optimality of group testing in the presence of misclassification several optimality properties of dorfman s 1943 group testing procedure are derived for estimation of the prevalence of a rare disease whose status is classified with error exact ranges of disease prevalence are obtained for which group testing provides more efficient estimation when group size increases

sequential determination of estimator as well as sample size on considere certains problemes d estimation ponctuelle ou par intervalles et on propose des methodes sequentielles pour le choix d un estimateur et de la taille de l echantillon sur lequel sera base l estimateur

a hypothesis testing approach toward identifying active contrasts the problem of identifying the active contrasts in an unreplicated fractional factorial design is approached from a hypothesis testing point of view the null hypothesis that all contrasts are inactive is first tested and if rejected the active contrasts causing rejection are identified and estimated the method is illustrated with examples from box and meyer compared with the confidence interval approach of dong and lenth and found to be a worthy competitor

estimating ordered binomial proportions with the use of group testing summary this paper considers group testing when the probability of response is increasing across the levels of an observed covariate we illustrate how previously known results in order restricted inference can be extended to situations wherein data are collected according to a group testing protocol and we derive maximum likelihood estimators for proportions under the increasing order restriction and group testing model finally we show how the use of group testing can dramatically reduce the bias and mean squared error of isotonic regression estimators obtained from one at atime testing these proposed methods are illustrated using data from an observational hiv study conducted in houston texas

estimation in the general linear model when the accuracy is specified before data collection an estimator of is accurate with accuracy a and confidence ay o y 1 if p bfl ea y for all 3 given a sequence y1 y2 of independent vector valued homoscedastic normally distributed random variables generated via the general linear model yi xi e the k dimensional parameter d3 is accurately estimated using a sequential version of the maximum probability estimator developed by l weiss and j wolfowitz the procedure given also generalizes c stein s fixed width confidence sets to several dimensions

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

identifying active contrasts by stepwise testing unreplicated fractional factorial designs are frequently used in industrial experimentation and are characterized by the absence of degrees of freedom for estimation of the error variance this article presents step down and step up testing procedures that efficiently identify the active contrasts significant effects in such experiments and simultaneously provide an accurate estimate of the error variance the methods allow the user to restrict the experimentwise error rate to a prespecified level use of the new methods is illustrated in terms of standard examples from the literature simulation shows that a version of the step up procedure outperforms its competitors

optimal two stage algorithms for group testing problems group testing refers to the situation in which one is given a set of objects cal o an unknown subset cal p subseteq cal o and the task of determining cal p by asking queries of the type does cal p intersect cal q where cal q is a subset of cal o group testing is a basic search paradigm that occurs in a variety of situations such as quality control testing searching in storage systems multiple access communications and data compression among others group testing procedures have been recently applied in computational molecular biology where they are used for screening libraries of clones with hybridization probes and sequencing by hybridization motivated by particular features of group testing algorithms used in biological screening we study the efficiency of two stage group testing procedures our main result is the first optimal two stage algorithm that uses a number of tests of the same order as the information theoretic lower bound on the problem we also provide efficient algorithms for the case in which there is a bernoulli probability distribution on the possible sets cal p and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of inhibitory items in cal o our results depend on a combinatorial structure introduced in this paper we believe that it will prove useful in other contexts too

optimal group testing designs for estimating prevalence with uncertain testing errors summary we construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity using optimal design theory for approximate designs we show that the most efficient design for simultaneously estimating the prevalence sensitivity and specificity requires three different group sizes with equal frequencies however if estimating prevalence as accurately as possible is the only focus the optimal strategy is to have three group sizes with unequal frequencies on the basis of a chlamydia study in the usa we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator we demonstrate that the locally d and ds optimal designs proposed have high efficiencies even when the prespecified values of the parameters are moderately misspecified

nonparametric regression analysis for group testing data group testing is a procedure used to reduce the cost and increase the speed of large screening studies in which infection or contamination of individuals is detected by a test carried out on a sample of for example blood urine or water instead of testing the sample of each individual the method involves pooling samples of groups of several individuals and testing those pooled samples we construct a nonparametric procedure for estimating the conditional probability of contamination given an explanatory variable when the observations are pooled data of this type we investigate asymptotic theoretical properties of the estimator and establish its consistency the procedure requires selecting an important smoothing parameter and we suggest a way to do this automatically from the data we illustrate the numerical performance of the method on some simulated examples and on data from the national health and nutrition examination survey we discuss extensions of the procedure to cases where the test is im

