multiple comparison of several linear regression models research on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means several years ago spurrier considered the multiple comparison of several simple linear regression lines he constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range when the models have the same design matrices this article extends spurrier s work in several directions first multiple linear regression models are considered and the design matrices are allowed to be different second the predictor variables are either unconstrained or constrained to finite intervals third the types of comparison allowed can be very flexible including pairwise many one and successive two simulation methods are proposed for the calculation of critical constants the methodologies are illustrated with examples

normalisers in limit groups let gamma be a limit group s subset gamma a non trivial subgroup and n the normaliser of s if h 1 s mathbb q has finite mathbb q dimension then s is finitely generated and either n s is finite or n is abelian this result has applications to the study of subdirect products of limit groups

nonparametric bayes modelling of count processes data on count processes arise in a variety of applications including longitudinal spatial and imaging studies measuring count responses the literature on statistical models for dependent count data is dominated by models built from hierarchical poisson components the poisson assumption is not warranted in many applied contexts and hierarchical poisson models make restrictive assumptions about overdispersion in marginal distributions in this article we propose a class of nonparametric bayes count process models constructed through rounding real valued underlying processes the proposed class of models accommodates situations in which separate count valued functional data are observed for each subject under study theoretical results on large support and posterior consistency are established and computational algorithms are developed based on markov chain monte carlo simulation the methods are evaluated via simulation and illustrated by application to longitudinal tumour counts and to asthma inhaler usage copyright 2013 oxford university press

monotone discriminant functions and their applications in rheumatology abstract some applications of discriminant analysis e g in rheumatology naturally require that the discriminator satisfies certain monotonicity constraints in terms of the measurements on which the classification is based this article presents a dynamic programming approach to the problem of finding the monotone function that minimizes the total misclassification cost incurred when classifying two types of cases on the basis of two variables measured on each case questions of uniqueness and convexity are explored and the way in which the solution varies with choice of misclassification costs is investigated the use of the bootstrap to estimate the accuracy of summary statistics of interest is discussed the methodology is illustrated using data on rheumatology patients some comparisons with linear discriminant functions and classification tree methods are made

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

testing for monotonicity of a regression mean by calibrating for linear functions a new approach to testing for monotonicity of a regression mean not requiring computation of a curve estimator or a bandwidth is suggested it is based on the notion of running gradients over short intervals although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip excess mass approach for testing modality hypotheses about densities like the latter methods the new technique does not suffer difficulties caused by almost flat parts of the target function in fact it is calibrated so as to work well for flat response curves and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders in this respect as well as in its construction the running gradients approach differs from alternative techniques based on the notion of a critical bandwidth

combining registration and fitting for functional models a registration method can be defined as a process of aligning features of a sample of curves by monotone transformations of their domain the aligned curves exhibit only amplitude variation and the domain transformations called warping functions capture the phase variation in the original curves in this article we precisely define a new type of registration process in which the warping functions optimize the fit of a principal components decomposition to the aligned curves the principal components are effectively the features that this process aligns we discuss the relationship of registration to closure of a function space under convex operations and define consistency for registration methods we define an explicit decomposition of functional variation into amplitude and phase partitions and develop an algorithm for combining registration with principal components analysis and apply it to simulated and real data

an efficient finite element method for simulation of droplet spreading on a topologically rough surface abstract we study numerically the dynamics of a three dimensional droplet spreading on a rough solid surface using a phase field model consisting of the coupled cahn hilliard and navier stokes equations with a generalized navier boundary condition gnbc an efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces we extend the gnbc to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation the semi implicit time discretization scheme results in a decoupled system for the phase function the velocity and the pressure in addition a mass compensation algorithm is introduced to preserve the mass of the droplet to efficiently solve the decoupled systems we present a highly parallel solution strategy based on domain decomposition techniques we validate the newly developed solution method through extensive numerical experiments particularly for those phenomena that can not be achieved by two dimensional simulations on a surface with circular posts we study how wettability of the rough surface depends on the geometry of the posts the contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed moreover we study the spreading process of an impacting droplet on a microstructured surface a qualitative agreement is achieved between the numerical and experimental results the parallel performance suggests that the proposed solution algorithm is scalable with over 4 000 processors cores with tens of millions of unknowns

