on the characteristic polynomial of a random unitary matrix we present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial z of a random n n unitary matrix as n first we show that evaluated at a finite set of distinct points is asymptotically a collection of i i d complex normal random variables this leads to a refinement of a recent central limit theorem due to keating and snaith and also explains the covariance structure of the eigenvalue counting function next we obtain a central limit theorem for ln z in a sobolev space of generalised functions on the unit circle in this limiting regime lower order terms which reflect the global covariance structure are no longer negligible and feature in the covariance structure of the limiting gaussian measure large deviations results for ln z a evaluated at a finite set of distinct points can be obtained for for higher order scalings we obtain large deviations results for ln z a evaluated at a single point there is a phase transition at a ln n which only applies to negative deviations of the real part reflecting a switch from global to local conspiracy

on the efficient use of the informational content of estimating equations implied probabilities and euclidean empirical likelihood abstract a number of information theoretic alternatives to gmm have recently been proposed in the literature for practical use and general interpretation the main drawback of these alternatives particularly in the case of conditional moment restrictions is that they give up the computational and interpretational simplicity of quadratic optimization the main contribution of this paper is to analyze the informational content of estimating equations within the unified framework of chi square distance improved inference by control variables closed form formulae for implied probabilities and information theoretic interpretations of continuously updated gmm are discussed in the two cases of unconditional and conditional moment restrictions

receiver operating characteristic analysis under tree orderings of disease classes receiver operating characteristic roc curve and its summary statistics e g the area under curve auc are commonly used to evaluate the diagnostic accuracy for disease processes with binary classification the roc curve has been extended to roc surface for scenarios with three ordinal classes or to hyper surface for scenarios with more than three classes for classifier under tree or umbrella ordering in which the marker measurement for one class is lower or higher than those for the other classes the commonly adopted diagnostic measures are the naive auc nauc based on a pooled class of all the unordered classes and the umbrella volume uv based on the concept of volume under surface however both nauc and uv have some limitations for example nauc depends on the sampling weights for all the classes in population and uv has only been introduced for three class settings in this article we initiate the idea of a new roc framework for tree or umbrella ordering denoted as troc and propose the area under troc curve denoted as tauc as an appropriate diagnostic measure the proposed troc and tauc share many nice features with the traditional roc and auc both parametric and nonparametric approaches are explored to construct the confidence interval estimation of tauc the performances of these methods are compared in simulation studies under a variety settings at the end the proposed methods are applied to a published microarray data set

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

comparing the areas under two or more correlated receiver operating characteristic curves a nonparametric approach methods of evaluating and comparing the performance of diagnostic tests are of increasing importance as new tests are developed and marketed when a test is based on an observed variable that lies on a continuous or graded scale an assessment of the overall value of the test can be made through the use of a receiver operating characteristic roc curve the curve is constructed by varying the cutpoint used to determine which values of the observed variable will be considered abnormal and then plotting the resulting sensitivities against the corresponding false positive rates when two or more empirical curves are constructed based on tests performed on the same individuals statistical analysis on differences between curves must take into account the correlated nature of the data this paper presents a nonparametric approach to the analysis of areas under correlated roc curves by using the theory on generalized u statistics to generate an estimated covariance matrix

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

langevin dynamics with constraints and computation of free energy differences in this paper we consider langevin processes with mechanical constraints the latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences the results of this paper can be divided into three parts i we propose a simple discretization of the constrained langevin process based on a standard splitting strategy we show how to correct the scheme so that it samples em exactly the canonical measure restricted on a submanifold using a metropolis rule in the spirit of the generalized hybrid monte carlo ghmc algorithm moreover we obtain in some limiting regime a consistent discretization of the overdamped langevin brownian dynamics on a submanifold also sampling exactly the correct canonical measure with constraints the corresponding numerical methods can be used to sample without any bias a probability measure supported by a submanifold ii for free energy computation using thermodynamic integration we rigorously prove that the longtime average of the lagrange multipliers of the constrained langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints a second order time discretization using the lagrange multipliers is proposed iii the jarzynski crooks fluctuation relation is proved for langevin processes with mechanical constraints evolving in time an original numerical discretization without time step error is proposed numerical illustrations are provided for ii and iii

