patrolling a perimeter abstract in this paper we study the problem of patrolling a perimeter the general situation considered here can correspond to different tactical problems and it is studied from the point of view of game theory to put the ideas in a context we describe it as follows an intruder seeks to carry out a sabotage on the perimeter of a protected zone he has to perform the action along n consecutive days and has to position himself each day at one of m strategic points placed on this border the first day he can take his place at any of the m points but on successive days he can move only to adjacent points furthermore the perimeter is protected by a patroller who will select each day one of the m points to inspect the strategic situation is modeled as a two person zero sum game which is developed on a cyclic set of m points over n time units we prove some interesting properties of the strategies solve the game in closed form under certain constraints and obtain bounds for the value of the game in several non solved cases

the strong law under random truncation the random truncation model is defined by the conditional probability distribution h x y p x x y y x y where x and y are independent random variables a problem of interest is the estimation of the distribution function f of x with data from the distribution h under random truncation f need not be fully identifiable from h and only a part of it say f 0 is we show that the nonparametric mle f n of f 0 obeys the strong law of large numbers in the sense that for any nonnegative measurable function o x the integrals o x df n x o x df 0 x almost surely as n tends to infinity similar results were first obtained by stute and wang for the right censoring model the results are useful in establishing the strong consistency of various estimates some of our results are derived from the weak consistency of f n obtained by woodroofe

nonparametric estimation for length biased and right censored data this paper considers survival data arising from length biased sampling where the survival times are left truncated by uniformly distributed random truncation times we propose a nonparametric estimator that incorporates the information about the length biased sampling scheme the new estimator retains the simplicity of the truncation product limit estimator with a closed form expression and has a small efficiency loss compared with the nonparametric maximum likelihood estimator which requires an iterative algorithm moreover the asymptotic variance of the proposed estimator has a closed form and a variance estimator is easily obtained by plug in methods numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors a data analysis of the canadian study of health and aging is conducted to illustrate the methods and theory

asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

two way unary automata versus logarithmic space we show that if l nl the classical logarithmic space classes then each unary 2nfa a two way nondeterministic finite automaton can be converted into an equivalent 2dfa a deterministic two way automaton keeping the number of states polynomial unlike other results of this kind here the deterministic simulation is valid for inputs of all lengths not only polynomially long ones this shows a connection between the standard logarithmic space complexity and the state complexity of two way unary automata it indicates that l could be separated from nl by proving a superpolynomial gap in the number of states for the conversion from unary 2nfas to 2dfa moreover without any unproven assumptions we show that each n state unary 2nfa can be simulated by an equivalent 2ufa an unambiguous 2nfa with a polynomial number of states

nonparametric estimation of a delay distribution based on left censored and right truncated data this paper proposes a nonparametric method for estimating a delay distribution based on left censored and right truncated data a variance covariance estimator is provided the method is applied to the australian aids data in which some data are left censored and some data are not left censored this situation arises with aids case reporting data in australia because reporting delays were recorded only from november 1990 rather than from the beginning of the epidemic there it is shown that inclusion of the left censored data as opposed to analyzing only the uncensored data improves the precision of the estimate

a unified approach to semiparametric transformation models under general biased sampling schemes we propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes the new estimator is obtained from a set of counting process based unbiased estimating equations developed through introducing a general weighting scheme that offsets the sampling bias the usual asymptotic properties including consistency and asymptotic normality are established under suitable regularity conditions a closed form formula is derived for the limiting variance and the plug in estimator is shown to be consistent we demonstrate the unified approach through the special cases of left truncation length bias the case cohort design and variants thereof simulation studies and applications to real datasets are presented

stochastic network interdiction using limited assets an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow we formulate and solve a stochastic version of the interdictor s problem minimize the expected maximum flow through the network when interdiction successes are binary random variables extensions are made to handle uncertain arc capacities and other realistic variations these two stage stochastic integer programs have applications to interdicting illegal drugs and to reducing the effectiveness of a military force moving materiel troops information etc through a network in wartime two equivalent model formulations allow jensen s inequality to be used to compute both lower and upper bounds on the objective and these bounds are improved within a sequential approximation algorithm successful computational results are reported on networks with over 100 nodes 80 interdictable arcs and 180 total arcs

