likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

a flexible approach to the crossing hazards problem we propose a simple and flexible framework for the crossing hazards problem the method is not confined to two sample problems but may also work with continuous exposure variables whose effect changes its sign at some time point of the observed follow up time penalized partial likelihood estimation relies upon the assumption of a smooth hazard ratio via low rank basis splines with a conventional difference penalty to ensure smoothness and additional ad hoc penalties to obtain restricted estimates useful in the context of crossing hazards the framework naturally also leads to a statistical test that has good power for revealing a global effect under several alternatives including crossing hazards we provide the results from a real data analysis and from some simulations to illustrate empirically the performance of the proposed approach as compared with the possible alternatives

assessing time by covariate interactions in proportional hazards regression models using cubic spline functions proportional hazards or cox regression is a popular method for modelling the effects of prognostic factors on survival use of cubic spline functions to model time by covariate interactions in cox regression allows investigation of the shape of a possible covariate time dependence without having to specify a specific functional form cubic spline functions allow one to graph such time by covariate interactions to test formally for the proportional hazards assumption and also to test for non linearity of the time by covariate interaction the functions can be fitted with existing software using relatively few parameters the regression coefficients are estimated using standard maximum likelihood methods

on tests against one sided hypotheses in some generalized linear models one sided hypotheses arise naturally in many situations when testing against such hypotheses it is desirable to take the available one sided information into account rather than simply applying a two sided test what we expect to gain by applying a one sided test instead of a two sided test is an increase in the power of the test we consider various tests of one sided hypotheses in a class of models that includes generalized linear and cox regression models the tests are likelihood ratio wald score generalized distance and a pearson chi square it is shown that these test statistics are asymptomatically equivalent in terms of local power this is a generalization of the well known corresponding result for two sided alternatives two examples are also discussed they are on 1 testing for interaction in binomial response models and 2 comparison of treatments with ordinal categorical responses

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

survival analysis with time varying regression effects using a tree based approach nonproportional hazards often arise in survival analysis as is evident in the data from the international non hodgkin s lymphoma prognostic factors project a tree based method to handle such survival data is developed for the assessment and estimation of time dependent regression effects under a cox type model the tree method approximates the time varying regression effects as piecewise constants and is designed to estimate change points in the regression parameters a fast algorithm that relies on maximized score statistics is used in recursive segmentation of the time axis following the segmentation a pruning algorithm with optimal properties similar to those of classification and regression trees cart is used to determine a sparse segmentation bootstrap resampling is used in correcting for overoptimism due to split point optimization the piecewise constant model is often more suitable for clinical interpretation of the regression parameters than the more flexible spline models the utility of the algorithm is shown on the lymphoma data where we further develop the published international risk index into a time varying risk index for non hodgkin s lymphoma

efficient particle filtering for jump markov systems application to time varying autoregressions we present an efficient particle filtering method to perform optimal estimation in jump markov nonlinear systems jmss such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure we take advantage of these specificities in order to develop a generic filtering methodology for these models the method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature namely the auxiliary particle filter and the unscented transform this algorithm is applied to the complex problem of time varying autoregressive estimation with an unknown time varying model order more precisely we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations we show that this problem can be formulated as a jms and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper simulations demonstrate the performance of our method compared to standard particle filtering techniques

fast filtering in switching approximations of non linear markov systems with applications to stochastic volatility we consider the problem of optimal statistical filtering in general non linear non gaussian markov dynamic systems the novelty of the proposed approach consists in approximating the non linear system by a recent markov switching process in which one can perform exact and optimal filtering with a linear time complexity all we need to assume is that the system is stationary or asymptotically stationary and that one can sample its realizations we evaluate our method using two stochastic volatility models and results show its efficiency