negative regret optional stopping and the elimination of outliers abstract this article examines the phenomenon of negative regret in sequential point estimation in which a stopping rule used in ignorance of the variance of the distribution sometimes performs better than the best fixed sample size when the variance is known an explanation in terms of a certain robustifying effect of the stopping rule is given results of simulation studies illustrating both negative regret and its explanation are also given suppose x 1 x 2 are iid with mean and variance 2 one may stop observing the sequence of x i s after any number of observations n and estimate by the sample mean subject to the loss if is known then the best fixed i e nonrandom sample size in the sense of minimum risk can be used if is unknown the best fixed sample size is unknown necessitating a sequential procedure for a sequential procedure of the type first proposed by robbins 1959 the regret expected additional loss from not knowing and using the sequential procedure instead

semiparametric group testing regression models group testing through the use of pooling has proven to be an efficient method of reducing the time and cost associated with screening for a binary characteristic of interest such as infection status a topic of key interest in the statistical literature involves the development of regression models that relate individual level covariates to testing responses observed from pooled specimens in this article we propose a general semiparametric framework that allows for the inclusion of multi dimensional covariates decoding information and imperfect testing the asymptotic properties of our estimators are presented and guidance on finite sample implementation is provided we illustrate the performance of our methods through simulation and by applying them to chlamydia and gonorrhea data collected by the nebraska public health laboratory as a part of the infertility prevention project

second order approximation to the risk of a sequential procedure given x 1 x 2 cdots i i d with mean mu and variance sigma 2 suppose that at stage n one wishes to estimate mu by the sample mean bar x n subject to the loss function l n a bar x n mu 2 n a 0 if sigma is known the optimal fixed sample size n 0 approx a 1 2 sigma can be used with corresponding risk r n 0 but if sigma is unknown there is no fixed sample size procedure that will achieve the risk r n 0 for the sequential estimation procedure with stopping rule t inf n geq n a n 1 sum n 1 x i bar x n 2 leq a 1 n 2 the second order approximation of woodroofe 1977 to the risk r t for normal x i is extended to the distribution free case specifically if the x i have finite moments of order greater than eight and are non lattice under certain conditions on the delay n a it is shown that the regret r t r n 0 c o 1 as a rightarrow infty where c depends on the first four moments of the distribution of the x i for the lattice case bounds of the form c 1 o 1 leq r t r n 0 leq c 2 o 1 are obtained where the c j are c pm 3 it follows from these approximations that the regret can take arbitrarily large negative values as the distribution of the x i varies in contrast to previous results for normal and gamma cases

random products of standard maps we develop a general geometric method to establish the existence of positive lyapunov exponents for a class of skew products the technique is applied to show non uniform hyperbolicity of some conservative partially hyperbolic diffeomorphisms having as center dynamics coupled products of standard maps notably for skew products whose fiber dynamics is given by a continuum of parameters in the froeschle family these types of coupled systems appear as some induced maps in models for the study of arnold diffusion consequently we are able to present new examples of partially hyperbolic diffeomorphisms having rich high dimensional center dynamics the methods are also suitable for studying cocycles over shift spaces and do not demand any low dimensionality condition on the fiber

learning immune defectives graph through group tests this paper deals with an abstraction of a unified problem of drug discovery and pathogen identification pathogen identification involves the identification of disease causing biomolecules drug discovery involves finding chemical compounds called lead compounds that bind to pathogenic proteins and eventually inhibit the function of the protein in this paper the lead compounds are abstracted as inhibitors pathogenic proteins as defectives and the mixture of ineffective chemical compounds and non pathogenic proteins as normal items a defective could be immune to the presence of an inhibitor in a test so a test containing a defective is positive if it does not contain its associated inhibitor the goal of this paper is to identify the defectives inhibitors and their associations with high probability or in other words learn the immune defectives graph idg efficiently through group tests we propose a probabilistic non adaptive pooling design a probabilistic two stage adaptive pooling design and decoding algorithms for learning the idg for the two stage adaptive pooling design we show that the sample complexity of the number of tests required to guarantee recovery of the inhibitors defectives and their associations with high probability i e the upper bound exceeds the proposed lower bound by a logarithmic multiplicative factor in the number of items to be precise lower and upper bounds of omega r d log n rd and o rd log n tests respectively are identified for classifying r inhibitors and d defectives amongst n items and identifying their associations for the non adaptive pooling design we show that the upper bound given by o r d 2 log n tests exceeds the proposed lower bound given by max omega r d log n rd omega r 2 log r log n omega d 2 tests by at most a logarithmic multiplicative factor in the number of items