regression models for the restricted residual mean life for right censored and left truncated data the hazard ratios resulting from a cox s regression hazards model are hard to interpret and to be converted into prolonged survival time as the main goal is often to study survival functions there is increasing interest in summary measures based on the survival function that are easier to interpret than the hazard ratio the residual mean time is an important example of those measures however because of the presence of right censoring the tail of the survival distribution is often difficult to estimate correctly therefore we consider the restricted residual mean time which represents a partial area under the survival function given any time horizon and is interpreted as the residual life expectancy up to of a subject surviving up to time t we present a class of regression models for this measure based on weighted estimating equations and inverse probability of censoring weighted estimators to model potential right censoring furthermore we show how to extend the models and the estimators to deal with delayed entries we demonstrate that the restricted residual mean life estimator is equivalent to integrals of kaplan meier estimates in the case of simple factor variables estimation performance is investigated by simulation studies using real data from danish monitoring cardiovascular risk factor surveys we illustrate an application to additive regression models and discuss the general assumption of right censoring and left truncation being dependent on covariates copyright 2017 john wiley sons ltd

descriptional complexity of unambiguous input driven pushdown automata it is known that a nondeterministic input driven pushdown automaton idpda a k a visibly pushdown automaton a k a nested word automaton with n states can be transformed to an equivalent deterministic automaton with 2 n 2 states b von braunmuhl and r verbeek 1983 8 and that this size is necessary in the worst case r alur and p madhusudan 2009 4 this paper demonstrates that the same worst case 2 n 2 size blow up occurs when converting a nondeterministic idpda to an unambiguous one and an unambiguous idpda to a deterministic one in addition the methods developed in this paper are used to demonstrate that the descriptional complexity of complementation for nondeterministic idpdas is 2 n 2 and that the descriptional complexity of homomorphisms for deterministic idpdas is 2 n 2

nonparametric estimation of transition probabilities for a general progressive multi state model under cross sectional sampling nonparametric estimation of the transition probability matrix of a progressive multi state model is considered under cross sectional sampling two different estimators adapted to possibly right censored and left truncated data are proposed the estimators require full retrospective information before the truncation time which when exploited increases efficiency they are obtained as differences between two survival functions constructed for sub samples of subjects occupying specific states at a certain time point both estimators correct the oversampling of relatively large survival times by using the left truncation times associated with the cross sectional observation asymptotic results are established and finite sample performance is investigated through simulations one of the proposed estimators performs better when there is no censoring while the second one is strongly recommended with censored data the new estimators are applied to data on patients in intensive care units icus

optimization of convex risk functions we consider optimization problems involving convex risk functions by employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models and optimality and duality theory for problems with convex risk functions

analysis of restricted mean survival time for length biased data summary in clinical studies with time to event outcomes the restricted mean survival time rmst has attracted substantial attention as a summary measurement for its straightforward clinical interpretation when the data are subject to length biased sampling which is frequently encountered in observational cohort studies existing methods to estimate the rmst are not applicable in this article we consider nonparametric and semiparametric regression methods to estimate the rmst under the setting of length biased sampling to assess the covariate effects on the rmst a semiparametric regression model that directly relates the covariates and the rmst is assumed based on the model we develop unbiased estimating equations to obtain consistent estimators of covariate effects by properly adjusting for informative censoring and length bias stochastic process theories are used to establish the asymptotic properties of the proposed estimators we investigate the finite sample performance through simulations and illustrate the methods by analyzing a prevalent cohort study of dementia in canada

analyzing multiple cross sectional samples with application to hospitalization time after surgeries repeated cross sectional sampling results in multiple biased samples with possibly different weight functions the standard non parametric maximum likelihood estimator for the lifetime distribution of interest solves a set of nonlinear equations and its variance has a very complicated form we suggest a simple closed form estimator for the case where entrances to the population of interest follow a poisson model the variance of the estimator and confidence intervals are easily calculated our motivating example concerns a series of cross sectional surveys conducted in israeli hospitals we discuss the bias mechanism in our data and suggest a simple design plan that provides valid estimators even when the weight functions are unknown the new method is applied to estimate the distribution of hospitalization time after bowel and hernia surgeries copyright 2015 john wiley sons ltd