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

likelihood based estimation of latent generalized arch structures garch models are commonly used as latent processes in econometrics financial economics and macroeconomics yet no exact likelihood analysis of these models has been provided so far in this paper we outline the issues and suggest a markov chain monte carlo algorithm which allows the calculation of a classical estimator via the simulated em algorithm or a bayesian solution in o t computational operations where t denotes the sample size we assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 uk sectorial stock returns and compare it to existing approximate solutions

problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak abstract we draw attention to two problems associated with the use of instrumental variables iv the importance of which for empirical work has not been fully appreciated first the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the iv estimates even if only a weak relationship exists between the instruments and the error in the structural equation second in finite samples iv estimates are biased in the same direction as ordinary least squares ols estimates the magnitude of the bias of iv estimates approaches that of ols estimates as the r 2 between the instruments and the endogenous explanatory variable approaches 0 to illustrate these problems we reexamine the results of a recent paper by angrist and krueger who used large samples from the u s census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment we find evidence that despite huge sample sizes th

exact inference for growth curves with intraclass correlation structure summary we consider repeated observations taken over time for each of several subjects for example one might consider the growth curve of a cohort of babies over time we assume a simple linear growth curve model exact results based on sufficient statistics exact tests of the null hypothesis that a coefficient is zero or exact confidence intervals for coefficients are not available to make inference on regression coefficients when an intraclass correlation structure is assumed this paper will demonstrate that such exact inference is possible using generalized inference

notes on the overlap measure as an alternative to the youden index how are they related the receiver operating characteristic roc curve is frequently used to evaluate and compare diagnostic tests as one of the roc summary indices the youden index measures the effectiveness of a diagnostic marker and enables the selection of an optimal threshold value cut off point for the marker recently the overlap coefficient which captures the similarity between 2 distributions directly has been considered as an alternative index for determining the diagnostic performance of markers in this case a larger overlap indicates worse diagnostic accuracy and vice versa this paper provides a graphical demonstration and mathematical derivation of the relationship between the youden index and the overlap coefficient and states their advantages over the most popular diagnostic measure the area under the roc curve furthermore we outline the differences between the youden index and overlap coefficient and identify situations in which the overlap coefficient outperforms the youden index numerical examples and real data analysis are provided

estimation of the area under the roc curve the area under the receiver operating characteristic curve is frequently used as a measure for the effectiveness of diagnostic markers in this paper we discuss and compare estimation procedures for this area these are based on i the mann whitney statistic ii kernel smoothing iii normal assumptions iv empirical transformations to normality these are compared in terms of bias and root mean square error in a large variety of situations by means of an extensive simulation study overall we find that transforming to normality usually is to be preferred except for bimodal cases where kernel methods can be effective

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

marginally specified priors for non parametric bayesian estimation prior specification for non parametric bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high often infinite dimension a statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter such as the population mean or variance the paper proposes a new framework for non parametric bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts an informative prior on a finite set of functionals and a non parametric conditional prior for the parameter given the functionals such priors can be easily constructed from standard non parametric prior distributions in common use and inherit the large support of the standard priors on which they are based additionally posterior approximations under these informative priors can generally be made via minor adjustments to existing markov chain approximation algorithms for standard non parametric prior distributions we illustrate the use of such priors in the context of multivariate density estimation using dirichlet process mixture models and in the modelling of high dimensional sparse contingency tables

bayesian nonparametric estimation of the median part i computation of the estimates let x i i 1 ldots n be i i d sim f theta where f theta x f x theta for some f that has median equal to 0 f is assumed unknown or only partially known and the problem is to estimate theta priors are put on the pair f theta the priors on f concentrate all their mass on c d f s with median equal to 0 these priors include dirichlet type priors the marginal posterior distribution of theta given x 1 ldots x n is computed the mean of the posterior is taken as the estimate of theta

