asymptotics for euclidean minimal spanning trees on random points asymptotic results for the euclidean minimal spanning tree onn random vertices inrd can be obtained from consideration of a limiting infinite forest whose vertices form a poisson process in allrd in particular we prove a conjecture of robert bland the sum of thed th powers of the edge lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofrd tends to a constant asn

a multivariate two sample test based on the number of nearest neighbor type coincidences for independent d variate random samples x 1 cdots x n 1 i i d f x y 1 cdots y n 2 i i d g x where the densities f and g are assumed to be continuous a e consider the number t of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample we show that if f g a e the limiting normal distribution of t as min n 1 n 2 rightarrow infty n 1 n 1 n 2 rightarrow tau 0 tau 1 does not depend on f an omnibus procedure for testing the hypothesis h 0 f g a e is obtained by rejecting h 0 for large values of t the result applies to a general distance generated by a norm on mathbb r d for determining nearest neighbors and it generalizes to the multisample situation

nonparametric tests for homogeneity based on non bipartite matching given a sequence of observations has a change occurred in the underlying probability distribution with respect to observation order this problem of detecting change points arises in a variety of applications including health prognostics for mechanical systems syndromic disease surveillance in geographically dispersed populations anomaly detection in information networks and multivariate process control in general detecting change points in high dimensional settings is challenging and most change point methods for multidimensional problems rely upon distributional assumptions or the use of observation history to model probability distributions we present three new nonparametric statistical tests for heterogeneity based on the combinatorial properties of minimum non bipartite matching mnbm the key idea underlying each of these tests is that if a sequence of independent random observations undergoes a change in distribution either an abrupt shift or a gradual drift a mnbm based on inter point

an analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems stability and convergence results are derived for the box and trapezoidal schemes applied to boundary value problems for linear singularly perturbed first order systems of o d e s without turning points

two sample testing in high dimensions summary we propose new methodology for two sample testing in high dimensional models the methodology provides a high dimensional analogue to the classical likelihood ratio test and is applicable to essentially any model class where sparse estimation is feasible sparse structure is used in the construction of the test statistic in the general case testing then involves non nested model comparison and we provide asymptotic results for the high dimensional setting we put forward computationally efficient procedures based on data splitting including a variant of the permutation test that exploits sparse structure we illustrate the general approach in two sample comparisons of high dimensional regression models differential regression and graphical models differential network showing results on simulated data as well as data from two recent cancer studies

direct estimation of density functionals using a polynomial basis a number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions such quantities are called density functionals as they map density functions onto the real line for example information divergence functions measure the dissimilarity between two probability density functions and are useful in a number of applications typically estimating these quantities requires complete knowledge of the underlying distribution followed by multidimensional integration existing methods make parametric assumptions about the data distribution or use nonparametric density estimation followed by high dimensional integration in this paper we propose a new alternative we introduce the concept of data driven basis functions functions of distributions whose value we can estimate given only samples from the underlying distributions without requiring distribution fitting or direct integration we derive a new data driven complete basis that is similar to the deterministic bernstein polynomial basis and develop two methods for performing basis expansions of functionals of two distributions we also show that the new basis set allows us to approximate functions of distributions as closely as desired finally we evaluate the methodology by developing data driven estimators for the kullback leibler divergences and the hellinger distance and by constructing empirical estimates of tight bounds on the bayes error rate

an exact distribution free test comparing two multivariate distributions based on adjacency summary a new test is proposed comparing two multivariate distributions by using distances between observations unlike earlier tests using interpoint distances the new test statistic has a known exact distribution and is exactly distribution free the interpoint distances are used to construct an optimal non bipartite matching i e a matching of the observations into disjoint pairs to minimize the total distance within pairs the cross match statistic is the number of pairs containing one observation from the first distribution and one from the second distributions that are very different will exhibit few cross matches when comparing two discrete distributions with finite support the test is consistent against all alternatives the test is applied to a study of brain activation measured by functional magnetic resonance imaging during two linguistic tasks comparing brains that are impaired by arteriovenous abnormalities with normal controls a second exact distribution free test is also discussed it ranks the pairs and sums the ranks of the cross matched pairs

atoms of the set of numerical semigroups with fixed frobenius number abstract given a positive integer g we denote by f g the set of all numerical semigroups with frobenius number g the set f g is a semigroup in this paper we study the generators of this semigroup