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

diffusion for chaotic plane sections of 3 periodic surfaces we study chaotic plane sections of some particular family of triply periodic surfaces the question about possible behavior of such sections was posed by s p novikov we prove some estimations on the diffusion rate of these sections using the connection between novikov s problem and systems of isometries some natural generalization of interval exchange transformations using thermodynamical formalism we construct an invariant measure for systems of isometries of a special class called the rauzy gasket and investigate the main properties of the lyapunov spectrum of the corresponding suspension flow

composite kernel machine regression based on likelihood ratio test for joint testing of genetic and gene environment interaction effect most common human diseases are a result from the combined effect of genes the environmental factors and their interactions such that including gene environment ge interactions can improve power in gene mapping studies the standard strategy is to test the snps one by one using a regression model that includes both the snp effect and the ge interaction however the snp by snp approach has serious limitations such as the inability to model epistatic snp effects biased estimation and reduced power thus in this article we develop a kernel machine regression framework to model the overall genetic effect of a snp set considering the possible ge interaction specifically we use a composite kernel to specify the overall genetic effect via a nonparametric function andwe model additional covariates parametrically within the regression framework the composite kernel is constructed as a weighted average of two kernels one corresponding to the genetic main effect and one corresponding to the ge interaction effect we propose a likelihood ratio test lrt and a restricted likelihood ratio test rlrt for statistical significance we derive a monte carlo approach for the finite sample distributions of lrt and rlrt statistics extensive simulations and real data analysis show that our proposed method has correct type i error and can have higher power than score based approaches under many situations

semiparametric inference in generalized mixed effects models summary the paper presents a study of the generalized partially linear model including random effects in its linear part we propose an estimator that combines likelihood approaches for mixed effects models with kernel methods following the methodology of hardie and co workers we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model the critical values are estimated by using a bootstrap procedure the asymptotic theory for the methods is provided as are the results of a simulation study these verify the feasibility and the excellent behaviour of the methods for samples of even moderate size the usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in galicia spain

the wilson hilferty transformation is locally saddlepoint interest in transform methods for normalising test statistics declined with the advent of computers more recently small sample asymptotic methods have been developed to approximate the distributions of complicated test statistics we propose a generalisation of a classical symmetrising transform to a similar range of statistics it is shown to behave comparably in a parametric neighbourhood to methods that exploit exponential tilting

generalization of likelihood ratio tests under nonstandard conditions in this paper we analyze the statistic which is the difference in the values of an estimating function evaluated at its local maxima on two different subsets of the parameter space assuming that the true parameter is in each subset but possibly on the boundary our results extend known methods by covering a large class of estimation problems which allow sampling from nonidentically distributed random variables specifically the existence and consistency of the local maximum estimators and asymptotic properties of useful hypothesis tests are obtained under certain law of large number and central limit type assumptions other models covered include those with general log likelihoods and or covariates as an example the large sample theory of two way nested random variance components models with covariates is derived from our main results

testing lack of fit in multiple regression summary we study lack of fit tests based on orthogonal series estimators a common feature of these tests is that they are functions of score statistics that employ data driven model dimensions the criteria used to select the dimension are score based versions of aic and bic the tests can be applied in a wide variety of settings including both continuous and discrete data with two or more covariates a model sequence i e a path in the alternative models space has to be chosen critical points and p values of the lack of fit tests can be obtained via asymptotic distribution theory or by use of the bootstrap data examples and a simulation study illustrate the applicability of the tests

a criterion for the simplicity of the lyapunov spectrum of square tiled surfaces we present a galois theoretical criterion for the simplicity of the lyapunov spectrum of the kontsevich zorich cocycle over the teichmuller flow on the mathrm sl 2 mathbb r orbit of a square tiled surface the simplicity of the lyapunov spectrum has been proved by a avila and m viana with respect to the so called masur veech measures associated to connected components of moduli spaces of translation surfaces but is not always true for square tiled surfaces of genus geqslant 3 we apply our criterion to square tiled surfaces of genus 3 with one single zero conditionally to a conjecture of delecroix and lelievre we prove with the aid of siegel s theorem on integral points on algebraic curves of genus 0 that all but finitely many such square tiled surfaces have simple lyapunov spectrum

on applicability of the interacting multiple model approach to state estimation for systems with sojourn time dependent markov model switching in this paper the attempt at the interacting multiple model imm method extension to the state estimation problem with semi markov sojourn time dependent markov stdm system model switching is analyzed it is demonstrated that such an stdm imm approach does not properly take into account the specific character of the stdm switching in the system and it becomes a reason for the reduction of estimation accuracy for this problem it is shown that a hypotheses merging should be restricted in such a way that not only the current system model but also the sojourn time in the model should be given in hypotheses to be tested some other aspects of bayesian estimation in a switching environment are also discussed