net reclassification index at event rate properties and relationships the net reclassification improvement nri is an attractively simple summary measure quantifying improvement in performance because of addition of new risk marker s to a prediction model originally proposed for settings with well established classification thresholds it quickly extended into applications with no thresholds in common use here we aim to explore properties of the nri at event rate we express this nri as a difference in performance measures for the new versus old model and show that the quantity underlying this difference is related to several global as well as decision analytic measures of model performance it maximizes the relative utility standardized net benefit across all classification thresholds and can be viewed as the kolmogorov smirnov distance between the distributions of risk among events and non events it can be expressed as a special case of the continuous nri measuring reclassification from the null model with no predictors it is also a criterion based on the value of information and quantifies the reduction in expected regret for a given regret function casting the nri at event rate as a measure of incremental reduction in expected regret more generally we find it informative to present plots of standardized net benefit relative utility for the new versus old model across the domain of classification thresholds then these plots can be summarized with their maximum values and the increment in model performance can be described by the nri at event rate we provide theoretical examples and a clinical application on the evaluation of prognostic biomarkers for atrial fibrillation copyright 2016 john wiley sons ltd

linear combinations of multiple diagnostic markers abstract the receiver operating characteristic roc curve is a simple and meaningful measure to assess the usefulness of diagnostic markers to use the information carried by multiple markers we note that fisher s linear discriminant function provides a linear combination of markers to maximize the sensitivity over the entire specificity range uniformly under the multivariate normal distribution model with proportional covariance matrices with no restriction on covariance matrices we also provide a solution of the best linear combination of markers in the sense that the area under the roc curve of this combination is maximized among all possible linear combinations we illustrate both situations discussed in the article with a cancer clinical trial data

a family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data summary in this paper we study a broad class of nonparametric statistics for comparing two diagnostic markers one can compare the sensitivities of these diagnostic markers over restricted ranges of specificity by selecting an appropriate statistic from this class as special cases one can compare the entire area under the receiver operator curve hanley mcneil 1982 or one can compare the sensitivities at a fixed common specificity usually we would recommend a comparison based on an average of sensitivities over a restricted high level of specificities test procedures and confidence intervals are based on asymptotic normality these procedures are applicable for paired data in which both diagnostic markers are performed on each subject and for unpaired data the procedures may be used to compare two real functions of multiple diagnostic markers as well as to compare individual markers

bayesian exponentially tilted empirical likelihood summary while empirical likelihood has been shown to exhibit many of the properties of conven tional parametric likelihoods a formal probabilistic interpretation has so far been lacking we show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric bayesian procedure which places a type of noninformative prior on the space of distributions this prior gives preference to distributions having a small support and among those sharing the same support it favours entropy maximising distributions the resulting nonparametric bayesian procedure admits a computationally convenient representation as an empirical likelihood type likelihood where the probability weights are obtained via exponential tilting the proposed methodology provides an attractive alternative to the bayesian bootstrap as a nonparametric limit of a bayesian procedure for moment condition models

long run accuracy of variational integrators in the stochastic context this paper presents a lie trotter splitting for inertial langevin equations geometric langevin algorithm and analyzes its long time statistical properties the splitting is defined as a composition of a variational integrator with an ornstein uhlenbeck flow assuming that the exact solution and the splitting are geometrically ergodic the paper proves the discrete invariant measure of the splitting approximates the invariant measure of inertial langevin equations to within the accuracy of the variational integrator in representing the hamiltonian in particular if the variational integrator admits no energy error then the method samples the invariant measure of inertial langevin equations without error numerical validation is provided using explicit variational integrators with first second and fourth order accuracy

bayesian empirical likelihood summary research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods this leads naturally to the possibility of using empirical likelihood as the basis for bayesian inference different ways in which this goal might be accomplished are considered the validity of the resultant posterior inferences is examined as are frequentist properties of the bayesian empirical likelihood intervals