nonparametric incidence estimation from prevalent cohort survival data incidence is an important epidemiological concept most suitably studied using an incident cohort study however data are often collected from the more feasible prevalent cohort study whereby diseased individuals are recruited through a cross sectional survey and followed in time in the absence of temporal trends in survival we derive an efficient nonparametric estimator of the cumulative incidence based on such data and study its asymptotic properties arbitrary calendar time variations in disease incidence are allowed age specific incidence and adjustments for both stratified sampling and temporal variations in survival are also discussed simulation results are presented and data from the canadian study of health and aging are analysed to infer the incidence of dementia in the canadian elderly population

on the degree of ambiguity of finite automata we investigate the ambiguity behavior of finite automata in connection with their inner structure we show that the degree of ambiguity of a finitely ambiguous nondeterministic finite automaton nfa with n states is at most 5n2 nn there is a simple criterion which characterizes the infinite degree of ambiguity of an nfa and which is decidable in polynomial time the degree of growth of the ambiguity of an nfa is computable in polynomial time starting from the first result we discuss the maximal finite degree of ambiguity of an nfa with n states and we present subclasses of nfas where this quantity is of order 2 n

communication complexity method for measuring nondeterminism in finite automata while deterministic finite automata seem to be well understood surprisingly many important problems concerning nondeterministic finite automata nfa s remain open one such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata in this paper the concept of communication complexity is applied in order to achieve progress in this problem area the main results are as follows 1 deterministic communication complexity provides lower bounds on the size of nfa s with bounded unambiguity applying this fact the proofs of several results about nfa s with limited ambiguity can be simplified and presented in a uniform way 2 there is a family of languages konk2 with an exponential size gap between nfa s with polynomial leaf number ambiguity and nfa s with ambiguity k this partially provides an answer to the open problem posed by b ravikumar and o ibarra 1989 siam j comput 18 1263 1282 and h leung 1998 siam j comput 27 1073 1082

nonparametric estimation for right censored length biased data a pseudo partial likelihood approach to estimate the lifetime distribution of right censored length biased data we propose a pseudo partial likelihood approach that allows us to derive two nonparametric estimators with its closed form estimators and explicit limiting variances this approach retains the simplicity of conditional analysis and has only a small efficiency loss compared with the unconditional analysis under some regularity conditions we show that the two estimators are uniformly consistent and converge weakly to gaussian processes a simulation study demonstrates that the proposed estimators have satisfactory finite sample performance application to an alzheimer s disease study is reported

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

multiplicative censoring renewal processes deconvolution and decreasing density nonparametric estimation on donne un estimateur du maximum de vraisemblance non parametrique pour une distribution de durees de vie il est base sur un modele d observations censurees de facon multiplicative et il generalise des problemes statistiques courants tels que l estimation d une fonction de repartition sous une contrainte de densite decroissante la deconvolution non parametrique d une variable aleatoire exponentielle ou un probleme d estimation dans les processus de renouvellement

conditional risk mappings we introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties in particular we prove a representation theorem for conditional risk mappings in terms of conditional expectations we also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings

estimation of the survival function with increasing failure rate based on left truncated and right censored data summary the maximum conditional likelihood estimator of the survival function with increasing hazard rate is derived based on left truncated and right censored data this estimator always exists whereas the fully nonparametric conditional maximum likelihood estimator may not exist a strong consistency theorem is established based on the total time on test transformation right censored survival observations arise naturally in biomedical studies of survival when some of the patients are not followed until death parametric and nonparametric methods for analysing such data have been considered by many authors in the single sample problem kaplan meier 1958 derived the nonparametric maximum likelihood estimator of the survival function based on right censored data in addition to right censoring data may be subject to left truncation this arises when the individuals enter the study at some known time after the time origin for example in studying the effects on mortality of occupational exposure to agents in a certain industry age would normally be taken as the primary time variable but observation on an individual would not commence until work in this industry started specifically we consider the following let x be a random variable representing lifetimes and let t c be the random variables describing the left truncation times and right censoring times respectively suppose that x follows the distribution f with associated survival function s 1 f we also assume that t c is independent of x and follows the joint distribution g with pr t c 1 the quantities observed are y min x c t and 8 where 8 1 if t x c and 8 0 if c x nothing is observed if x t in effect observations are made from the distribution of y t 8