transversal homoclinic points of a class of conservative diffeomorphisms abstract we develop a global graph transformation to obtain estimates for certain invariant manifolds of a class of area preserving diffeomorphisms with symmetries the existence of homoclinic or heteroclinic points and the analyticity of the angle between the invariant manifolds at them is proved for the henon and the standard maps a lower bound of this angle is given for a large set of values of the parameters

sequentially deciding between two experiments for estimating a common success probability abstract to estimate a success probability p two experiments are available individual bernoulli p trials or the product of individual bernoulli p trials this problem has its roots in reliability where either single components can be tested or a system of identical components can be tested a total of n experiments can be performed and the problem is to sequentially select some combination allocation of these two experiments along with an estimator of p to achieve low mean squared error mse of the final estimate this scenario is similar to that of the better known group testing problem but here the goal is to estimate failure rates rather than to identify defective units the problem also arises in epidemiological applications such as estimating disease prevalence information maximization considerations and analysis of the asymptotic mse of several estimators lead to the following adaptive procedure use the maximum likelihood estimator mle to estimate p and if this estimator is b

using group testing to estimate a proportion and to test the binomial model group testing has been extensively studied as an efficient way to classify units as defective or satisfactory when the proportion p of defectives is small it can also be used to estimate p often substantially reducing the mean squared error mse of p and cost per unit information group testing is useful for larger p in the estimation problem than in the classification problem but for larger p more care must be taken in choosing the group size k k being too large not only increases mse p but adversely affects the robustness of p to both errors in testing misclassification and errors in the assumed binomial model procedures that retest units from defective groups if even feasible are shown to reduce cost per unit information very little in the estimation problem but can provide useful information for testing the model methods are given for using data from tests of unequal sized groups to estimate p and for testing the validity of the binomial model

sequential estimation of the mean of a first order stationary autoregressive process on considere un estimateur ponctuel sequentiel base sur une moyenne d echantillon et on montre qu il est asymptotiquement efficace en risque lorsque le cout par observation tend vers zero

a sequential procedure with asymptotically negative regret for estimating a normal mean rn e ln acr2 n n is minimized by taking n n ao 2 1 2 and the corresponding minimum fixed sample size risk is rn 2n since u2 is unknown robbins 1959 proposed the following type of sequential procedure let 1 1 t inf n m n avn n 1 2 i where m is the initial sample size and vn e n xn 2 and estimate u by xt woodroofe 1977 showed that if m 4 the regret of the procedure rt rn 1 2 o 1 as a oc the purpose of this article is to show that there does exist a sequential procedure for which the regret is negative at u 0 and 1 2 at u 0 asymptotically instead of vn n as an estimator of j 2 consider an estimator o n of the form

on deconvolution with repeated measurements in a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known although in many applications it is unrealistic to make this assumption the problem is often insoluble without it however if additional data are available then it is possible to estimate consistently the unknown error density data are seldom available directly on the transformation but repeated or replicated measurements increasingly are becoming available such data consist of intrinsic values that are measured several times with errors that are generally independent working in this setting we treat the nonparametric deconvolution problems of density estimation with observation errors and regression with errors in variables we show that even if the number of repeated measurements is quite small it is possible for modified kernel estimators to achieve the same level of performance they would if the error distribution were known indeed density and regression estimators can be constructed from replicated data so that they have the same first order properties as conventional estimators in the known error case without any replication but with sample size equal to the sum of the numbers of replicates practical methods for constructing estimators with these properties are suggested involving empirical rules for smoothing parameter choice

expansiveness hyperbolicity and hausdorff dimension we show that there exists a simple upper bound on the dimension of a hyperbolic compact set of a dynamical system in terms of topological entropy and a uniform contraction rate on the stable and unstable manifolds this allows us to give proofs of several apparently unrelated theorems

nonlinear dynamics from the wilson lagrangian a nonlinear hamiltonian dynamics is derived from the wilson action in lattice gauge theory let d be a linear space of lattice dirac operators d a defined by some lattice gauge field a we consider the lagrangian d tr d a im 4 on d where m c is a mass parameter critical points of this functional are given by solutions of a nonlinear discrete wave equation which describe the time evolution of the gauge fields a in the simplest case the dynamical system is a cubic henon map in general it is a symplectic coupled map lattice we prove the existence of non trivial critical points in two examples