numerical methods for stiff two point boundary value problems we consider the two point boundary value problem for stiff systems of ordinary differential equations for systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions a priori estimates are obtained problems with turning points can be treated with this theory and we discuss this in detail we give robust difference approximations and present error estimates for these schemes in particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions numerical examples are presented for both linear and nonlinear problems

the random minimal spanning tree in high dimensions for the minimal spanning tree on n independent uniform points in the d dimensional unit cube the proportionate number of points of degree k is known to converge to a limit alpha k d as n to infty we show that alpha k d converges to a limit alpha k as d to infty for each k the limit alpha k arose in earlier work by aldous as the asymptotic proportionate number of vertices of degree k in the minimum weight spanning tree on k vertices when the edge weights are taken to be independent identically distributed random variables we give a graphical alternative to aldous s characterization of the alpha k

an automatic orthonormalization method for solving stiff boundary value problems abstract a new initial value method is described based on a remark by drury for solving stiff linear differential two point cigenvalue and boundary value problems the method is extremely reliable it is especially suitable for high order differential systems and it is capable of accommodating realms of stiffness which other methods cannot reach the key idea behind the method is to decompose the stiff differential operator into two non stiff operators one of which is nonlinear the nonlinear one is specially chosen so that it advances an orthonormal frame indeed the method is essentially a kind of automatic orthonormalization the second is auxiliary but it is needed to determine the required function the usefulness of the method is demonstrated by calculating some eigenfunctions for an orr sommerfeld problem when the reynolds number is as large as 10

bias associated with using the estimated propensity score as a regression covariate the use of propensity score methods to adjust for selection bias in observational studies has become increasingly popular in public health and medical research a substantial portion of studies using propensity score adjustment treat the propensity score as a conventional regression predictor through a monte carlo simulation study austin and colleagues investigated the bias associated with treatment effect estimation when the propensity score is used as a covariate in nonlinear regression models such as logistic regression and cox proportional hazards models we show that the bias exists even in a linear regression model when the estimated propensity score is used and derive the explicit form of the bias we also conduct an extensive simulation study to compare the performance of such covariate adjustment with propensity score stratification propensity score matching inverse probability of treatment weighted method and nonparametric functional estimation using splines the simulation scenarios are designed to reflect real data analysis practice instead of specifying a known parametric propensity score model we generate the data by considering various degrees of overlap of the covariate distributions between treated and control groups propensity score matching excels when the treated group is contained within a larger control pool while the model based adjustment may have an edge when treated and control groups do not have too much overlap overall adjusting for the propensity score through stratification or matching followed by regression or using splines appears to be a good practical strategy

inference for empirical wasserstein distances on finite spaces summary the wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits to overcome this obstacle for probability measures supported on finitely many points we derive the asymptotic distribution of empirical wasserstein distances as the optimal value of a linear programme with random objective function this facilitates statistical inference e g confidence intervals for sample based wasserstein distances in large generality our proof is based on directional hadamard differentiability failure of the classical bootstrap and alternatives are discussed the utility of the distributional results is illustrated on two data sets

a wilcoxon mann whitney type test for infinite dimensional data the wilcoxon mann whitney test is a robust competitor of the t test in the univariate setting for finite dimensional multivariate non gaussian data several extensions of the wilcoxon mann whitney test have been shown to outperform hotelling s t 2 test in this paper we study a wilcoxon mann whitney type test based on spatial ranks in infinite dimensional spaces we investigate its asymptotic properties and compare it with several existing tests the proposed test is shown to be robust with respect to outliers and to have better power than some competitors for certain distributions with heavy tails we study its performance using real and simulated data

on multivariate runs tests for randomness this paper proposes several extensions of the concept of runs to the multivariate setup and studies the resulting tests of multivariate randomness against serial dependence two types of multivariate runs are defined i an elliptical extension of the spherical runs proposed by marden 1999 and ii an original concept of matrix valued runs the resulting runs tests themselves exist in various versions one of which is a function of the number of data based hyperplanes separating pairs of observations only all proposed multivariate runs tests are affine invariant and highly robust in particular they allow for heteroscedasticity and do not require any moment assumption their limiting distributions are derived under the null hypothesis and under sequences of local vector arma alternatives asymptotic relative efficiencies with respect to gaussian portmanteau tests are computed and show that while marden type runs tests suffer severe consistency problems tests based on matrix valued runs perform u