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

roc analysis for markers with mass at zero the receiver operating characteristic roc curve and in particular the area under the curve auc is commonly used to examine the discriminatory ability of diagnostic markers certain markers while basically continuous and non negative have a positive probability mass spike at the value zero we discuss a flexible modelling approach to such data and contrast it with the standard non parametric approach we show how the modelling approach can be extended to take account of the effect of explanatory variables we motivate this problem and illustrate the modelling approach using data on the coronary calcium score measured by electron beam tomography which is a marker for atherosclerosis

efficient molecular dynamics using geodesic integration and solvent solute splitting we present an approach to langevin dynamics in the presence of holonomic constraints based on decomposition of the system into components representing geodesic flow constrained impulse and constrained diffusion we show that a particular ordering of the components results in an integrator that is an order of magnitude more accurate for configurational averages than existing alternatives moreover by combining the geodesic integration method with a solvent solute force splitting we demonstrate that stepsizes of at least 8 fs can be used for solvated biomolecules with high sampling accuracy and without substantially altering diffusion rates approximately increasing by a factor of two the efficiency of molecular dynamics sampling for such systems the methods described in this article are easily implemented using the standard apparatus of modern simulation codes

eigenvalue distributions of random unitary matrices let u be an n n random matrix chosen from haar measure on the unitary group for a fixed arc of the unit circle let x be the number of eigenvalues of m which lie in the specified arc we study this random variable as the dimension n grows using the connection between toeplitz matrices and random unitary matrices and show that x e x var x 1 2 is asymptotically normally distributed in addition we show that for several fixed arcs i1 im the corresponding random variables are jointly normal in the large n limit

asymptotic distribution of auc nris and idi based on theory of u statistics the change in area under the curve auc the integrated discrimination improvement idi and net reclassification index nri are commonly used measures of risk prediction model performance some authors have reported good validity of associated methods of estimating their standard errors se and construction of confidence intervals whereas others have questioned their performance to address these issues we unite the auc idi and three versions of the nri under the umbrella of the u statistics family we rigorously show that the asymptotic behavior of auc nris and idi fits the asymptotic distribution theory developed for u statistics we prove that the auc nris and idi are asymptotically normal unless they compare nested models under the null hypothesis in the latter case asymptotic normality and existing se estimates cannot be applied to auc nris or idi in the former case se formulas proposed in the literature are equivalent to se formulas obtained from u statistics theory if we ignore adjustment for estimated parameters we use sukhatme randles dewet condition to determine when adjustment for estimated parameters is necessary we show that adjustment is not necessary for ses of the auc and two versions of the nri when added predictor variables are significant and normally distributed the ses of the idi and three category nri should always be adjusted for estimated parameters these results allow us to define when existing formulas for se estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models we also use the u statistic theory to develop a new se estimate of auc copyright 2017 john wiley sons ltd

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

bayesian inference for semiparametric binary regression abstract we propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale predictors enter linearly we demonstrate bayesian inference calculations in this model by modifying the dirichlet process we obtain a natural prior measure over this semiparametric model and we use polya sequence theory to formulate this measure in terms of a finite number of unobserved variables we design a markov chain monte carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer

central limit theorems for sequences of multiple stochastic integrals we characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1 some applications are given in particular to study the limiting behavior of quadratic functionals of gaussian processes

confidence intervals for p y1 y2 with normal outcomes in linear models recently there is an emerging interest in the inference of p y1 y2 where y1 and y2 stand for two independent continuous random variables so far most of the research in this field focuses on simply comparing two outcomes without adjusting for covariates this paper mainly presents a large sample approach based on a noncentral t distribution for the confidence interval estimation of p y1 y2 with normal outcomes in linear models furthermore the performance of the proposed large sample approach is compared with that of a generalized variable approach and a bootstrap approach simulation studies demonstrate that for small to medium sample sizes both the large sample approach and the generalized variable approach provide confidence intervals with satisfying coverage probabilities whereas the bootstrap approach can be slightly liberal for certain scenarios the proposed approaches are applied to three real life data sets copyright 2008 john wiley sons ltd

bayesian empirical likelihood for quantile regression bayesian inference provides a flexible way of combining data with prior information however quantile regression is not equipped with a parametric likelihood and therefore bayesian inference for quantile regression demands careful investigation this paper considers the bayesian empirical likelihood approach to quantile regression taking the empirical likelihood into a bayesian framework we show that the resultant posterior from any fixed prior is asymptotically normal its mean shrinks toward the true parameter values and its variance approaches that of the maximum empirical likelihood estimator a more interesting case can be made for the bayesian empirical likelihood when informative priors are used to explore commonality across quantiles regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas e g high or low percentile levels through empirical likelihood the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains by using an mcmc algorithm in the computation we avoid the daunting task of directly maximizing empirical likelihood the finite sample performance of the proposed method is investigated empirically where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels a theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method