goodness of fit tests for conditional models under censoring and truncation the problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring a general method is applied to derive tests for the polynomial regression the proportional hazards the additive risks and the proportional odds models bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study

a note on the product limit estimator under right censoring and left truncation summary in many applications involving follow up studies individuals lifetimes may be subject to left truncation in addition to the usual right censoring here we consider the product limit estimator of the survival curve s or an appropriate conditional version of s the asymptotic behaviour of the estimator is briefly described together with an example

on the equivalence and containment problems for unambiguous regular expressions regular grammars and finite automata the known proofs that the equivalence and containment problems for regular expressions regular grammars and nondeterministic finite automata are pspace complete sm depend upon consideration of highly unambiguous expressions grammars and automata here we prove that such dependence is inherent deterministic polynomial time algorithms are presented for the equivalence and containment problems for unambiguous regular expressions unambiguous regular grammars and unambiguous finite automata the algorithms are then extended to ambiguity bounded by a fixed k our algorithms depend upon several elementary observations on the solutions of systems of homogeneous linear difference equations with constant coefficients and their relationship with the number of derivations of strings of a given length n by a regular grammar

semiparametric analysis of survival data with left truncation and dependent right censoring summary studies of chronic life threatening diseases often involve both mortality and morbidity in observational studies the data may also be subject to administrative left truncation and right censoring because mortality and morbidity may be correlated and mortality may censor morbidity the lynden bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the nonterminal event we propose a semiparametric estimator for this survival function based on a joint model for the two time to event variables which utilizes the gamma frailty specification in the region of the observable data first we develop a novel estimator for the gamma frailty parameter under left truncation using this estimator we then derive a closed form estimator for the marginal distribution of the nonterminal event the large sample properties of the estimators are established via asymptotic theory the methodology performs well with moderate sample sizes both in simulations and in an analysis of data from a diabetes registry

separating exponentially ambiguous finite automata from polynomially ambiguous finite automata we resolve an open problem raised by ravikumar and ibarra siam j comput 18 1989 pp 1263 1282 on the succinctness of representations relating to the types of ambiguity of finite automata we show that there exists a family of nondeterministic finite automata an over a two letter alphabet such that for any positive integer n an is exponentially ambiguous and has n states whereas the smallest equivalent deterministic finite automaton has 2n states and any smallest equivalent polynomially ambiguous finite automaton has 2n 1 states

quantile regression for doubly censored data double censoring often occurs in registry studies when left censoring is present in addition to right censoring in this work we propose a new analysis strategy for such doubly censored data by adopting a quantile regression model we develop computationally simple estimation and inference procedures by appropriately using the embedded martingale structure asymptotic properties including the uniform consistency and weak convergence are established for the resulting estimators moreover we propose conditional inference to address the special identifiability issues attached to the double censoring setting we further show that the proposed method can be readily adapted to handle left truncation simulation studies demonstrate good finite sample performance of the new inferential procedures the practical utility of our method is illustrated by an analysis of the onset of the most commonly investigated respiratory infection pseudomonas aeruginosa in children with cystic fibrosis through the use of the u s cystic fibrosis registry

length biased sampling with right censoring when survival data arise from prevalent cases ascertained through a cross sectional study it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases length biased data have been treated both unconditionally and conditionally in the literature in the latter case where length bias is viewed as being induced by random left truncation of the survival times the truncating distribution is assumed to be unknown conditioning on the observed truncation times hence causes very little loss of information in many instances however it can be supposed that the truncating distribution is uniform and it has been pointed out that under these circumstances an unconditional analysis will be more informative there are no results in the current literature that give the asymptotic properties of the unconditional nonparametric maximum likelihood estimator npmle of the unbiased survivor function in the presence of cen

ambiguity and structural ambiguity of symmetric difference nfas abstract okhotin showed an exponential trade off in the conversion from nondeterministic unary automata to unambiguous nondeterministic unary automata we show that the trade off in the case of unary symmetric difference automata to finitely structurally ambiguous unary symmetric difference automata is linear with constant 1 in the number of states in particular for every n state unary nondeterministic symmetric difference automaton there is an equivalent finitely structurally ambiguous n state unary symmetric difference nondeterministic automaton we also consider the complexity of deciding unambiguity for k deterministic finite automata and investigate the interplay between ambiguity and structural ambiguity