a weighted edge count two sample test for multivariate and object data abstracttwo sample tests for multivariate data and non euclidean data are widely used in many fields parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models in this article we study a nonparametric testing procedure that uses graphs representing the similarity among observations it can be applied to any data types as long as an informative similarity measure on the sample space can be defined the classic test based on a similarity graph has a problem when the two sample sizes are different we solve the problem by applying appropriate weights to different components of the classic test statistic the new test exhibits substantial power gains in simulation studies its asymptotic permutation null distribution is derived and shown to work well under finite samples facilitating its application to large datasets the new test is illustrated through an analysis on a real dataset of network data

optimal estimation of wasserstein distance on a tree with an application to microbiome studies the weighted unifrac distance a plug in estimator of the wasserstein distance of read counts on a tree has been widely used to measure the microbial community difference in microbiome studies ou

a new graph based two sample test for multivariate and object data abstracttwo sample tests for multivariate data and especially for non euclidean data are not well explored this article presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples it can be applied to multivariate data and non euclidean data as long as a dissimilarity measure on the sample space can be defined which can usually be provided by domain experts existing tests based on a similarity graph lack power either for location or for scale alternatives the new test uses a common pattern that was overlooked previously and works for both types of alternatives the test exhibits substantial power gains in simulation studies its asymptotic permutation null distribution is derived and shown to work well under finite samples facilitating its application to large datasets the new test is illustrated on two applications the assessment of covariate balance in a matched observational study and the comparison of network data under different co

ensemble subsampling for imbalanced multivariate two sample tests some existing nonparametric two sample tests for equality of multivariate distributions perform unsatisfactorily when the two sample sizes are unbalanced in particular the power of these tests tends to diminish with increasingly unbalanced sample sizes in this article we propose a new testing procedure to solve this problem the proposed test based on the nearest neighbor method by schilling employs a novel ensemble subsampling scheme to remedy this issue more specifically the test statistic is a weighted average of a collection of statistics each associated with a randomly selected subsample of the data we derive the asymptotic distribution of the test statistic under the null hypothesis and show that the new test is consistent against all alternatives when the ratio of the sample sizes either goes to a finite limit or tends to infinity via simulated data examples we demonstrate that the new test has increasing power with increasing sample size ratio when the size of the smaller sample is fixe

building a stronger instrument in an observational study of perinatal care for premature infants an instrument is a random nudge toward acceptance of a treatment that affects outcomes only to the extent that it affects acceptance of the treatment nonetheless in settings in which treatment assignment is mostly deliberate and not random there may exist some essentially random nudges to accept treatment so that use of an instrument might extract bits of random treatment assignment from a setting that is otherwise quite biased in its treatment assignments an instrument is weak if the random nudges barely influence treatment assignment or strong if the nudges are often decisive in influencing treatment assignment although ideally an ostensibly random instrument is perfectly random and not biased it is not possible to be certain of this thus a typical concern is that even the instrument might be biased to some degree it is known from theoretical arguments that weak instruments are invariably sensitive to extremely small biases for this reason strong instruments are preferred the strength of an

a kernel two sample test we propose a framework for analyzing and comparing distributions which we use to construct statistical tests to determine if two samples are drawn from different distributions our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel hilbert space rkhs and is called the maximum mean discrepancy mmd we present two distribution free tests based on large deviation bounds for the mmd and a third test based on the asymptotic distribution of this statistic the mmd can be computed in quadratic time although efficient linear time approximations are available our statistic is an instance of an integral probability metric and various classical metrics on distributions are obtained when alternative function classes are used in place of an rkhs we apply our two sample tests to a variety of problems including attribute matching for databases using the hungarian marriage method where they perform strongly excellent performance is also obtained when comparing distributions over graphs for which these are the first such tests

approximation dans les espaces metriques et theorie de l estimation we investigate the relations between the speed of estimation and the metric structure of the parameter space especially in the case when its metric dimension is infinite given some distance d on generally hellinger distance in the case of n i i d variables we consider the minimax risk for n observations r n q mathop inf sup limits t n theta in theta text ie theta d q theta t n t n being any estimate of we shall look for functions r such that for positive constants c 1 q and c 2 q c 1 r q n r n q c2 r q n r n is the speed of estimation and we shall show under fairly general conditions including i i d variables and regular cases of markov chains and stationnary gaussian processes that r n is determined up to multiplicative constants by the metric structure of we shall also give a construction for some sort of universal estimates the risk of which is bounded by c 2 r q n in all cases where the preceding theory applies