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

a flexible and fast method for automatic smoothing abstract the choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators the optimal choice depends on the data at hand a data driven bandwidth selection close to the optimal one would make these curve estimators objective more reliable and easier to use minimizing residual mean squared error criteria such as cross validation have been frequently proposed to estimate the optimal smoothing parameter empirical and theoretical evidence indicates that cross validation rules and related methods lead to rather variable estimated optimal bandwidths the method presented here builds on estimating the asymptotically optimal bandwidth from the data since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula such selection rules are called plug in estimators the functional that quantifies bias is approximated by the integrated squared second derivative of the regre

chaotic trajectories in the standard map the concept of anti integrability a rigorous proof is given in the standard map associated with a frenkel kontorowa model for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k k0 these chaotic trajectories with finite entropy per site are coded by integer sequences mi such that the sequence bi mi 1 mi 1 2mi be bounded by some integer b the bound k0 in k depends on b and can be lowered for coding sequences mi fulfilling more restrictive conditions the obtained chaotic trajectories correspond to stationary configurations of the frenkel kontorowa model with a finite non zero photon gap called gap parameter in dimensionless units this property implies that the trajectory or the configuration ui can be uniquely continued as a uniformly continuous function of the model parameter k in some neighborhood of the initial configuration a non zero gap parameter implies that the lyapunov coefficient is strictly positive when it is defined in addition the existence of dilating and contracting manifolds is proven for these chaotic trajectories exotic trajectories such as ballistic trajectories are also proven to exist as a consequence of these theorems the concept of anti integrability emerges from these theorems in the anti integrable limit which can be only defined for a discrete time dynamical system the coordinates of the trajectory at time i do not depend on the coordinates at time i 1 thus at this singular limit the existence of chaotic trajectories is trivial and the dynamical system reduces to a bernoulli shift it is well known that the kam tori of symplectic dynamical originates by continuity from the invariant tori which exists in the integrible limit under certain conditions in a similar way it appears that the chaotic trajectories of dynamical systems originate by continuity from those which exists at the anti integrable limits also under certain conditions

the analysis of unreplicated factorial experiments using all possible comparisons this article proposes a new procedure for analyzing small unreplicated factorial experiments this procedure is based on using likelihood ratio tests to compare competing models an easy method of implementing the procedure is presented and then demonstrated on a real set of data results of a simulation study are presented that indicate that the new procedure compares favorably with lenth s method tables of constants are supplied that allow the new procedure to be easily applied to the analysis of 8 run 12 run and 16 run experiments

inference for effect saturated fractional factorials industrial scientists and engineers often use experimental designs in which all degrees of freedom are used to estimate effects and consequently no classical estimate of the error is possible robust scale estimates provide an alternative measure of the error in this study several such scale estimators are evaluated based on the power or related significance tests the pseudo standard error method of lenth provides the best overall performance lenth s t approximation for critical values was found to be inaccurate however so new tables are provided additional recommendations are made according to the experimenter s prior belief in the number of likely important factors

estimating prevalence by group testing using generalized linear models a method is described for estimating prevalence by group testing using generalized linear models this provides a simple way of analysing such data using widely available software existing methodology to correct for overdispersion using quasi likelihoods is applied to the group testing model the methods are illustrated by an estimation of salmonella contamination in eggs and of yellow fever virus infection in a mosquito population

on the prevalence of horseshoes in this paper the symbolic dynamics of several differentiable systems are investigated it is shown that many well known dynamical systems including axiom a systems piecewise monotonic maps of the interval the lorenz attractor and abraham smale examples have inside them subsystems conjugate to subshifts of finite type these subsystems have hyperbolic structures and hence are stable they can also be chosen to have entropy arbitrarily close to that of the ambient system let f m m be a diffeomorphism of a manifold into itself and let q f be its nonwandering set while it is usually difficult to describe completely the orbit structure of f one could look for large invariant subsets of q f on which the dynamics of f are simple to characterize this idea is due to rufus bowen who proposed that one asks the following given e 0 does there exist a hyperbolic f invariant set a c 2 f with the property that l fja is conjugate to a subshift of finite type and 2 h f iae h f e where h f is the topological entropy of f we say that f is in the sense of entropy a limit of hyperbolic subshifts of finite type if a above exists for every 0 the main result of this paper is that many dynamical systems we know are limits of this kind they include axiom a diffeomorphisms and flows piecewise monotonic maps of the interval the poincare map of the lorenz attractor 15 and certain abraham smale examples 1 perhaps this new class of systems accounts for some of the other non axiom a examples as well e g 11 17 19 23 24 28 but that remains to be decided recall the definition of a subshift of finite type let 1 n be given the discrete topology and l i 1 n the product topology let a l e be defined by ax i x i where x i denotes the ith coordinate of x let a au be annxn matrix of o s and l s let ea xel axx 1 for alliez then ai a is called a subshift of finite type if 2 l 1 n and y x e y a i 1 for all i 0 then aiya is called a one sided subshift of finite type from now on subshifts of finite type will be abbreviated as ssft received by the editors january 26 1979 ams mos subject classifications 1970 primary 58f15 secondary 28a65