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

saddlepoint approximations for distributions of quadratic forms in normal variables reference stat article 1999 001doi 10 1093 biomet 86 4 929view record in web of science record created on 2006 04 21 modified on 2017 05 12

weighted log rank statistics for comparing two distributions summary the derivation of locally most powerful rank statistics for comparing two censored samples against parametric alternatives is reformulated for more general classes of alternatives a particular class is considered which includes the case of two weibull distributions differing in shape parameter

simplicity of lyapunov spectra proof of the zorich kontsevich conjecture we prove the zorich kontsevich conjecture that the non trivial lyapunov exponents of the teichmuller ow on any connected component of a stratum of the moduli space of abelian differentials on compact riemann surfaces are all distinct by previous work of zorich and kontsevich this implies the existence of the complete asymptotic lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

on the asymptotics of constrained m estimation limit theorems for an m estimate constrained to lie in a closed subset of r d are given under two different sets of regularity conditions a consistent sequence of global optimizers converges under chernoff regularity of the parameter set a n consistent sequence of local optimizers converges under clarke regularity of the parameter set in either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value limit theorems for the optimal value are also obtained agreeing with chernoff s result in the case of maximum likelihood with global optimizers

entropic latent variable integration via simulation this paper introduces a general method to convert a model defined by moment conditions that involve both observed and unobserved variables into equivalent moment conditions that involve only observable variables this task can be accomplished without introducing infinite dimensional nuisance parameters using a least favorable entropy maximizing distribution we demonstrate through examples and simulations that this approach covers a wide class of latent variables models including some game theoretic models and models with limited dependent variables interval valued data errors in variables or combinations thereof both point and set identified models are transparently covered in the latter case the method also complements the recent literature on generic set inference methods by providing the moment conditions needed to construct a generalized method of moments type objective function for a wide class of models extensions of the method that cover conditional moments independence restrictions and some state space models are also given

diagnostics for assessing regression models abstract we concern ourselves with diagnostics for checking the overall and local goodness of fit of a model s x used in the regression of y on x u 0 1 d the model for s x is a functional form that depends on a finite number of unknown parameters two statistics and w are proposed that measure the level of agreement between the model fit to the data and the nonparametric kernel estimator on m preselected points in u conditions are given under which and w are asymptotically equivalent both of these statistics measure overall lack of fit and are related to the deviance their asymptotic distribution under the null model and under local alternatives is derived this work is motivated by the local mean deviance plot of landwehr pregibon and shoemaker for assessing overall lack of fit in logistic regression their plot is summarized by our test statistics and is extended to other likelihood based regressions of y on x

connected components of the moduli spaces of abelian differentials with prescribed singularities consider the moduli space of pairs c where c is a smooth compact complex curve of a given genus and is a holomorphic 1 form on c with a given list of multiplicities of zeroes we describe connected components of this space this classification is important in the study of dynamics of interval exchange transformations and billiards in rational polygons and in the study of geometry of translation surfaces

square tiled surfaces and rigid curves on moduli spaces abstract we study the algebro geometric aspects of teichmuller curves parameterizing square tiled surfaces with two applications a there exist infinitely many rigid curves on the moduli space of hyperelliptic curves they span the same extremal ray of the cone of moving curves their union is a zariski dense subset hence they yield infinitely many rigid curves with the same properties on the moduli space of stable n pointed rational curves for even n b the limit of slopes of teichmuller curves and the sum of lyapunov exponents for the teichmuller geodesic flow determine each other which yields information about the cone of effective divisors on the moduli space of curves