estimating survival curves with left truncated and interval censored data under monotone hazards we show that the nonparametric maximum likelihood estimator npmle of a survival function may severely underestimate the survival probabilities at very early times for left truncated and interval censored data as an alternative we propose to compute the nonparametric mle under a nondecreasing hazard assumption the monotone mle by a gradient projection algorithm when the assumption holds the projection step is accomplished via an isotonic regression algorithm the pool adjacent violators algorithm this gradient projection algorithm is computationally efficient and converges globally monte carlo simulations show superior performance of the monotone mle over that of the npmle in terms of either bias or variance even for large samples the methodology is illustrated with the application to the wisconsin epidemiological study of diabetic retinopathy data to estimate the probability of incidence of retinopathy

relating the type of ambiguity of finite automata to the succinctness of their representation we consider the problem of how the size of a nondeterministic finite automaton nfa representing a regular language depends on the degree of ambiguity of the nfa we obtain results for the unary and bounded inputs and partial results for the unrestricted inputs one of the main results of this paper shows that for unrestricted inputs deterministic unambiguous and nondeterministic machines form a hierarchy with respect to the number of states solving an open problem of stearns and hunt we also propose a new approach to the study of the succinctness of representation through regularity preserving closure properties and obtain some results in this direction

state complexity of unique rational operations for each basic language operation we define its unique counterpart as being the operation that results in a language whose words can be obtained uniquely through the given operation these unique operations can arguably be viewed as combined basic operations placing this work in the popular area of state complexity of combined operations on regular languages we study the state complexity of unique rational operations and we provide upper bounds and empirical results meant to cast light into this matter equally important we hope to have provided a generic methodology for estimating their state complexity

risk averse stochastic path detection abstract we introduce the stochastic path detection problem and propose a risk averse solution approach the problem comprises an invader and a protector that both operate on a network with a number of possible source destination paths the protector aims at allocating security resources on the network such that the invader s path is detected with high probability the invader s choice of path is known to the protector in terms of a probability distribution reflecting the protector s beliefs errors in these beliefs induce the risk of a low detection probability we derive a linear programming approximation and leverage the theory of coherent risk measures to consider risk aversion with respect to errors in the protector s beliefs the performance of the resulting risk averse detection policy is numerically compared with the performance of the risk neutral policy we show that the risk averse policy significantly mitigates the risk of facing a low detection probability in the presence of large errors in the protector s beliefs

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

unambiguous finite automata over a unary alphabet nondeterministic finite automata nfa with at most one accepting computation on every input string are known as unambiguous finite automata ufa this paper considers ufas over a one letter alphabet and determines the exact number of states in dfas needed to represent unary languages recognized by n state ufas in terms of a new number theoretic function g the growth rate of g n and therefore of the ufa dfa tradeoff is estimated as e q n l n 2 n 3 the conversion of an n state unary nfa to a ufa requires ufas with g n o n 2 e 1 o 1 n l n n states where g n is the greatest order of a permutation of n elements known as landau s function in addition it is shown that representing the complement of n state unary ufas requires ufas with at least n 2 o 1 states in the worst case while the kleene star requires up to exactly n 1 2 1 states

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

finite automata and unary languages abstract we prove that o e n log n states are sufficient to simulate an n state 1nfa recognizing a unary language by a 1dfa the lower bound is the same similar tight bounds are shown for the simulation of a 2dfa by a 1dfa and a 1nfa we also show that o n 2 states are sufficient and necessary to simulate an n state 1nfa recognizing a unary language by a 2dfa

confidence bands for survival functions with censored data a comparative study consider the problem of obtaining simultaneous confidence bands for the survival function s x when the data are arbitrarily right censored the usual pointwise confidence intervals based on greenwood s variance formula can be adapted to yield a large sample confidence band this band has in a certain sense equal precision at each point of s x it is compared with the censored versions of the kolmogorov band and the renyi band the comparisons are made in terms of the widths and the adequacy of large sample approximations and are carried out under various censoring models and degrees of censoring the bands are illustrated by applying them to data from a mechanical switch life test

