successive approximations functions several examples illustrate our results under different sets of assumptions

adjusted score tests of homogeneity for poisson processes abstract tests of homogeneity are being increasingly used for the analysis of event time data but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes here we consider tests of homogeneity for recurrent event data in which the null model is a poisson process and the alternative is a mixed poisson process we examine score and adjusted score statistics in the context of parametric and semiparametric regression models where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic we report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power we also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples but the adjusted score test based on a piecewise exponential model has satisfactory performance the latter thus prov

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

existence and uniqueness of solutions to the bellman equation in the unbounded case we study the problem of the existence and uniqueness of solutions to the bellman equation in the presence of unbounded returns we introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space and on the application of some metric fixed point theorems with appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions furthermore the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models it is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the bellman operator

estimation of reliability in field performance studies likelihood based methods are developed for the analysis of field performance studies with particular attention centered on the estimation of regression coefficients in parametric models failure record data are those in which the time to failure and the regressor variables are observed only for those items that fail in some prespecified follow up or warranty period 0 t it is noted that for satisfactory inference about baseline failure rates or regression effects it is usually necessary to supplement the failure record data either by incorporating specific prior information about x or by taking a supplementary sample of items that survive t general methods are outlined and specific formulas for various likelihood based methods are obtained when the failure time model is exponential or weibull in these models the methods are compared with respect to asymptotic efftciency of estimation several extensions to more complicated sampling plans are considered

constrained markov decision models with weighted discounted rewards this paper deals with constrained optimization of markov decision processes both objective function and constraints are sums of standard discounted rewards but each with a different discount factor such models arise e g in production and in applications involving multiple time scales we prove that it a feasible policy exists then there exists an optimal policy which is i stationary nonrandomized from some step onward ii randomized markov before this step but the total number of actions which are added by randomization is bounded by the number of constraints optimality of such policies for multi criteria problems is also established these new policies have the pleasing aesthetic property that the amount of randomization they require over any trajectory is restricted by the number of constraints this result is new even for constrained optimization with a single discount factor where the optimality of randomized stationary policies is known however a randomized stationary policy may req

markov decision processes with iterated coherent risk measures this paper considers a markov decision process in borel state and action spaces with the aggregated or say iterated coherent risk measure to be minimised for this problem we establish the bellman optimality equation as well as the value and policy iteration algorithms and show the existence of a deterministic stationary optimal policy the cost function while being allowed to be unbounded from below in the sense that its negative part needs be bounded by some nonnegative real valued possibly unbounded weight function can be arbitrarily unbounded from above and possibly infinitely valued

nonatomic total rewards markov decision processes with multiple criteria we consider a markov decision process with an uncountable state space for which the vector performance functional has the form of expected total rewards under the single condition that initial distribution and transition probabilities are nonatomic we prove that the performance space coincides with that generated by nonrandomized markov policies we also provide conditions for the existence of optimal policies when the goal is to maximize one component of the performance vector subject to inequality constraints on other components we illustrate our results with examples of production and financial problems

nonparametric estimation with recurrent event data the problem of nonparametric estimation for the distribution function governing the time to occurrence of a recurrent event in the presence of censoring is considered we derive nelson aalen and kaplan meier type estimators for the distribution function and establish their respective finite sample and asymptotic properties we allow for random observation periods for each subject under study and explicitly account for the informative sum quota nature of the data accrual scheme these allowances complicate technical matters considerably and in particular invalidate the direct use of martingale methods consistency and weak convergence of our estimators are obtained by extending an approach due to sellke who considered a single renewal process i e recurrent events on a single subject observed over an infinite time period a useful feature of the present analysis is that strong parallels are drawn to the usual single event setting providing a natural route toward developing extensions that involve

maximum rate transmission with improved diversity gain for interference networks interference alignment ia was shown to be effective for interference management in improving transmission rate in terms of the degree of freedom dof gain on the other hand orthogonal space time block codes were widely used in point to point multiantenna channels to enhance transmission reliability in terms of the diversity gain in this paper we connect these two ideas i e ia and space time block coding to improve the designs of alignment precoders for multiuser networks specifically we consider the use of alamouti codes for ia because of their rate one transmission and achievability of full diversity in point to point systems the alamouti codes protect the desired link by introducing orthogonality between the two symbols in one alamouti codeword and create alignment at the interfering receiver we show that the proposed alignment methods can maintain the maximum dof gain and improve the ergodic mutual information in the long term regime while increasing the diversity gain to 2 in the short term regime the presented examples of interference networks have two antennas at each node and include the two user x channel the interfering multiaccess channel and the interfering broadcast channel