goodness of fit testing in mathbb r m based on the weighted empirical distribution of certain nearest neighbor statistics let x1 x be a random sample in r from an unknown density f x recently bickel and breiman have introduced a goodness of fit test for this situation based on the empirical distribution function of the variables wi expt ng x1 v ri i 1 n where g x is the hypothesized density and v r represents the volume of the nearest neighbor sphere centered at xi under the null hypothesis h f x g x the empirical process is asymptotically independent of g in this paper a weighted version of the empirical process is shown to produce tests which are still essentially distribution free under h but in addition have asymptotic power against sequences of alternatives contiguous to g the optimal weight function is obtained as a function of the particular sequence of alternatives chosen and consistency behavior against fixed alternatives is determined monte carlo results illustrate the power performance of the tests for various densities and weight functions

error bound in a central limit theorem of double indexed permutation statistics an error bound in the normal approximation to the distribution of the double indexed permutation statistics is derived the derivation is based on stein s method and on an extension of a combinatorial method of bolthausen the result can be applied to obtain the convergence rate of order n 1 2 for some rank related statistics such as kendall s tau spearman s rho and the mann whitney wilcoxon statistic its applications to graph related nonparametric statistics of multivariate observations are also mentioned

ensemble subsampling for imbalanced multivariate two sample tests chen l dou w w and qiao z 2013 journal of the american statistical association 108 1308 1323

data driven nonparametric existence and association problems we investigate two closely related nonparametric hypothesis testing problems in the first problem i e the existence problem we test whether a testing data stream is generated by one of a set of composite distributions in the second problem i e the association problem we test which one of the multiple distributions generates a testing data stream we assume that some distributions in the set are unknown and instead only training sequences generated by the corresponding distributions are available for both problems we construct the generalized likelihood tests and characterize the error exponents of the maximum error probabilities for the existence problem we show that the error exponent is mainly captured by the chernoff information between the set of composite distributions and alternative distributions for the association problem we show that the error exponent is captured by the minimum chernoff information between each pair of distributions as well as the kullback leibler divergences between the approximated distributions via training sequences and the true distributions we also show that the ratio between the lengths of training and testing sequences plays an important role in determining the error decay rate

generalized linear model for partially ordered data within the rich literature on generalized linear models substantial efforts have been devoted to models for categorical responses that are either completely ordered or completely unordered few studies have focused on the analysis of partially ordered outcomes which arise in practically every area of study including medicine the social sciences and education to fill this gap we propose a new class of generalized linear models the partitioned conditional model that includes models for both ordinal and unordered categorical data as special cases we discuss the specification of the partitioned conditional model and its estimation we use an application of the method to a sample of the national longitudinal study of youth to illustrate how the new method is able to extract from partially ordered data useful information about smoking youths that is not possible using traditional methods

signed rank statistics for coherent predictions a generalization of wilcoxon s signed rank test is proposed for testing a dose response relationship with one or more outcomes the test is useful in matched observational studies or in nonrandomized experiments that use dose response relationships and predictions about multiple outcomes in an effort to distinguish actual treatment effects from hidden biases a sensitivity analysis indicating whether a dose response relationship or multiple predictions are confirmed with sufficient strength to reduce sensitivity to hidden bias is performed together the test and the sensitivity analysis help to quantify the degree to which a coherent pattern of associations is present or absent and the degree to which this strengthens or fails to strengthen evidence of cause and effect formal properties of tests of this kind are examined the form of the optimal test is determined though this test is not usable because it depends upon the values of the unknown parameters under study also examined are the conditions under which the proposed test resembles the optimal test as well as the impact of various violations of those conditions on power an example involving matched pairs exposed to varying doses of cadmium is considered in detail

empirically estimable classification bounds based on a nonparametric divergence measure information divergence functions play a critical role in statistics and information theory in this paper we show that a nonparametric f divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the same distribution and for the case where there exists some mismatch between training and test distributions we confirm these theoretical results by designing feature selection algorithms using the criteria from these bounds and by evaluating the algorithms on a series of pathological speech classification tasks