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

a two sample censored data rank test for acceleration a score test for the null hypothesis of proportional hazards against rank regression alternatives is proposed as a complement to the logrank test for comparing censored survival curves the test statistic has an asymptotic normal distribution that is independent of the logrank distribution under the null hypothesis and its power is good against acceleration alternatives i e with crossing hazards where the logrank test fails monte carlo studies indicate that its small sample properties are comparable to those of the logrank and ranksum procedures

testing the fit of a parametric function abstract general methods for testing the fit of a parametric function are proposed the idea underlying each method is to accept the prescribed parametric model if and only if it is chosen by a model selection criterion several different selection criteria are considered including one based on a modified version of the akaike information criterion and others based on various score statistics the tests have a connection with nonparametric smoothing because they use orthogonal series estimators to detect departures from a parametric model an important aspect of the tests is that they can be applied in a wide variety of settings including generalized linear models spectral analysis the goodness of fit problem and longitudinal data analysis implementation using standard statistical software is straightforward asymptotic distribution theory for several test statistics is described and the tests are shown to be consistent against essentially any alternative hypothesis simulations and a data exampl

variable selection and function estimation in additive nonparametric regression using a data based prior abstract a hierarchical bayesian approach is proposed for variable selection and function estimation in additive nonparametric gaussian regression models and additive nonparametric binary regression models the prior for each component function is an integrated wiener process resulting in a posterior mean estimate that is a cubic smoothing spline each of the explanatory variables is allowed to be in or out of the model and the regression functions are estimated by model averaging to allow variable selection and model averaging data based priors are used for the smoothing parameter and the slope at 0 of each component function a two step markov chain monte carlo method is used to efficiently obtain the data based prior and to carry out variable selection and function estimation it is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously the methodology is illustrated for a binary regressio

balanced truncation for discrete time markov jump linear systems this technical note investigates the model reduction problem for mean square stable discrete time markov jump linear systems for this class of systems a balanced truncation algorithm is developed the reduced order model is suboptimal however the approximation error which is captured by means of the stochastic gain is bounded from above by twice the sum of singular numbers associated to the truncated states of each mode such a result allows rigorous simplification of the dynamics of each mode in an independent manner with respect to a metric which is relevant from a robust control point of view

prym varieties and teichmuller curves this paper gives a uniform construction of infinitely many primitive teichmuller curves v mg for g 2 3 and 4

degrees of freedom tests for smoothing splines when using smoothing splines to estimate a function the user faces the problem of choosing the smoothing parameter several techniques are available for selecting this parameter according to certain optimality criteria here we take a different point of view and we propose a technique for choosing between two alternatives for example allowing for two different levels of degrees of freedom the problem is addressed in the framework of a mixed effects model whose assumptions ensure that the resulting estimator is unbiased a likelihood ratio type test statistic is proposed and its exact distribution is derived tests of linearity and overall effect follow directly we then extend this idea to additive models where it provides a more attractive alternative than multi parameter optimisation and where it gives exact distributional results that can be used in an analysis of deviance type approach examples on real data and a simulation study of level and power complete the paper

filtering of nonlinear stochastic feedback systems this paper concerns the filtering problem for a class of stochastic nonlinear systems where the drift term may depend either on some external function open loop system or on the system output closed loop system through a controller such systems are denoted feedback systems the following result is proven for feedback systems the optimal filter in the open loop case remains optimal when the feedback is closed the proof is obtained by showing equivalence of suitable expressions for the estimators of the open loop and closed loop systems obtained using the kallianpur striebel formula g kallianpur and c striebel ann math statist 39 1968 pp 785 801

isolation equidistribution and orbit closures for the sl 2 r action on moduli space we prove results about orbit closures and equidistribution for the sl 2 r action on the moduli space of compact riemann surfaces which are analogous to the theory of unipotent ows the proofs of the main theorems rely on the measure classication theorem of the rst two authors and a certain isolation property of closed sl 2 r invariant manifolds developed in this paper

restricted likelihood ratio lack of fit tests using mixed spline models penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non linearity in the smooth function estimates this motivates the study of lack of fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values for this one sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies and finite sample approximations to the asymptotic distribution are provided test statistics are studied for simple as well as multiple regression models