robust optimal control using conditional risk mappings in infinite horizon abstract we use one step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled markov process in discrete time infinite horizon the nonnegative one step costs are assumed to be lower semi continuous but not necessarily bounded we derive the conditions for the existence of the optimal strategies and solve the problem explicitly by giving the robust dynamic programming equations under very mild conditions we further give an optimal approximation to the solution and illustrate our algorithm in two examples of optimal investment and lq regulator problems

berge s theorem for noncompact image sets abstract for an upper semi continuous set valued mapping from one topological space to another and for a lower semi continuous function defined on the product of these spaces berge s theorem states lower semi continuity of the minimum of this function taken over the image sets it assumes that the image sets are compact for hausdorff topological spaces this paper extends berge s theorem to set valued mappings with possible noncompact image sets and studies relevant properties of minima

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

space time processing for x channels using precoders in this paper we investigate how to send space time codes with full diversity and low decoding complexity for x channels using precoders first we assume that we have 2 transmitters and 2 receivers each transmitter sends different codewords to each receiver at the same time we propose an orthogonal transmission scheme that combines space time block coding and array processing to achieve low complexity decoding and full diversity for transmitted signals to our best knowledge this is the first scheme which can achieve low complexity decoding and full diversity for any transmitted codeword in x channel when all the users transmit at the same time finally we show that under certain conditions our proposed scheme can be extended to a general case with any number of transmitters and receivers each with any number of antennas simulation results validate our theoretical analysis

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

residuals in generalized linear models abstract generalized linear models are regression type models for data not normally distributed appropriately fitted by maximum likelihood rather than least squares typical examples are models for binomial or poisson data with a linear regression model for a given ordinarily nonlinear function of the expected values of the observations use of such models has become very common in recent years and there is a clear need to study the issue of appropriate residuals to be used for diagnostic purposes several definitions of residuals are possible for generalized linear models the statistical package glim baker and nelder 1978 routinely prints out residuals where v is the function relating the variance to the mean of y and is the maximum likelihood estimate of the ith mean as fitted to the regression model these residuals are the signed square roots of the contributions to the pearson goodness of fit statistic another choice of residual is the signed square root of the contribution to the devia

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

estimation of rate and mean functions from truncated recurrent event data abstract this article investigates data on recurrent events that arise from sources such as warranty claims where the observation period for a unit is unknown until it experiences at least one event this creates a type of truncation in the data we consider nonparametric estimation of means and rates of the event occurrences with such zero truncated data and examine the case where the population size and the distribution of observation times across units are at least approximately known we study the behaviors of the proposed estimators by simulation we examine some car warranty data by applying the methodology developed here and considering the underlying assumptions

convergence of dynamic programming models weak conditions are presented for approximating dynamic programming models for a sequence of these models continuous convergence of the sequence of associated optimal value functions is obtained under the condition that state and action space converge in the sense of kuratowski and that the mappings of admissible actions as well as the transition law the discount factors and the reward functions converge continuously further a relation for the associated sets of optimal actions is given the analysis is based on results about convergence preserving properties of supremum value functions and integrals the approximation results are extended to so called upper semi continuous convergent sequences and are related to discretization procedures by using projections

constrained discounted dynamic programming this paper deals with constrained optimization of markov decision processes with a countable state space compact action sets continuous transition probabilities and upper semicontinuous reward functions the objective is to maximize the expected total discounted reward for one reward function under several inequality constraints on similar criteria with other reward functions suppose a feasible policy exists for a problem with m constraints we prove two results on the existence and structure of optimal policies first we show that there exists a randomized stationary optimal policy which requires at most m actions more than a nonrandomized stationary one this result is known for several particular cases second we prove that there exists an optimal policy which is i stationary nonrandomized from some step onward ii randomized markov before this step but the total number of actions which are added by randomization is at most m iii the total number of actions that are added by nonstationarity is at most m we also establish pareto optimality of policies from the two classes described above for multi criteria problems we describe an algorithm to compute optimal policies with properties i iii for constrained problems the policies that satisfy properties i iii have the pleasing aesthetic property that the amount of randomization they require over any trajectory is restricted by the number of constraints in contrast a randomized stationary policy may require an infinite number of randomizations over time