the winding of stationary gaussian processes this paper studies the winding of a continuously differentiable gaussian stationary process f mathbb r rightarrow mathbb c in the interval 0 t we give formulae for the mean and the variance of this random variable the variance is shown to always grow at least linearly with t and conditions for it to be asymptotically linear or quadratic are given moreover we show that if the covariance function together with its second derivative are in l 2 mathbb r then the winding obeys a central limit theorem these results correspond to similar results for zeroes of real valued stationary gaussian functions by malevich cuzick slud and others

what to expect from net reclassification improvement with three categories the net reclassification improvement nri has become a popular measure of incremental usefulness of markers added to risk prediction models however the expected magnitude of the three category nri is not well understood leading researchers to rely on statistical significance in this paper we describe a slight modification to the original definition of the nri which weighs each reclassification by the number of categories by which a given individual is reclassified this modification resolves some recent criticisms of the three category nri and at the same time has a minimal impact on its magnitude then we show that using this modified definition the event and nonevent nris have simple interpretations as sums of changes in sensitivities and specificities calculated at the risk thresholds we exploit this relationship to arrive at closed form solutions for the nri under normality within the event and nonevent subgroups we observe that the size of the intermediate risk category and the event rate have limited impact on the magnitude of the nri as expected the nri increases with the strength of the added marker and this relationship appears fairly proportional for markers with non weak net effect size above 0 25 furthermore we conclude that using the nri as a metric it is harder to improve models that already perform well

inference of the youden index and associated threshold using empirical likelihood for quantiles the youden index is a widely used measure in the framework of medical diagnostics where the effectiveness of a biomarker screening marker or predictor for classifying a disease status is studied when the biomarker is continuous it is important to determine the threshold or cut off point to be used in practice for the discrimination between diseased and healthy populations we introduce two methods aimed at estimating the youden index and its associated threshold the first one is a modified version of a recent approach based on the delta method and the second one is based on the adjusted empirical likelihood for quantiles in the setting of a two sample problem we also include cis for both of them in the simulation study we compare both methods under different scenarios finally a real example of prostatic cancer well known in the literature is analysed to provide the reader with a better understanding of the new methodology copyright 2011 john wiley sons ltd

testing for improvement in prediction model performance authors have proposed new methodology in recent years for evaluating the improvement in prediction performance gained by adding a new predictor y to a risk model containing a set of baseline predictors x for a binary outcome d we prove theoretically that null hypotheses concerning no improvement in performance are equivalent to the simple null hypothesis that y is not a risk factor when controlling for x h0 p d 1 x y p d 1 x therefore testing for improvement in prediction performance is redundant if y has already been shown to be a risk factor we also investigate properties of tests through simulation studies focusing on the change in the area under the roc curve auc an unexpected finding is that standard testing procedures that do not adjust for variability in estimated regression coefficients are extremely conservative this may explain why the auc is widely considered insensitive to improvements in prediction performance and suggests that the problem of insensitivity has to do with use of invalid procedures for inference rather than with the measure itself to avoid redundant testing and use of potentially problematic methods for inference we recommend that hypothesis testing for no improvement be limited to evaluation of y as a risk factor for which methods are well developed and widely available analyses of measures of prediction performance should focus on estimation rather than on testing for no improvement in performance copyright 2013 john wiley sons ltd

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

joint confidence region estimation for area under roc curve and youden index in the field of diagnostic studies the area under the roc curve auc serves as an overall measure of a biomarker diagnostic test s accuracy youden index defined as the overall correct classification rate minus one at the optimal cut off point is another popular index for continuous biomarkers of binary disease status although researchers mainly evaluate the diagnostic accuracy using auc for the purpose of making diagnosis youden index provides an important and direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to auc furthermore auc and youden index are generally correlated in this paper we initiate the idea of evaluating diagnostic accuracy based on auc and youden index simultaneously as the first step toward this direction this paper only focuses on the confidence region estimation of auc and youden index for a single marker we present both parametric and non parametric approaches for estimating joint confidence region of auc and youden index we carry out extensive simulation study to evaluate the performance of the proposed methods in the end we apply the proposed methods to a real data set copyright 2013 john wiley sons ltd