dynamic cox modelling based on fractional polynomials time variations in gastric cancer prognosis the most popular model used for survival analysis is the proportional hazards regression model proposed by cox this is mainly due to its exceptional simplicity nevertheless the fundamental assumption of the cox model is the proportionality of the hazards for many applications however this assumption is doubtful proposals to extend the cox model for non proportional hazards to allow for dynamic effect structures usually either depend on prespecifications or require non standard estimation techniques and are thus not favoured in application moreover tests to verify the dynamic effect structures are not straightforward or lack omnibus power in this paper we propose a flexible method for modelling dynamic effects in survival data within the cox framework the method is based on fractional polynomials as introduced by royston and altman this allows for a transformation of the dynamic predictor which leads back to the conventional cox model and hence fitting is straightforward using standard estimation techniques in addition it offers the possibility of easily verifying the existence of time variation we describe a model selection algorithm which selects time varying effects only when evidence is given in the data we illustrate the properties of the approach in a simulation study and compare it with other methods in a survival study of gastric cancer patients we apply the approach to analyse dynamic structures in the effects of prognostic factors

characterizations of lattice surfaces we answer a question of vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles we show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality we deduce several other characterizations of the lattice property

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

wald criteria for jointly testing equality and inequality restrictions on montre comment le test de wald s applique a des ensembles de restrictions d egalite et d inegalite et on presente la distribution pour de grands echantillons du test sous l hypothese nulle

flexible modelling of discrete failure time including time varying smooth effects discrete survival models have been extended in several ways more flexible models are obtained by including time varying coefficients and covariates which determine the hazard rate in an additive but not further specified form in this paper a general model is considered which comprises both types of covariate effects an additional extension is the incorporation of smooth interaction between time and covariates thus in the linear predictor smooth effects of covariates which may vary across time are allowed it is shown how simple duration models produce artefacts which may be avoided by flexible models for the general model which includes parametric terms time varying coefficients in parametric terms and time varying smooth effects estimation procedures are derived which are based on the regularized expansion of smooth effects in basis functions the approach is used to model the sojourn time in a psychiatric hospital it is demonstrated how initial conditions which have non linear influence are damped over time

zorich conjecture for hyperelliptic rauzy veech groups we describe the structure of hyperelliptic rauzy diagrams and hyperelliptic rauzy veech groups in particular this provides a solution of the hyperelliptic cases of a conjecture of zorich on the zariski closure of rauzy veech groups

testing goodness of fit in regression a general approach for specified alternatives when fitting generalized linear models or the cox proportional hazards model it is important to have tools to test for lack of fit because lack of fit comes in all shapes and sizes distinguishing among different types of lack of fit is of practical importance we argue that an adequate diagnosis of lack of fit requires a specified alternative model such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis we know the direction of the departure from the model the goodness of fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases connections with penalized likelihood and random effects are discussed and the application of the proposed approach is illustrated with medical examples tailored functions for goodness of fit testing have been implemented in the r package globaltest copyright 2012 john wiley sons ltd

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

time dependent effects of fixed covariates in cox regression a nonparametric modification is proposed for cox s proportional hazards model cox 1972 journal of the royal statistical society series b 34 187 220 where the covariates are fixed but their effects are allowed to vary in time parameters are introduced for the covariate effects at the uncensored survival times estimates are obtained by maximizing the penalized partial log likelihood that arises if a penalty function of the first order differences of consecutive parameters is subtracted from the partial log likelihood the choice of the smoothing parameter which determines the weight of the penalty is based on akaike s information criterion the methods are illustrated in a set of ovarian cancer data and in a set of kidney transplantation data

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

non parametric small area estimation using penalized spline regression the paper proposes a small area estimation approach that combines small area random effects with a smooth non parametrically specified trend by using penalized splines as the representation for the non parametric trend it is possible to express the non parametric small area estimation problem as a mixed effect model regression the resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood we present theoretical results on the prediction mean squared error of the estimator proposed and on likelihood ratio tests for random effects and we propose a simple non parametric bootstrap approach for model inference and estimation of the small area prediction mean squared error the applicability of the method is demonstrated on a survey of lakes in north eastern usa