percival variational principle for invariant measures and commensurate incommensurate phase transitions in one dimensional chains we prove for a one dimensional system of classical particles with potential energy u alpha gamma sum limits n left alpha v x n f x n 1 x n gamma right the existence of such a smooth function 0 0 that the system with potential energyu has the equilibrium state at the temperaturet 0 this is the incommensurate phase with the ratio of periods equal to the prescribed irrational number badly approximated by rational ones a simple geometric condition for the invariant curve of the corresponding dynamical system is established under which it is the support of the invariant measure minimizing percival s energy functional

nonparametric methods for group testing data taking dilution into account summary group testing methods are used widely to assess the presence of a contaminant based on measurements of the concentration of a biomarker for example to test the presence of a disease in pooled blood samples the test would be perfect if it produced a positive result whenever the con 10 taminant was present and a negative result otherwise however in practice the test is always at least somewhat imperfect for example because it is sensitive to the proportion of contaminated items in the group rather than to the sheer existence of one or more contaminated items we develop a nonparametric method for accommodating this dilution effect our approach allows us to estimate under minimal assumptions the probability m x that an item is contaminated 15 conditional on the value x of an explanatory variable and to estimate the probability q that an individual chosen at random is disease free and the specificity sp and the sensitivity se of the test these are all ill posed problems where poor convergence rates are usually encountered however despite these pessimistic expectations our estimators of q sp and se are root n consistent where n denotes the total number of individuals in all the groups and our estimator of 20 m x converges at the rate it would enjoy if q sp and se were known

a queueing model for general group screening policies and dynamic item arrivals classification of items as good or bad can often be achieved more economically by examining the items in groups rather than individually if the result of a group test is good all items within it can be classified as good whereas one or more items are bad in the opposite case whether it is necessary to identify the bad items or not and if so how is described by the screening policy in the course of time a spectrum of group screening models has been studied each including some policy however the majority ignores that items may arrive at random time epochs at the testing center in real life situations this dynamic aspect leads to two decision variables the minimum and maximum group size in this paper we analyze a discrete time batch service queueing model with a general dependency between the service time of a batch and the number of items within it we deduce several important quantities by which the decision variables can be optimized in addition we highlight that every possible screening policy can in principle be studied by defining the dependency between the service time of a batch and the number of items within it appropriately

new approaches to nonparametric and semiparametric regression for univariate and multivariate group testing data summary we consider non and semi parametric estimation of a conditional probability curve in the case of group testing data where the individuals are pooled randomly into groups and only the pooled data are available we derive a nonparametric weighted estimator 15 that has optimality properties accounting for group sizes and show how to extend it to multivariate settings including the partially linear model in the group testing context it is natural to assume that the probability curve depends on the covariates only through a linear combination of them motivated by this we develop a nonparametric estimator based on the single index model we study theoretical properties of the sug 20 gested estimators and derive data driven procedures practical properties of the methods are demonstrated via real and simulated examples and shown to have smaller median integrated square error than existing competitors

amount of rotation about a point and the morse index for the case of exact area preserving monotone twist diffeomorphisms we give formulas relating the amount of rotation about an orbit and certain morse indices

quick and easy analysis of unreplicated factorials box and meyer 1986 introduced a method for assessing the sizes of contrasts in unreplicated factorial and fractional factorial designs this is a useful technique and an associated graphical display popularly known as a bayes plot makes it even more effective this article presents a competing technique that is also effective and is computationally simple an advantage of the new method is that the results are given in terms of the original units of measurement this direct association with the data may make the analysis easier to explain