partly functional temporal process regression with semiparametric profile estimating functions summary marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models recent work on fully functional temporal process regression tpr offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying the existing esti mation procedure however prevents successive goodness of fit test for covariate coefficients in comparing a sequence of nested models this article proposes a partly functional tpr model in the line of marginal mean models some covari ate effects are time independent while others are completely unspecified in time this class of models is very rich includ ing the fully functional model and the semiparametric model as special cases to estimate the parameters we propose semiparametric profile estimating equations which are solved via an iterative algorithm starting at a consistent estimate from a fully functional model in the existing work no smoothing is needed in contrast to other varying coefficient meth ods the weak convergence of the resultant estimators are developed using the empirical process theory successive tests of time varying effects and backward model selection procedure can then be carried out the practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients

nonstationary discrete time deterministic and stochastic control systems with infinite horizon this article is about nonstationary nonlinear discrete time deterministic and stochastic control systems with borel state and control spaces possibly noncompact control constraint sets and unbounded costs the control problem is to minimise an infinite horizon total cost performance index using dynamic programming arguments we show that under suitable assumptions the optimal cost functions satisfy optimality equations which in turn give a procedure to find optimal control policies

a convex analytic approach to markov decision processes this paper develops a new framework for the study of markov decision processes in which the control problem is viewed as an optimization problem on the set of canonically induced measures on the trajectory space of the joint state and control process this set is shown to be compact convex one then associates with each of the usual cost criteria infinite horizon discounted cost finite horizon control up to an exit time a naturally defined occupation measure such that the cost is an integral of some function with respect to this measure these measures are shown to form a compact convex set whose extreme points are characterized classical results about existence of optimal strategies are recovered from this and several applications to multicriteria and constrained optimization problems are briefly indicated

super orthogonal space time trellis codes we introduce a new class of space time codes called super orthogonal space time trellis codes these codes combine set partitioning and a super set of orthogonal space time block codes in a systematic way to provide full diversity and improved coding gain over earlier space time trellis code constructions we also study the optimality of our set partitioning and provide coding gain analysis codes operating at different rates up to the highest theoretically possible rate for different number of states can be designed by using our optimal set partitioning super orthogonal space time trellis codes can provide a tradeoff between rate and coding gain simulation results show more than 2 db improvements over the codes presented in the literature while providing a systematic design methodology

degrees of freedom region of the mimo x channel we provide achievability as well as converse results for the degrees of freedom region of a multiple input multiple output mimo x channel i e a system with two transmitters two receivers each equipped with multiple antennas where independent messages need to be conveyed over fixed channels from each transmitter to each receiver the inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message with m 1 antennas at each node we find that the total sum rate degrees of freedom are bounded above and below as 1 les eta x les 4 3 if m 1 and channel matrices are nondegenerate then the precise degrees of freedom eta x 4 3 m thus the mimo x channel has noninteger degrees of freedom when m is not a multiple of 3 simple zero forcing without dirty paper encoding or successive decoding suffices to achieve the 4 3 m degrees of freedom if the channels vary with time frequency then the channel with single antennas m 1 at all nodes has exactly 4 3 degrees of freedom the key idea for the achievability of the degrees of freedom is interference alignment i e signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired we also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio

towards a general asymptotic theory for cox model with staggered entry a general asymptotic theory is established for the two parameter cox score process with staggered entry data it extends in several directions the existing theory developed by sellke and siegmund slud and gu and lai an essential tool employed here is a modern empirical process theory as elucidated in a recent monograph by pollard

constrained discounted markov decision processes with borel state spaces abstract we study discrete time discounted constrained markov decision processes cmdps with borel state and action spaces these cmdps satisfy either weak w continuity conditions that is the transition probability is weakly continuous and the reward function is upper semicontinuous in state action pairs or setwise s continuity conditions that is the transition probability is setwise continuous and the reward function is upper semicontinuous in actions our main goal is to study models with unbounded reward functions which are often encountered in applications e g in consumption investment problems we provide some general assumptions under which the optimization problems in cmdps are solvable in the class of randomized stationary policies and in the class of chattering policies introduced in this paper if the initial distribution and transition probabilities are atomless then using a general purification result of feinberg and piunovskiy we show the existence of a deterministic stationary optimal policy our main results are illustrated by examples