nonparametric estimation with left truncated semicompeting risks data summary nonparametric estimators for competing risks data can be applied to semicompeting risks data a type of multi state data where a terminating event may censor a non terminating event after forcing the data into the competing risks format complications may arise with left truncation of the terminating event where the competing risks analysis naively truncates the nonterminating event using the left truncation time for the terminating event which may lead to large efficiency losses we propose nonparametric estimators which use all semicompeting risks information and do not require artificial truncation the uniform consistency and weak convergence of the estimators are established and variance estimators are provided simulation studies and an analysis of a diabetes registry demonstrate large efficiency gains over the naive estimators

on the finite valuedness problem for sequential machines abstract for a set a a 1 a m of n x n matrices with nonnegative integer entries let p a be the set of all finite products of matrices in a we show that there is a square space algorithm to decide given a whether or not p a is finite as a corollary we show that there is an exponential space algorithm to decide given a nondeterministic mealy sequential machine m with accepting states whether there exists an integer d 0 such that on every input the number of accepting computations of m producing distinct outputs is at most d if d exists the smallest such d can be computed in space exponential in size m log d the space bound reduces to polynomial for the analogous problem of ambiguity of nondeterministic finite acceptors

risk adjusted probability measures in portfolio optimization with coherent measures of risk abstract we consider the problem of optimizing a portfolio of n assets whose returns are described by a joint discrete distribution we formulate the mean risk model using as risk functionals the semideviation deviation from quantile and spectral risk measures using the modern theory of measures of risk we derive an equivalent representation of the portfolio problem as a zero sum matrix game and we provide ways to solve it by convex optimization techniques in this way we reconstruct new probability measures which constitute part of the saddle point of the game these risk adjusted measures always exist irrespective of the completeness of the market we provide an illustrative example in which we derive these measures in a universe of 200 assets and we use them to evaluate the market portfolio and optimal risk averse portfolios

pseudo partial likelihood for proportional hazards models with biased sampling data we obtain a pseudo partial likelihood for proportional hazards models with biased sampling data by embedding the biased sampling data into left truncated data the log pseudo partial likelihood of the biased sampling data is the expectation of the log partial likelihood of the left truncated data conditioned on the observed data in addition asymptotic properties of the estimator that maximize the pseudo partial likelihood are derived applications to length biased data biased samples with right censoring and proportional hazards models with missing covariates are discussed

estimation in the cox proportional hazards model with left truncated and interval censored data nous montrons que l estimateur non parametrique du maximum de vraisemblance npmle du coefficient de regression obtenu a partir de la vraisemblance jointe du coefficient de regression et de la survie de base est correct pour le modele de cox a hasards proportionnels avec des donnees tronquees a gauche et censurees par intervalle mais le npmle pent sous estimer la survie de base deux alternatives sont egalement etudiees premierement la vraisemblance marginale en etendant satten 1996 aux donnees tronquees la survie de base etant eliminee comme un parametre nuisible deuxiemement l estimateur monotone du maximum de vraisemblance qui maximise la vraisemblance jointe en supposant que la fonction de hasard est non decroissante pour la distribution de base ceci a ete initialement propose pour resoudre la sous estimation de la survie par le npmle dans le cas de donnees tronquees a gauche sans covariate tsai 1988 le boostrap est utilise a des fins d inference et des simulations sont realisees pour evaluer leur performance les methodes sont appliquees pour evaluer leur performance les methodes sont appliquees aux donnees de l etude du massachusetts health care panel afin de comparer chez les seniors en fonction du sexe les probabilites de perte d independance fonctionnelle

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

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is

a comparison of hazard rate estimators for left truncated and right censored data summary left truncation and right censoring arise frequently in practice for life data this paper is concerned with the estimation of the hazard rate function for such data two types of nonparametric estimators based on kernel smoothing methods are considered the first one is obtained by convolving a kernel with a cumulative hazard estimator the second one is in the form of a ratio of two statistics local properties including consistency asymptotic normality and mean squared error expressions are presented for both estimators these properties facilitate locally adaptive bandwidth choice the two types of estimators are then compared based on their theoretical and empirical performances the effect of overlooking the truncation factor is demonstrated through the channing house data