topological entropy of standard type monotone twist maps we study invariant measures of families of monotone twist maps s q p 2q p v q q with periodic morse potential v we prove that there exist a constant c c v such that the topological entropy satisfies htop s log c 3 in particular htop s for we show also that there exist arbitrary large such that s has nonuniformly hyperbolic invariant measures with positive metric entropy for large the measures are hyperbolic and for a class of potentials which includes v q sin q the lyapunov exponent of the map s with invariant measure grows monotonically with

robustness of group testing in the estimation of proportions in binomial group testing unlike one at a time testing the test unit consists of a group of individuals and each group is declared to be defective or nondefective a defective group is one that is presumed to include one or more defective e g infected positive individuals and a nondefective group to contain only nondefective individuals the usual binomial model considers the individuals being grouped as independent and identically distributed bernoulli random variables under the binomial model and presuming that groups are tested and classified without error it has been shown that when the proportion of defective individuals is low group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives we discuss the robustness of group testing for estimating proportions when the underlying assumptions of i no testing errors and ii independent individuals are violated to evaluate the effect of these model violations two dilution effect models and a serial correlation model are considered group testing proved to be quite robust to serial correlation in the presence of a dilution effect smaller group sizes should be used but most of the benefits of group testing can still be realized

a design adaptive local polynomial estimator for the errors in variables problem local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature their simplest version the local constant estimator can be easily extended to the errors in variables context by exploiting its similarity with the deconvolution kernel density estimator the generalization of the higher order versions of the estimator however is not straightforward and has remained an open problem for the last 15 years we propose an innovative local polynomial estimator of any order in the errors in variables context derive its design adaptive asymptotic properties and study its finite sample performance on simulated examples we provide not only a solution to a long standing open problem but also provide methodological contributions to error in variable regression including local polynomial estimation of derivative functions

continuity properties of entropy on donne une borne superieure sur le defaut en semicontinuite superieure des entropies topologiques et metriques d une auto application c r d une variete c r r 1

optimal algorithms for two group testing problems and new bounds on generalized superimposed codes two variants of the well known group testing problem are considered in the first variant a finite set of items o and an unknown subset psubeo are given and one wants to identify the set p by asking the least number of questions of the form is qcapp 1 where qsubeo this problem naturally arises in the design of efficient contention resolution algorithms for certain random multiple access communication systems berger et al random multiple access communication and group testing ieee trans commun vol 32 no 7 pp 769 779 1984 in the second variant of the problem the answer to the question is qcapp 1 is correctly yes if qcapp 1 and no if qcapp 0 and it is left to a possibly malicious adversary otherwise this model was introduced in damaschke randomized group testing for mutually obscuring defectives inf process lett vol 67 pp 131 135 1998 in the context of chemical compound testing in this correspondence several algorithms for these group testing problems are presented trying to optimize different measures of performance the overall number of tests performed by the algorithm the number of stages in which tests can be arranged and the decoding complexity of identifying the elements of p from tests outcomes some of the given algorithms are optimal with respect to more than one of the above criteria instrumental to the results presented in the correspondence are new and improved bounds on certain generalization of superimposed codes introduced in dyachkov and rykov a generalization of superimposed codes and its application to the multiple access channel in proc 1984 ieee int symp inf theory pp 62 64 de bonis and vaccaro constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels theoretic comput sci vol 306 no 1 3 pp 223 243 2003 a result that it is believed to be of independent interest

equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for frenkel kontorova models there is a well known correspondence between the dynamics of symplectic twist maps which represent an important class of hamiltonian systems and the equilibrium states of a class of variational problems in solid state physics known as frenkel kontorova models in this paper it is shown that the key concepts of uniform hyperbolicity in the first context and phonon gap in the second context are equivalent this allows one to transfer many ideas between the two and hence to deduce new results for example we prove the uniform hyperbolicity of certain invariant sets for symplectic twist maps constructed from so called non degenerate anti integrable limits by aubry and abramovici using the concept of phonon gap and deduce that they have measure zero we prove existence of many multi defect equilibrium states for a frenkel kontorova system if it has a single non degenerate defect equilibrium state via standard results in the theory of uniform hyperbolicity

isospectral deformations of random jacobi operators we show the integrability of infinite dimensional hamiltonian systems obtained by making isospectral deformations of random jacobi operators over an abstract dynamical system the time 1 map of these so called random toda flows can be expressed by aqr decomposition