characterizing the scale dimension of a high dimensional classification problem classi cation of high dimensional data is inherently di1cult we present an exploratory data analysis methodology for characterizing the scale dimension of a classi cation problem the idea is to characterize the support of one distinguished target class as a collection of balls covering the class with each ball centeredat an observation in that class such that the radius is maximal without containing observations from the other classes the scale dimension is de ned to be the number of distinct radii ball sizes required to cover the class without covering observations from the other class a greedy algorithm is used to t the balls the balls then provide a description of the support of the target class with information about the complexity of the classi cation problem implicit in the number radii adjacency and position of the balls clustering the balls by radius and pruning the cluster tree yields an estimate of the scale dimension for the problem we illustrate the methodology with pedagogical simulations anda chemical sensor data analysis application publishedby elsevier science ltdon behalf of pattern recognition society

gir based ensemble sampling approaches for imbalanced learning abstract this paper presents two adaptive ensemble sampling approaches for imbalanced learning one is the undersampling based approach and the other one is the oversampling based approach with the objectives of bias reduction and adaptive learning both of these two approaches are based on a novel class imbalance metric termed generalized imbalance ratio gir instead of the conventional sample size ratio specifically these two sampling based approaches adaptively split the imbalanced learning problem into multiple balanced learning subproblems in a probabilistic way which forces the classifiers trained in the subproblems focus on those difficult to learn samples in each subproblem several weak classifiers are trained in a boosting manner a final stronger classifier is further built by combining all these weak classifiers in a bagging manner extensive experiments are conducted on real life uci imbalanced data sets to evaluate the performance of the proposed methods the superior performance demonstrates the effectiveness of the proposed methods and indicates wide potential applications in data mining

a pdf free change detection test based on density difference estimation the ability to detect online changes in stationarity or time variance in a data stream is a hot research topic with striking implications in this paper we propose a novel probability density function free change detection test which is based on the least squares density difference estimation method and operates online on multidimensional inputs the test does not require any assumption about the underlying data distribution and is able to operate immediately after having been configured by adopting a reservoir sampling mechanism thresholds requested to detect a change are automatically derived once a false positive rate is set by the application designer comprehensive experiments validate the effectiveness in detection of the proposed method both in terms of detection promptness and accuracy

on the multivariate runs test for independent d variate random variables x 1 x m with common density f and y 1 y n with common density g let r m n be the number of edges in the minimal spanning tree with vertices x 1 x m y 1 y n that connect points from different samples friedman and rafsky conjectured that a test of h 0 f g that rejects h 0 for small values of r m n should have power against general alternatives we prove that r m n is asymptotically distribution free under h 0 and that the multivariate two sample test based on r m n is universally consistent

phylogenetic tree construction using markov chain monte carlo abstract we describe a bayesian method based on markov chain simulation to study the phylogenetic relationship in a group of dna sequences under simple models of mutational events our method produces a markov chain whose stationary distribution is the conditional distribution of the phylogeny given the observed sequences our algorithm strikes a reasonable balance between the desire to move globally through the space of phylogenies and the need to make computationally feasible moves in areas of high probability because phylogenetic information is described by a tree we have created new diagnostics to handle this type of data structure an important byproduct of the markov chain monte carlo phylogeny building technique is that it provides estimates and corresponding measures of variability for any aspect of the phylogeny under study

reducing multidimensional two sample data to one dimensional interpoint comparisons the most popular technique for reducing the dimensionality in comparing two multidimensional samples of x f and y g is to analyze distributions of interpoint comparisons based on a univariate function h e g the interpoint distances we provide a theoretical foundation for this technique by showing that having both i the equality of the distributions of within sample comparisons h x 1 x 2 l h y 1 y 2 and ii the equality of these with the distribution of between sample comparisons h x 1 x 2 l h x 3 y 3 is equivalent to the equality of the multivariate distributions f g

graph theoretic measures of multivariate association and prediction interpoint distance based graphs can be used to define measures of association that extend kendall s notion of a generalized correlation coefficient the authors present particular statistics that provide distribution free tests of independence sensitive to alternatives involving non monotonic relationships moreover since ordering plays no essential role the ideas that fully applicable in a multivariate setting the authors also define an asymmetric coefficient measuring the extent to which a vector x can be used to make single valued predictions of a vector y the authors discuss various techniques for proving that such statistics are asymptotically normal as an example of the effectiveness of their approach the authors present an application to the examination of residuals from multiple regression 18 references 2 figures 1 table

