regularized sandwich estimators for analysis of high dimensional data using generalized estimating equations summary a modification of generalized estimating equations gees methodology is proposed for hypothesis testing of high dimensional data with particular interest in multivariate abundance data in ecology an important application of interest in thousands of environmental science studies such data are typically counts characterized by high dimensionality in the sense that cluster size exceeds number of clusters n k and over dispersion relative to the poisson distribution usual gee methods cannot be applied in this setting primarily because sandwich estimators become numerically unstable as n increases we propose instead using a regularized sandwich estimator that assumes a common correlation matrix r and shrinks the sample estimate of r toward the working correlation matrix to improve its numerical stability it is shown via theory and simulation that this substantially improves the power of wald statistics when cluster size is not small we apply the proposed approach to study the effects of nutrient addition on nematode communities and in doing so discuss important issues in implementation such as using statistics that have good properties when parameter estimates approach the boundary and using resampling to enable valid inference that is robust to high dimensionality and to possible model misspecification

efficient bootstrap simulation on donne deux idees pour renforcer une simulation la premiere est d equilibrer les echantillons simules la seconde est de faire un usage explicite des approximations qui ne demandent pas de simulation

an analogue of minimal surface theory in we shall discuss the class of surfaces with holomorphic right gauss maps in non compact duals of compact semi simple lie groups e g sl n c su n which contains minimal surfaces in r n and constant mean curvature 1 surfaces in h 3 a weierstrass type representation formula and a chern osserman type inequality for such surfaces are given

a new approach to function based hypothesis testing in location scale families motivated by two applications in the mining industry we introduce a new approach to testing the hypothesis that two sampled distributions are simply location and scale changes of one another the test applicable to both paired data and two sample data is based on the empirical characteristic function more conventional techniques founded on the empirical distribution function suffer from serious drawbacks when used to test for location scale families in the motivating applications knowing that the distributions differ only in location and scale has significant operational and economic advantages enabling protocols for one type of data to be applied directly to another supplementary material in the form of matlab code is available online

determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time abstract we consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given the problem considered is one dimensional and the unknown heat source is supposed to be space dependent only the existence and uniqueness results are proved

a parametrization of the weierstrass formulae and perturbation of complete minimal surfaces in r3 into the hyperbolic 3 space

fractional calculus with an integral operator containing a generalized mittag leffler function in the kernel in this paper we introduce and investigate a fractional calculus with an integral operator which contains the following family of generalized mittag leffler functions e a b c k z email protected n 0 c k email protected email protected z nn z b email protected c r a max 0 r k 1 r k 0 in its kernel l n being the familiar pochhammer symbol a number of corollaries and consequences of the main results presented here are also considered

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

an inverse problem for a generalized fractional diffusion we propose a method for determining the solution and source term of a generalized time fractional diffusion equation the method is based on selecting a bi orthogonal basis of l 2 space corresponding to a nonself adjoint boundary value problem uniqueness is proven and an existence result is obtained for smooth initial and final conditions the asymptotic behavior of the generalized mittag leffler function is used to relax the smoothness requirement on these conditions

robust and efficient one way manova tests we propose robust tests as alternatives to the classical wilks lambda test in one way manova the robust tests use highly robust and efficient multisample multivariate s estimators or mm estimators instead of the empirical covariances the properties of several robust test statistics are compared under the null hypothesis the distribution of the test statistics is proportional to a chi square distribution as an alternative to the asymptotic distribution we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis we show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples we also investigate the power of the new tests as well as their robustness against outliers finally we illustrate the use of these robust test statistics on a real data example some additional results are provided as supplemental material

pairwise comparisons of trimmed means for two or more groups the paper takes up the problem of performing all pairwise comparisons amongj independent groups based on 20 trimmed means currently a method that stands out is the percentile t bootstrap method where the bootstrap is used to estimate the quantiles of a studentized maximum modulus distribution when all pairs of population trimmed means are equal however a concern is that in simulations the actual probability of one or more type i errors can drop well below the nominal level when sample sizes are small a practical issue is whether a method can be found that corrects this problem while maintaining the positive features of the percentile t bootstrap three new methods are considered here one of which achieves the desired goal another method which takes advantage of theoretical results by singh 1998 performs almost as well but is not recommended when the smallest sample size drops below 15 in some situations however it gives substantially shorter confidence intervals

a review of bootstrap confidence intervals on passe en revue plusieurs methodes distinctes basees sur le bootstrap pour construire des intervalles de confiance