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

ergodic control of markov chains with constraints the general case the problem of controlling a markov chain on a countable state space with ergodic or long run average cost is studied in the presence of additional constraints requiring finitely many say m other ergodic costs to satisfy prescribed bounds under extremely general conditions it is proved that an optimal stationary randomized strategy can be found that requires at most m randomizations this generalizes a result of ross

the warranty problem its statistical and game theoretic aspects manufacturers of consumer products such as automobiles usually offer warranties guaranteeing the product or its parts for example for five years or 50 000 miles whichever comes first there are at least two issues of interest to applied mathematicians and statisticians that arise from warranty considerations the first is the specification of an optimum price warranty combination and the second is the forecast of a reserve fund to meet warranty claims against the product the former involves a consideration of the item s reliability its rate of usage the consumer s attitude toward a specific warranty and the competitor s actions all of which lead towards a game theoretic formulation of the problem the latter involves the analysis of a special kind of time series in two dimensions for which the use of dynamic linear models appears to be natural this is an expository paper due to the timeliness of the topic the focus here is on problem definition its scope and its formulation in a manner th

interference alignment with diversity for the 2 times 2 x network with four antennas a transmission scheme based on the alamouti code which we call the li jafarkhani jafar ljj scheme was recently proposed for the 2 times 2 x network i e two transmitter tx two receiver x network with two antennas at each node this scheme was claimed to achieve a sum degrees of freedom dof of 8 3 and also a diversity gain of two when fixed finite constellations are employed at each tx furthermore each tx required the knowledge of only its own channel unlike the jafar shamai scheme which required global csit to achieve the maximum possible sum dof of 8 3 in this paper we extend the ljj scheme to the 2 times 2 x network with four antennas at each node the proposed scheme also assumes only local channel knowledge at each tx we prove that the proposed scheme achieves the maximum possible sum dof of 16 3 in addition we also prove that using any fixed finite constellation with appropriate rotation at each tx the proposed scheme achieves a diversity gain of at least four

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

dynamic programming equations for discounted constrained stochastic control in this paper the application of the dynamic programming approach to constrained stochastic control problems with expected value constraints is demonstrated specifically two such problems are analyzed using this approach the problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint and the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint using the dynamic programming approach optimality equations which are the chief contribution of this paper are obtained for these problems in particular the dynamic programming operators for problems with expectation constraints differ significantly from those of standard dynamic programming and problems with worst case constraints for the discounted cost infinite horizon cases existence and uniqueness of solutions to the dynamic programming equations are explicitly shown by using the banach fixed point theorem to show that the corresponding dynamic programming operators are contractions the theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems the example problems are based on a two state markov model that represents an error prone system that is to be maintained

more risk sensitive markov decision processes we investigate the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite horizon that is generated by a markov decision process mdp in contrast to a risk neutral decision maker this optimization criterion takes the variability of the cost into account it contains as a special case the classical risk sensitive optimization criterion with an exponential utility we show that this optimization problem can be solved by an ordinary mdp with extended state space and give conditions under which an optimal policy exists in the case of an infinite time horizon we show that the minimal discounted cost can be obtained by value iteration and can be characterized as the unique solution of a fixed point equation using a sandwich argument interestingly it turns out that in the case of a power utility the problem simplifies and is of similar complexity than the exponential utility case however has not been treated in the literature so far we also establish the validity and convergence of the policy improvement method a simple numerical example namely the classical repeated casino game is considered to illustrate the influence of the certainty equivalent and its parameters finally the average cost problem is also investigated surprisingly it turns out that under suitable recurrence conditions on the mdp for convex power utility the minimal average cost does not depend on the parameter of the utility function and is equal to the risk neutral average cost this is in contrast to the classical risk sensitive criterion with exponential utility

estimating a distribution function with truncated data let mathscr p be a finite population with n geq 1 elements for each e in mathscr p let x e and y e be independent positive random variables with unknown distribution functions f and g and suppose that the pairs x e y e are i i d we consider the problem of estimating f g and n when the data consist of those pairs x e y e for which e in mathscr p and y e leq x e the nonparametric maximum likelihood estimators mles of f and g are described and their asymptotic properties as n rightarrow infty are derived it is shown that the mles are consistent against pairs f g for which f and g are continuous g 1 0 leq f 1 0 and g 1 1 leq f 1 1 sqrt n times estimation error for f converges in distribution to a gaussian process if int infty 0 1 g df infty but may fail to converge if this integral is infinite