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

evaluation of subset matching methods and forms of covariate balance this paper conducts a monte carlo simulation study to evaluate the performance of multivariate matching methods that select a subset of treatment and control observations the matching methods studied are the widely used nearest neighbor matching with propensity score calipers and the more recently proposed methods optimal matching of an optimally chosen subset and optimal cardinality matching the main findings are i covariate balance as measured by differences in means variance ratios kolmogorov smirnov distances and cross match test statistics is better with cardinality matching because by construction it satisfies balance requirements ii for given levels of covariate balance the matched samples are larger with cardinality matching than with the other methods iii in terms of covariate distances optimal subset matching performs best iv treatment effect estimates from cardinality matching have lower root mean square errors provided strong requirements for balance specifically fine balance or strength k balance plus close mean balance in standard practice a matched sample is considered to be balanced if the absolute differences in means of the covariates across treatment groups are smaller than 0 1 standard deviations however the simulation results suggest that stronger forms of balance should be pursued in order to remove systematic biases due to observed covariates when a difference in means treatment effect estimator is used in particular if the true outcome model is additive then marginal distributions should be balanced and if the true outcome model is additive with interactions then low dimensional joints should be balanced copyright 2016 john wiley sons ltd

a multidimensional goodness of fit test based on interpoint distances abstract distributional assumptions can be examined with multidimensional goodness of fit tests we propose a conceptually simple test with an appealing logic and accessible asymptotic properties which is generalizable to a variety of problems and appears to work well against diverse alternatives to test whether a k dimensional random sample x1 x n follows the distribution g consider a triangle formed by two randomly selected data points x i and x j and a variable y g our statistic estimates the likelihood that the side formed by the line from x i to x j is the smallest the middle or the largest side of the triangle

spatial clustering for inhomogeneous populations a new method for detecting spatial clustering of events in populations with non uniform density is proposed the method is based on selecting controls from the population at risk and computing interpoint distances for the combined sample nonparametric tests are developed which are based on the number of cases among the k nearest neighbours of each case and the number of cases nearer than the k nearest control the performance of these tests is evaluated analytically and by simulation and the method is applied to a data set on the locations of cases of childhood leukaemia and lymphoma in a defined geographical area

a distribution free two sample run test applicable to high dimensional data we propose a multivariate generalization of the univariate two sample run test based on the shortest hamiltonian path the proposed test is distribution free in finite samples while most existing two sample tests perform poorly or are even inapplicable to high dimensional data our test can be conveniently used in high dimension low sample size situations we investigate its power when the sample size remains fixed and the dimension of the data grows to infinity simulated and real datasets demonstrate our method s superiority over existing nonparametric two sample tests

new multivariate tests for assessing covariate balance in matched observational studies we propose new tests for assessing whether covariates in a treatment group and matched control group are balanced in observational studies the tests exhibit high power under a wide range of multivariate alternatives some of which existing tests have little power for the asymptotic permutation null distributions of the proposed tests are studied and the p values calculated through the asymptotic results work well in simulation studies facilitating the application of the test to large data sets the tests are illustrated in a study of the effect of smoking on blood lead levels the proposed tests are implemented in an r package balancecheck

collocation for singular perturbation problems i first order systems with constant coefficients the application of collocation methods for the numerical solution of singularly perturbed ordinary differential equations is investigated collocation at gauss radau and lobatto points is considered for both initial and boundary value problems for first order systems with constant coefficients particular attention is paid to symmetric schemes for boundary value problems these problems may have boundary layers at both interval ends br our analysis shows that certain collocation schemes in particular those based on gauss or lobatto points do perform very well on such problems provided that a fine mesh with steps proportional to the layers width is used in the layers only and a coarse mesh just fine enough to resolve the solution of the reduced problem is used in between ways to construct appropriate layer meshes are proposed of all methods considered the lobatto schemes appear to be the most promising class of methods as they essentially retain their usual superconvergence power for the smooth reduced solution whereas gauss legendre schemes do not br we also investigate the conditioning of the linear systems of equations arizing in the discretization of the boundary value problem for a row equilibrated version of the discretized system we obtain a pleasantly small bound on the maximum norm condition number which indicates that these systems can be solved safely by gaussian elimination with scaled partial pivoting