on estimating the distribution function for quality of life in cancer clinical trials summary the analysis of quality of life data collected at periodic intervals in a cancer clinical trial must account for those patients data that are missing because of death or administrative censoring we examine estimates of the cumulative distribution function of an interpolated area under a quality of life curve as summaries of the quality of life experience of a treat ment group a proposed estimator although biased offers an improvement over a kaplan meier estimator that assumes incorrectly that the censoring is noninformative modalities may be an area in which quality of life measurements can be particularly infor mative because patient s self reported quality of life may not correspond to investigators perceptions e g see sugarbaker et al 1982 many of the statistical issues involved with assessing quality of life have been discussed by cox et al 1992 we focus in this paper on an unresolved issue pertinent to cancer clin ical trials estimating the distribution function of area under the curve auc quality of life scores for a treatment group to put the issue in context we note that in a typical cancer clinical trial both the proportion of patients who die on study as well as the proportion of patients whose data are censored because the patient is alive at the time of analysis are not small if quality of life is measured at fixed times after a patient is entered onto the trial then one must account for the data missing for both reasons it may be possible to score the quality of life measurements so that a score of zero for a patient who is not alive at that time point is reasonable we assume this throughout we also assume that the quality of life data at a given time point can usefully be summarized by a small set of scores corre

intentionally biased bootstrap methods summary a class of weighted bootstrap techniques called biased bootstrap or b bootstrap methods is introduced it is motivated by the need to adjust empirical methods such as the uniform bootstrap in a surgical way to alter some of their features while leaving others unchanged depending on the nature of the adjustment the b bootstrap can be used to reduce bias or to reduce variance or to render some characteristic equal to a predetermined quantity examples of the last application include a b bootstrap approach to hypothesis testing in nonparametric contexts where the b bootstrap enables simulation under the null hypothesis even when the hypothesis is false and a b bootstrap competitor to tibshirani s variance stabilization method an example of the bias reduction application is adjustment of nadaraya watson kernel estimators to make them competitive with local linear smoothing other applications include density estimation under constraints outlier trimming sensitivity analysis skewness or kurtosis reduction and shrinkage

a studentized permutation test for the comparison of spatial point patterns in this study a new test is proposed for the hypothesis that two or more observed point patterns are realizations of the same spatial point process model to this end the point patterns are divided into disjoint quadrats on each of which an estimate of ripley s k function is calculated the two groups of empirical k functions are compared by a permutation test using a studentized test statistic the proposed test performs convincingly in terms of empirical level and power in a simulation study even for point patterns where the k function estimates on neighboring subsamples are not strictly exchangeable it also shows improved behavior compared with a test suggested by diggle et al for the comparison of groups of independently replicated point patterns in an application to two point patterns from pathology that represent capillary positions in sections of healthy and cancerous tissue our studentized permutation test indicates statistical significance although the patterns cannot be clearly distin

a three step method for choosing the number of bootstrap repetitions this paper considers the problem of choosing the number of bootstrap repetitions b for bootstrap standard errors confidence intervals confidence regions hypothesis tests p values and bias correction for each of these problems the paper provides a three step method for choosing b to achieve a desired level of accuracy accuracy is measured by the percentage deviation of the bootstrap standard error estimate confidence interval length test s critical value test s p value or bias corrected estimate based on b bootstrap simulations from the corresponding ideal bootstrap quantities for which b the results apply quite generally to parametric semiparametric and nonparametric models with independent and dependent data the results apply to the standard nonparametric iid bootstrap moving block bootstraps for time series data parametric and semiparametric bootstraps and bootstraps for regression models based on bootstrapping residuals monte carlo simulations show that the proposed methods work very well

a data driven smooth test of symmetry in this paper we propose a data driven smooth test of symmetry we first transform the raw data via the probability integral transformation according to a symmetrized empirical distribution and show that under the null hypothesis of symmetry the transformed data has a limiting uniform distribution reducing testing for symmetry to testing for uniformity employing neyman s smooth test of uniformity we show that only odd ordered orthogonal moments of the transformed data are required in constructing the test statistic we present a standardized smooth test that is distribution free asymptotically and derive the asymptotic behavior of the test and establish its consistency extension to dependent data case is discussed we investigate the finite sample performance of the proposed tests on both homogeneous and mixed distributions with unobserved heterogeneity an empirical application on testing symmetry of wage adjustment process based on heterogeneous wage contracts with different durations is provided

an inverse source problem for a two parameter anomalous diffusion with local time datum abstract we determine the space dependent source term for a two parameter fractional diffusion problem subject to nonlocal non self adjoint boundary conditions and two local time distinct datum a bi orthogonal pair of bases is used to construct a series representation of the solution and the source term the two local time conditions spare us from measuring the fractional integral initial conditions commonly associated with fractional derivatives on the other hand they lead to delicate 2 2 linear systems for the fourier coefficients of the source term and of the fractional integral of the solution at t 0 the asymptotic behavior and estimates of the generalized mittag leffler function are used to establish the solvability of these linear systems and to obtain sufficient conditions for the existence of our construction analytical and numerical examples are provided