a two stage adaptive group testing procedure for estimating small proportions abstract a method for adaptively estimating a proportion p using group testing procedures is presented and analyzed with emphasis placed on a two stage procedure this estimator is compared to the usual group testing estimator via asymptotic and small sample relative efficiency the adaptive estimator is generally recommended with the restriction that adaptations i e adjustments of group size are based on at least 10 measurements responses but if one is confident that one has a very good a priori estimate of p then the usual estimator is recommended monte carlo simulations show that a normal approximation is adequate for generating confidence intervals with confidence coefficients as high as 95

on the informativeness and accuracy of pooled testing in estimating prevalence of a rare disease application to hiv screening summary when screening for a rare disease the large number of expected false positives makes it difficult to obtain a positive estimate of prevalence using current screening methodology pooled testing not only reduces the probability of this occurring but also improves the accuracy of the estimator these findings are illustrated by screening for the human immunodeficiency virus

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

roc curve analysis for biomarkers based on pooled assessments interleukin 6 is a biomarker of inflammation which has been suggested as having potential discriminatory ability for myocardial infarction because of its high assaying cost it is very expensive to evaluate this marker in order to reduce this cost we propose pooling the specimens in this paper we examine the efficiency of roc curve analysis specifically the estimation of the area under the roc curve when dealing with pooled data we study the effect of pooling when there are only a fixed number of individuals available for testing and pooling is carried out to save on the number of assays alternatively we examine how many pooled assays of size g are necessary to provide essentially the same information as n individual assays we measure loss of information by means of the change in root mean square error of the estimate of the area under the roc curve and study the extent of this loss via a simulation study

estimation of conditional prevalence from group testing data with missing covariates we consider estimating the conditional prevalence of a disease from data pooled according to the group testing mechanism consistent estimators have been proposed in the literature but they rely o

misclassified group tested current status data author s petito l jewell nicholas p abstract group testing introduced by dorfman 1943 has been used to reduce costs when estimating the prevalence of a binary characteristic based on a screening test of formula see text groups that include formula see text independent individuals in total if the unknown prevalence is low and the screening test suffers from misclassification it is also possible to obtain more precise prevalence estimates than those obtained from testing all formula see text samples separately tu et al 1994 in some applications the individual binary response corresponds to whether an underlying time to event variable formula see text is less than an observed screening time formula see text a data structure known as current status data given sufficient variation in the observed formula see text values it is possible to estimate the distribution function formula see text of formula see text nonparametrically at least at some points in its support using the pool adjacent violators algorithm ayer et al 1955 here we consider nonparametric estimation of formula see text based on group tested current status data for groups of size formula see text where the group tests positive if and only if any individuals unobserved formula see text is less than the corresponding observed formula see text we investigate the performance of the group based estimator as compared to the individual test nonparametric maximum likelihood estimator and show that the former can be more precise in the presence of misclassification for low values of formula see text potential applications include testing for the presence of various diseases in pooled samples where interest focuses on the age at incidence distribution rather than overall prevalence we apply this estimator to the age at incidence curve for hepatitis c infection in a sample of u s women who gave birth to a child in 2014 where group assignment is done at random and based on maternal age we discuss connections to other work in the literature as well as potential extensions

the use of a square array scheme in blood testing when testing blood samples for the presence of disease considerable efficiencies may be achieved by pooling samples and testing them as a batch it is shown that placing the samples in a square array and pooling rows and columns has substantial advantages particularly in the reduction of false negatives the commonly used 8 12 array is also considered

applications of bulk queues to group testing models with incomplete identification abstract a population of items is said to be group testable i if the items can be classified as good and bad and ii if it is possible to carry out a simultaneous test on a batch of items with two possible outcomes success indicating that all items in the batch are good or failure indicating a contaminated batch in this paper we assume that the items to be tested arrive at the group testing centre according to a poisson process and are served i e group tested in batches by one server the service time distribution is general but it depends on the batch size being tested these assumptions give rise to the bulk queueing model m g m m 1 where m and m m are the decision variables where each batch size can be between m and m we develop the generating function for the steady state probabilities of the embedded markov chain we then consider a more realistic finite state version of the problem where the testing centre has a finite capacity and present an expected profit objective function we compute the optimal values of the decision variables m m that maximize the expected profit for a special case of the problem we determine the optimal decision explicitly in terms of the lambert function