testing equality of cell populations based on shape and geodesic distance image cytometry has emerged as a valuable in vitro screening tool and advances in automated microscopy have made it possible to readily analyze large cellular populations of image data the purpose of this paper is to illustrate the viability of using cell shape to test equality of cell populations based on image data shape space theory is reviewed from which differences between shapes can be quantified in terms of geodesic distance several multivariate nonparametric statistical hypothesis tests are adapted to test equality of cell populations it is illustrated that geodesic distance can be a better feature than cell spread area and roundness in distinguishing between cell populations tests based on geodesic distance are able to detect natural perturbations of cells whereas kolmogorov smirnov tests based on area and roundness are not

on dichotomy and well conditioning in bvp we investigate the relationships between the stability bounds of the problem on the one hand and the growth behaviour of the fundamental solution on the other hand it is shown that if these stability bounds are moderate i e if the problem is well conditioned then the homogeneous solution space is dichotomic which means that it can be split into a subspace of nondecreasing and a complementary subspace of nonincreasing modes this is done by carefully examining the green s functions if these exhibit an exponential behaviour then the solution space is also exponentially dichotomic on the other hand we also show that exponential dichotomy implies moderate stability constants i e well conditioning from this it follows that both concepts are more or less equivalent

sums of functions of nearest neighbor distances moment bounds limit theorems and a goodness of fit test abstract the limiting behavior of sums of functions of nearest neighbor distances is studied for an m dimensional sample a central limit theorem and moment bounds for such sums and an invariance principle for the empirical process of nearest neighbor distances are both established as a consequence the asymptotic behavior of a practicable goodness of fit test is obtained based on nearest neighbor distances

general framework stability and error analysis for numerical stiff boundary value methods this paper provides a general framework called theoretical multiple shooting within which various numerical methods for stiff boundary value ordinary differential problems can be analyzed a global stability and error analysis is given allowing as much as possible the specificities of an actual numerical method to come in only locally we demonstrate the use of our results for both one sided and symmetric difference schemes the class of problems treated includes some with internal e g turning point layers

multivariate two sample tests based on nearest neighbors abstract a new class of simple tests is proposed for the general multivariate two sample problem based on the possibly weighted proportion of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample large values of the test statistics give evidence against the hypothesis h of equality of the two underlying distributions asymptotic null distributions are explicitly determined and shown to involve certain nearest neighbor interaction probabilities simple infinite dimensional approximations are supplied the unweighted version yields a distribution free test that is consistent against all alternatives optimally weighted statistics are also obtained and asymptotic efficiencies are calculated each of the tests considered is easily adapted to a permutation procedure that conditions on the pooled sample power performance for finite sample sizes is assessed in simulations

continuous orthonormalization for boundary value problems abstract continuous orthonormalization describes an initial value method for linear 2 point boundary value problems which provides an orthogonal basis for the solution space at all points of the interval in this paper the equations of continuous orthonormalization are derived with elementary projection arguments to provide geometric insight and motivate some modifications of an earlier algorithm the method is then applied to some oscillatory and stiff boundary value problems to demonstrate that it is simple to use problem independent and as adaptive as the initial value code which is used to integrate the equations of continuous orthonormalization

frechet analysis of variance for random objects summaryfrechet mean and variance provide a way of obtaining a mean and variance for metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and operations examples of such data objects include covariance matrices graph laplacians of networks and univariate probability distribution functions we derive a central limit theorem for the frechet variance under mild regularity conditions using empirical process theory and also provide a consistent estimator of the asymptotic variance these results lead to a test for comparing k populations of metric space valued data objects in terms of frechet means and variances we examine the finite sample performance of this novel inference procedure through simulation studies on several special cases that include probability distributions and graph laplacians leading to a test for comparing populations of networks the proposed approach has good finite sample performance in simulations for different kinds of random objects we illustrate the proposed methods by analysing data on mortality profiles of various countries and resting state functional magnetic resonance imaging data