complete surfaces of constant mean curvature 1 in the hyperbolic 3 space in the study of minimal surfaces in the euclidean 3 space the weierstrass representation plays an important role bryant br showed that an analogue of the weierstrass representation formula holds for surfaces of constant mean curvature i in the hyperbolic 3 space x3 in this article we abbreviate the term constant mean curvature i as cmc 1 like minimal surfaces in the euclidean space the hyperbolic gauss map of cmc 1 surfaces is defined as a holomorphic map to c u oo however in contrast to the euclidean case the hyperbolic gauss map of a cmc 1 surface may not be extended across the ends even if the total gaussian curvature is finite we call a complete cmc 1 surface whose gauss map can be extended across all of its ends a cmc 1 surface of regular ends in this article we produce an explicit tool to construct cmc 1 surfaces of regular ends in section 2 we show that such surfaces are constructed by solving some ordinary differential equations with regular singularity in our cmc 1 category ossermann s inequality is not expected and the cohn vossen inequality is the best possible one we show in section 4 that the equality of the cohn vossen inequality never holds for complete cmc 1 surfaces in xh3 in section 5 we give a necessary and sufficient condition that a regular end of a cmc 1 surface be embedded in section 6 we classify complete cmc 1 surfaces of genus 0 with two regular ends our classification contains new examples furthermore in section 7 we construct several new cmc 1 surfaces with regular embedded ends each of these examples has a nontrivial deformation which is mentioned in section 3 it should be remarked that our construction does not work for surfaces with irregular ends but there is another construction by perturbing minimal surfaces in the euclidean 3 space the authors constructed cmc 1 surfaces all of whose ends are irregular see uy1

fractional master equations and fractal time random walks fractional master equations containing fractional time derivatives of order 0 ensuremath le 1 are introduced on the basis of a recent classification of time generators in ergodic theory it is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks the corresponding waiting time density ensuremath psi t is obtained exactly as ensuremath psi t mathit t mathrm ensuremath omega mathrm ensuremath 1 c mathit e mathrm ensuremath omega mathrm ensuremath omega mathit t mathrm ensuremath omega c where mathit e mathrm ensuremath omega mathrm ensuremath omega x is the generalized mittag leffler function this waiting time distribution is singular both in the long time as well as in the short time limit

random walk approximation of fractional order multiscaling anomalous diffusion random walks are developed to approximate the solutions of multiscaling fractional order anomalous diffusion equations the essential elements of the diffusion are described by the matrix order scaling indexes and the mixing measure which describes the diffusion coefficient in every direction two forms of the governing equation also called the multiscaling fractional diffusion equation based on fractional flux and fractional divergence are considered where the diffusion coefficient and the drift vary in space the particle tracking algorithm is also extended to approximate anomalous diffusion with a streamline dependent mixing measure using a streamline projection technique in this and other general cases the random walk method is the only known way to solve the nonhomogeneous equations five numerical examples demonstrate the flexibility simplicity and efficiency of the random walk method

an inverse source problem for a two parameter anomalous diffusion equation with nonlocal boundary conditions we consider the inverse problem of determination of the solution and a source term for a time fractional diffusion equation in two dimensional space the time fractional derivative is the hilfer derivative a bi orthogonal system of functions in l2 obtained from the associated non self adjoint spectral problem and its adjoint problem is used to prove the existence and uniqueness of the solution of the inverse problem the stability of the solution of the inverse problem on the given data is proved

bootstrap testing of the rank of a matrix via least squared constrained estimation to test if an unknown matrix m0 has a given rank null hypothesis noted h0 we consider a statistic that is a squared distance between an estimator and the submanifold of fixed rank matrix under h0 this statistic converges to a weighted chi squared distribution we introduce the constrained bootstrap cs bootstrap to estimate the law of this statistic under h0 an important point is that even if h0 fails the cs bootstrap reproduces the behavior of the statistic under h0 as a consequence the cs bootstrap is employed to estimate the nonasymptotic quantile for testing the rank we provide the consistency of the procedure and the simulations shed light on the accuracy of the cs bootstrap with respect to the traditional asymptotic comparison more generally the results are extended to test whether an unknown parameter belongs to a submanifold of the euclidean space finally the cs bootstrap is easy to compute it handles a large family of tests and it works under mild assumptions

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

two guidelines for bootstrap hypothesis testing two guidelines for nonparametric bootstrap hypothesis testing are highlighted the first recommends that resampling be done in a way that reflects the null hypothesis even when the true hypothesis is distant from the null the second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction violation of the first guideline can seriously reduce the power of a test sometimes this reduction is spectacular since it is most serious when the null hypothesis is grossly in error the second guideline is of some importance when the conclusion of a test is equivocal it has no direct bearing on power but improves the level accuracy of a test