use of binomial group testing in tests of hypotheses for classification or quantitative covariables summary in group testing the test unit consists of a group of individuals if the group test is positive then one or more individuals in the group are assumed to be positive a group observation in binomial group testing can be say the test result positive or negative for a pool of blood samples that come from several different individuals it has been shown that when the proportion p of infected individuals is low group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of those infected we extend the potential applications of group testing to hypothesis testing problems wherein one wants to test for a relationship between p and a classification or quantitative covariable asymptotic relative efficiencies ares of tests based on group testing versus the usual individual testing are obtained the pitman are strongly favors group testing in many cases small sample results from simulation studies are given and are consistent with the large sample asymptotic findings we illustrate the potential advantages of group testing in hypothesis testing using hiv 1 seroprevalence data

nonparametric and parametric estimators of prevalence from group testing data with aggregated covariates group testing is a technique employed in large screening studies involving infectious disease where individuals in the study are grouped before being observed parametric and nonparametric estimators of conditional prevalence have been developed in the group testing literature in the case where the binary variable indicating the disease status is available only for the group but the explanatory variable is observed for each individual however for reasons such as the high cost of assays the confidentiality of the patients or the impossibility of measuring a concentration under a detection limit the explanatory variable is observable only in an aggregated form and the existing techniques are no longer valid we develop consistent parametric and nonparametric estimators of the conditional prevalence in this complex problem we establish theoretical properties of our estimators and illustrate their practical performance on simulated and real data we extend our techniques to the case where the group s

group testing regression models with fixed and random effects group testing where subjects are tested in pools rather than individually has a long history of successful application in infectious disease screening in this article we develop group testing regression models to include covariate effects that are best regarded as random we present approaches to fit mixed effects models using maximum likelihood investigate likelihood ratio and score tests for variance components and evaluate small sample performance using simulation we illustrate our methods using chlamydia and gonorrhea data collected by the state of nebraska as part of the infertility prevention project

efficient estimation of the prevalence of multiple rare traits we consider a population with multiple traits of interest where our goal is to estimate the proportions of individuals with the traits when traits are rare group testing can improve efficiency previous work of hughes oliver swallow 1994 developed an adaptive two stage design for group testing of only one trait we extend this work to the multi trait case we derive the optimum group sizes using compound d optimum design theory estimation is based on maximum likelihood estimators which are shown to be consistent and asymptotically normal we apply our design to a problem of estimating the prevalence of hiv chlamydia and syphilis in ethiopian women

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

group testing with blockers and synergism discovery and development of a new drug can cost hundreds of millions of dollars pharmaceutical companies have used group testing methodology routinely as one of the efficient high throughput screening techniques to search for lead compounds among collections of hundreds of thousands of chemical compounds the lead compounds can be modified to produce new and effective molecules which eventually may lead to new drugs this article develops models and estimation procedures to obtain quantitative information from data in such applications it investigates group testing procedures and studies cost efficiency when the standard assumption adopted by dorfman that tested items act independently of one another is violated the investigation is focused on but not limited to the square array pooling method and the methodologies developed are illustrated through simulations and a drug discovery dataset from glaxo wellcome inc

anti integrability in dynamic and variational problems abstract we show using a series of examples that the existence of a singular limit called anti integrable can be useful for proving the existence of chaotic solutions and elucidating some of their properties leading to some new and unexpected results in particular the existence proof of chaotic trajectories in large classes of dynamical systems with discrete time becomes straightforward the method applies even for maps in infinite dimension symplectic or not similar ideas can be used for proving the existence of breathers or self localised modes and of chaotic distributions of breathers in any array of weakly coupled non linear oscillators with continuous time the existence of insulating bipolaronic structures in electron phonon systems electronic self localisation at large electron phonon coupling can also be proven on the same basis

sequential confidence bands for densities this paper proposes a fully sequential procedure for constructing a fixed width confidence band for an unknown density on a finite interval and shows the procedure has the desired coverage probability asymptotically as the width of the band approaches zero the procedure is based on a result of bickel and rosenblatt its implementation in the sequential setting cannot be obtained using anscombe s theorem because the normalized maximal deviations between the kernel estimate and the true density are not uniformly continuous in probability u c i p instead we obtain a slightly weaker version of the u c i p property and a correspondingly stronger convergence property of the stopping rule these together yield the desired results

nonparametric regression with homogeneous group testing data in this talk we introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence in particular when the level of pooling is moderate then despite the cost savings the method enjoys the same convergence rate as in the case of no pooling in the setting of over pooling the convergence rate differs from that of an optimal estimator by no more than a logarithmic factor our approach improves on the random pooling nonparametric predictor which is currently the only nonparametric method available unless there is no pooling in which case the two approaches are identical