four group decodable space time block codes two new rate one full diversity space time block codes stbcs are proposed they are characterized by the lowest decoding complexity among the known rate one stbc arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection the first and the second codes are delay optimal if the number of transmit antennas is a power of 2 and even respectively the exact pairwise error probability is derived to allow for the performance optimization of the two codes compared with existing low decoding complexity stbc the two new codes offer several advantages such as higher code rate lower encoding decoding delay and complexity lower peak to average power ratio and better performance

methods for the analysis and prediction of warranty claims this article discusses methods whereby reports of warranty claims can be used to estimate the expected number of warranty claims per unit in service as a function of the time in service these methods provide estimates that are adjusted for delays or lags corresponding to the time from the claim until it is entered into the data base used for analysis forecasts of the number and cost of claims on the population of all units in service are also developed along with standard errors for these forecasts the methods are based on a log linear poisson model for numbers of warranty claims both the case of a known distribution of reporting lag and simultaneous estimation of that distribution are considered the use of residuals for model checking extensions to allow for extra poisson variation and the estimation of warranty costs are also considered

risk averse dynamic programming for markov decision processes we introduce the concept of a markov risk measure and we use it to formulate risk averse control problems for two markov decision models a finite horizon model and a discounted infinite horizon model for both models we derive risk averse dynamic programming equations and a value iteration method for the infinite horizon problem we develop a risk averse policy iteration method and we prove its convergence we also propose a version of the newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence finally we discuss relations to min max markov decision models

existence and uniqueness of a fixed point for local contractions this paper proves the existence and uniqueness of a fixed point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1 more importantly it shows how this fixed point result can apply to study the existence and uniqueness of solutions to some recursive equations that arise in economic dynamics

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

marginal likelihood and unit roots we develop new tests for the hypothesis of unit roots that are based on the marginal likelihood of the general linear model the marginal likelihood allows the incorporation of invariance arguments in the likelihood function it turns out that marginal likelihood tests for unit roots appear to be more powerful than other unit root tests for some basic models power functions almost coincide with the power envelopes even in small samples general correlation structures can be incorporated either by standard likelihood procedures or by adjustments of the test statistics on the basis of asymptotic distributions

multiple objective nonatomic markov decision processes with total reward criteria we consider a markov decision process with an uncountable state space and multiple rewards for each policy its performance is evaluated by a vector of total expected rewards under the standard continuity assumptions and the additional assumption that all initial and transition probabilities are nonatomic we prove that the set of performance vectors for all policies is equal to the set of performance vectors for nonrandomized markov policies this result implies the existence of optimal nonrandomized markov policies for nonatomic constrained markov decision processes with total rewards we provide two examples of applications of our results to constrained multiple objective problems in inventory control and finance

splitting randomized stationary policies in total reward markov decision processes this paper studies a discrete time total reward markov decision process mdp with a given initial state distribution a randomized stationary policy can be split on a given set of states if the occupancy measure of this policy can be expressed as a convex combination of the occupancy measures of stationary policies each selecting deterministic actions on the given set and coinciding with the original stationary policy outside of this set for a stationary policy necessary and sufficient conditions are provided for splitting it at a single state as well as sufficient conditions for splitting it on the whole state space these results are applied to constrained mdps the results are refined for absorbing including discounted mdps with finite state and actions spaces in particular this paper provides an efficient algorithm that presents the occupancy measure of a given policy as a convex combination of the occupancy measures of finitely many stationary deterministic policies this algorithm generates the splitting policies in a way that each pair of consecutive policies differs at exactly one state the results are applied to constrained problems to efficiently compute an optimal policy by computing and splitting a stationary optimal policy

risk sensitive markov control processes we introduce a general framework for measuring risk in the context of markov control processes with risk maps on general borel spaces that generalize known concepts of risk measures in mathematical finance operations research and behavioral economics within the framework applying weighted norm spaces to incorporate unbounded costs also we study two types of infinite horizon risk sensitive criteria discounted total risk and average risk and solve the associated optimization problems by dynamic programming for the discounted case we propose a new discount scheme which is different from the conventional form but consistent with the existing literature while for the average risk criterion we state lyapunov like stability conditions that generalize known conditions for markov chains to ensure the existence of solutions to the optimality equation