bayesian analysis of constrained parameter and truncated data problems using gibbs sampling abstract constrained parameter problems arise in a wide variety of applications including bioassay actuarial graduation ordinal categorical data response surfaces reliability development testing and variance component models truncated data problems arise naturally in survival and failure time studies ordinal data models and categorical data studies aimed at uncovering underlying continuous distributions in many applications both parameter constraints and data truncation are present the statistical literature on such problems is very extensive reflecting both the problems widespread occurrence in applications and the methodological challenges that they pose however it is striking that so little of this applied and theoretical literature involves a parametric bayesian perspective from a technical viewpoint this perhaps is not difficult to understand the fundamental tool for bayesian calculations in typical realistic models is multidimensional numerical integration which often is problem

generalized confidence intervals abstract the definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances under certain conditions the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals the proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models a repeated sampling property of generalized p values is also given with this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values finally pratt s paradox is revisited and a procedure that resolves the paradox is given

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

an ergodic sampling scheme for constrained hamiltonian systems with applications to molecular dynamics this article addresses the problem of computing the gibbs distribu tion of a hamiltonian system that is subject to holonomic constraints in doing so we extend recent ideas of cances et al m2an vol 41 no 2 pp 351 389 2007 who could prove a law of large numbers for unconstrained molecular systems with a separable hamiltonian em ploying a discrete version of hamilton s principle studying ergodicity for constrained hamiltonian systems we specifically focus on the numerical discretization error even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization the discretization error is taken care of by means of a hybrid monte carlo al gorithm that allows for sampling bias free expectation values with respect to the gibbs measure independently of the stable step size we give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide

fluctuations of the increment of the argument for the gaussian entire function the gaussian entire function is a random entire function characterised by a certain invariance with respect to isometries of the plane we study the fluctuations of the increment of the argument of the gaussian entire function along planar curves we introduce an inner product on finite formal linear combinations of curves with real coefficients that we call the signed length which describes the limiting covariance of the increment we also establish asymptotic normality of fluctuations

rattle a velocity version of the shake algorithm for molecular dynamics calculations an algorithm called rattle for integrating the equations of motion in molecular dynamics calculations for molecular models with internal constraints is presented the algorithm is similar to shake which is one of the standard methods for performing such calculations rattle calculates the positions and velocities at the next time from the positions and velocities at the present time step without requiring information about the earlier history like shake it is based on the verlet algorithm and retains the simplicity of using cartesian coordinates for each of the atoms to describe the configuration of a molecule with internal constraints rattle guarantees that the coordinates and velocities of the atoms in a molecule satisfy the internal constraints at each time step rattle has two advantages over shake on computers of fixed precision it is of higher precision than shake since it deals directly with the velocities it is easier to modify rattle for use with the recently developed constant temperature and constant pressure molecular dynamics methods and with the nonequilibrium molecular dynamics methods that make use of rescaling of the atomic velocities

an arithmetic model for the total disorder process we prove a multidimensional extension of selberg s central limit theorem for the logarithm of the riemann zeta function on the critical line the limit is a totally disordered process whose coordinates are all independent and gaussian

bayesian computation via empirical likelihood approximate bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable however the well established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate bayesian computation parameters summary statistics distance tolerance while being convergent in the number of observations furthermore bypassing model simulations may lead to significant time savings in complex models for instance those found in population genetics the bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size the method is illustrated using several examples including estimation of standard distributions time series and population genetics models

correlation functions for random complex zeroes strong clustering and local universality we prove strong clustering of k point correlation functions of zeroes of gaussian entire functions in the course of the proof we also obtain universal local bounds for k point functions of zeroes of arbitrary nondegenerate gaussian analytic functions in the second part of the paper we show that strong clustering yields the asymptotic normality of fluctuations of some linear statistics of zeroes of gaussian entire functions in particular of the number of zeroes in measurable domains of large area this complements our recent results from the paper fluctuations in random complex zeroes