global rank tests for multiple possibly censored outcomes clinical trials often collect multiple outcomes on each patient as the treatment may be expected to affect the patient on many dimensions for example a treatment for a neurological disease such as als is intended to impact several dimensions of neurological function as well as survival the assessment of treatment on the basis of multiple outcomes is challenging both in terms of selecting a test and interpreting the results several global tests have been proposed and we provide a general approach to selecting and executing a global test the tests require minimal parametric assumptions are flexible about weighting of the various outcomes and are appropriate even when some or all of the outcomes are censored the test we propose is based on a simple scoring mechanism applied to each pair of subjects for each endpoint the pairwise scores are then reduced to a summary score and a rank sum test is applied to the summary scores this can be seen as a generalization of previously proposed nonparametric global tests e g o brien 1984 we discuss the choice of optimal weighting schemes based on power and relative importance of the outcomes as the optimal weights are generally unknown in practice we also propose an adaptive weighting scheme and evaluate its performance in simulations we apply the methods to analyze the impact of a treatment on neurological function and death in an als trial

semigroup ideals and linear diophantine equations abstract we give a purely algebraic algorithm to calculate the ideal of a semigroup with torsion as application and using grobner bases we provide an algorithm to determine whether a linear system of equations with integer coefficients having some of the equations in congruences admits non negative integer solutions

sensitivity analysis for the cross match test with applications in genomics the cross match test is an exact distribution free test of no treatment effect on a high dimensional outcome in a randomized experiment the test uses optimal nonbipartite matching to pair 2i subjects into i pairs based on similar outcomes and the cross match statistic a is the number of times that a treated subject was paired with a control rejecting for small values of a if the test is applied in an observational study in which treatments are not randomly assigned then it may be comparing treated and control subjects who are not comparable and thus may falsely reject a true null hypothesis of no treatment effect we develop a sensitivity analysis for the cross match test and apply it in an observational study of the effects of smoking on gene expression levels in addition we develop a sensitivity analysis for several multiple testing procedures using the cross match test and apply it to 1627 molecular function categories in gene ontology

on some difference schemes for singular singularly perturbed boundary value problems singularly perturbed boundary value ordinary differential problems are considered where the problem defining the reduced solution is singular for numerical approximation families of symmetric difference schemes which are equivalent to certain collocation schemes based on gauss and lobatto points are used convergence results previously obtained for the regular singularly perturbed case are extended while gauss schemes are extended with no change lobatto schemes require a small modification in the mesh selection procedure with meshes as prescribed in the text highly accurate solutions can be obtained with these schemes for singular singularly perturbed problems at a very reasonable cost this is demonstrated by examples

nonnegative elements of subgroups of ℤn abstract we give a method to compute all nonnegative integer solutions of a homogeneous system of linear equations we use this method to provide an algorithm to compute all nonnegative integer solutions of homogeneous systems of equations having some of the equations in congruences

a nonparametric approach to high dimensional k sample comparison problems summaryhigh dimensional k sample comparison is a common task in applications we construct a class of easy to implement distribution free tests based on new nonparametric tools and unexplored connections with spectral graph theory the test is shown to have various desirable properties and a characteristic exploratory flavour that has practical consequences for statistical modelling numerical examples show that the proposed method works surprisingly well across a broad range of realistic situations

decoupling and stability of algorithms for boundary value problems the ordinary differential equations occurring in linear boundary value problems characteristically have both stable and unstable solution modes therefore a stable numerical algorithm should avoid both forward and backward integration of solutions on large intervals it is shown that most methods like multiple shooting collocation invariant imbedding and difference methods derive their stability from the fact that they all decouple the continuous or the discrete problem sooner or later for instance when solving a linear system this decoupling is related to the dichotomy of the ordinary differential equations in fact it turns out that the inherent initial value instability is an important prerequisite for a stable utilization of the decoupled representations from which the solutions are computed how this stability is related to the use of the boundary conditions is also investigated

a riccati transformation method for solving linear bvps i theoretical aspects a method of solving linear two point boundary value problems bvps for first order systems of ordinary differential equations odes is considered of particular interest is the class of singularly perturbed bvps the method attempts to split the integration of the rapidly increasing decreasing solution components typical for such problems into different initial value problems ivps the case of separated boundary conditions bcs is considered and their ability to detect solution components that eventually increase decrease is exploited by using the riccati transformation the original bvp is then reformulated as three ivps one of them being a matrix riccati equation the riccati equation is nonlinear and a multiple embedding setting must be used the entire method is then fit theoretically into a multiple shooting like framework and the original bvp as a chain of subproblems is studied in this way a generalized decoupling result is presented which enables the study of stability to be brough