exact likelihood ratio tests for penalised splines summary penalised spline based additive models allow a simple mixed model representation where the variance components control departures from linear models the smoothing parameter is the ratio of the random coefficient and error variances and tests for linear regression reduce to tests for zero random coefficient variances we propose exact likelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines their spectral decompositions are used as the basis of fast simulation algorithms we derive the asymptotic local power properties of the tests under weak conditions in particular we characterise the local alternatives that are detected with asymptotic probability one confidence intervals for the smoothing parameter are obtained by inverting the tests for a fixed smoothing parameter versus a general alternative we discuss f and r tests and show that ignoring the variability in the smoothing parameter estimator can have a dramatic effect on their null distributions the powers of several known tests are investigated and a small set of tests with good power properties is identified the restricted likelihood ratio test is among the best in terms of power

prym covers theta functions and kobayashi curves in hilbert modular surfaces algebraic curves in hilbert modular surfaces that are totally geodesic for the kobayashi metric have very interesting geometric and arithmetic properties e g they are rigid there are very few methods known to construct such algebraic geodesics that we call kobayashi curves we give an explicit way of constructing kobayashi curves using determinants of derivatives of theta functions this construction also allows to calculate the euler characteristics of the teich m uller curves constructed by mcmullen using prym covers

a two stage procedure for comparing hazard rate functions summary comparison of two hazard rates is important in applications that are related to times to occurrence of a specific event conventional comparison procedures such as the log rank gehan wilcoxon and peto peto tests are powerful only when the two hazard rates do not cross each other because crossing hazard rates are common in practice several procedures have been proposed in the literature for comparing such rates however most of these procedures consider only the alternative hypothesis with crossing hazard rates many other realistic cases including those when the two hazard rates run parallel to each other are excluded from consideration we propose a two stage procedure that considers all possible alternatives including ones with crossing or running parallel hazard rates to define its significance level and p value properly a new procedure for handling the crossing hazard rates problem is suggested which has the property that its test statistic is asymptotically independent of the test statistic of the log rank test we show that the two stage procedure with the log rank test and the suggested procedure for handling the crossing hazard rates problem used in its two stages performs well in applications in comparing two hazard rates

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

spline based tests in survival analysis this paper examines a method for testing hypotheses on covariate effects in a proportional hazards model and also on how effects change over time in regression analysis of survival data the technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models the basic idea is to formulate a flexible parametric alternative using fixed knot splines together with a penalty function that penalizes noisy alternatives more than smooth ones to focus the power of the tests toward smooth alternatives the test statistics are the analogs of ordinary likelihood based statistics only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log likelihood large sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases numerical results suggest these approximations may be adequate with moderate sized samples

teichmuller curves in moduli space eisenstein series and an application to triangular billiards there exists a teichmuller disc n containing the riemann surface ofy2 x n 1 in the genus n 1 2 teichmuller space such that the stabilizer of n in the mapping class group has a fundamental domain of finite poincare volume in n application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles n n n 2 n and to the uniform distribution of infinite billiard trajectories in the same triangles

optimal filter approximations in conditionally gaussian pairwise markov switching models we consider a general triplet markov gaussian linear system bf x bf r bf y where bf x is an hidden continuous random sequence bf r is an hidden discrete markov chain bf y is an observed continuous random sequence when the triplet bf x bf r bf y is a classical conditionally gaussian linear state space model cglssm the mean square error optimal filter is not workable with a reasonable complexity and different approximate methods e g based on particle filters are used we propose two contributions the first one is to extend the cglssm to a new more general model called the conditionally gaussian pairwise markov switching model cgpmsm in which bf x is not necessarily markov given bf r the second contribution is to consider a particular case of cgpmsm in which bf r bf y is markov and in which an exact filter optimal in the sense of mean square error can be performed with linear time complexity some experiments show that the proposed method and the suited particle filter have comparable efficiency while the second one is much faster

inference in smoothing spline analysis of variance summary smoothing spline analysis of variance decomposes a multivariate function into additive components this decomposition not only provides an efficient way to model a multivariate function but also leads to meaningful inference by testing whether a certain component equals 0 no formal procedure is yet available to test such a hypothesis we propose an asymptotic method based on the likelihood ratio to test whether a functional component is 0 this test allows us to choose an optimal model and to compare groups of curves we first develop the general theory by exploiting the connection between mixed effects models and smoothing splines we then apply this to compare two groups of curves and to select an optimal model in a two dimensional problem a small simulation is used to assess the finite sample performance of the likelihood ratio test