estimating the accuracy of polymerase chain reaction based tests using endpoint dilution polymerase chain reaction pcr based tests for various microorganisms or target dna sequences are generally acknowledged to be highly sensitive yet the concept of sensitivity is ill defined in the literature on these tests we propose that sensitivity should be expressed as a function of the number of target dna molecules in the sample or specificity when the target number is 0 however estimating this sensitivity curve is problematic since it is difficult to construct samples with a fixed number of targets nonetheless using serially diluted replicate aliquots of a known concentration of the target dna sequence we show that it is possible to disentangle random variations in the number of target dna molecules from the underlying test sensitivity we develop parametric nonparametric and semiparametric spline based models for the sensitivity curve the methods are compared on a new test for m genitalium

phase field modeling and simulation of three phase flow on solid surfaces phase field models are widely used to describe the two phase system the evolution of the phase field variables is usually driven by the gradient flow of a total free energy functional the generalization of the approach to an n phase n 3 system requires some extra consistency conditions on the free energy functional in order for the model to give physically relevant results a projection approach is proposed for the derivation of a consistent free energy functional for the three phase cahn hilliard equations the system is then coupled with the navier stokes equations to describe the three phase flow on solid surfaces with moving contact line an energy stable scheme is developed for the three phase flow system the discrete energy law of the numerical scheme is proved which ensures the stability of the scheme we also show some numerical results for the dynamics of triple junctions and four phase contact lines

estimating smooth monotone functions many situations call for a smooth strictly monotone function f of arbitrary flexibility the family of functions defined by the differential equation d 2 f w df where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions the solution to this equation is f c 0 c 1 d 1 exp d 1 w where c 0 and c 1 are arbitrary constants and d 1 is the partial integration operator a basis for expanding w is suggested that permits explicit integration in the expression of f in fitting data it is also useful to regularize f by penalizing the integral of w 2 since this is a measure of the relative curvature in f applications are discussed to monotone nonparametric regression to the transformation of the dependent variable in non linear regression and to density estimation

an extension of multiple correspondence analysis for identifying heterogeneous subgroups of respondents an extension of multiple correspondence analysis is proposed that takes into account cluster level heterogeneity in respondents preferences choices the method involves combining multiple correspondence analysis and k means in a unified framework the former is used for uncovering a low dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents the proposed method offers an integrated graphical display that provides information on cluster based structures inherent in multivariate categorical data as well as the interdependencies among the data an empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches

two theorems about equationally noetherian groups abstract an algebraic set over a groupgis the set of all solutions of some system f x1 xn 1 f g x1 xn of equations overg a groupgis equationally noetherian if every algebraic set overgis the set of all solutions of a finite subsystem of the given one we prove that a virtually equationally noetherian group is equationally noetherian and that the quotient of an equationally noetherian group by a normal subgroup which is a finite union of algebraic sets is again equationally noetherian on the other hand the wreath productw u tof a non abelian groupuand an infinite grouptis not equationally noetherian

modeling price dynamics in ebay auctions using differential equations empirical research of online auctions has grown dramatically in recent years studies using publicly available bid data from such websites as ebay com have found many divergences of bidding behavior and auction outcomes compared with ordinary offline auctions and auction theory among the main differences between online and offline auctions are the former s longer duration anonymity of bidders and sellers and low barriers of entry all of these factors lead to dynamics in the bid arrival and price process that change throughout the auction in this work we examine the price process in a large and diverse set of ebay auctions for both low and high valued items in terms of item auction bidder and seller characteristics we propose a family of differential equation models that captures online auction dynamics in particular we show that a second order linear differential equation well approximates the dynamics that occur in our diverse set of auctions we also introduce a multiple comparisons test fo

analysis of the cahn hilliard equation with a relaxation boundary condition modeling the contact angle dynamics we analyze the cahn hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary an l estimate is established which enables us to prove the global existence of the solution we also study the sharp interface limit of the system the dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations

derivation of the wenzel and cassie equations from a phase field model for two phase flow on rough surface in this paper the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system when the size of the roughness becomes small we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique the wenzel and cassie equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition the homogenization results are proved rigorously by the convergence theory

a class of grouped brunk estimators and penalized spline estimators for monotone regression we study a class of monotone univariate regression estimators we use b splines to approximate an underlying regression function and estimate spline coefficients based on grouped data we investigate asymptotic properties of two monotone estimators a grouped brunk estimator and a penalized monotone estimator these estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression function asymptotic distributions are developed and are shown to be independent of spline degrees and the number of knots simulation results and car data illustrate performance of the proposed estimators

bayesian isotonic density regression density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions and are well supported in many applications a rich variety of bayesian methods have been proposed for density regression but it is not clear whether such priors have full support so that any true data generating model can be accurately approximated this article develops a new class of density regression models that incorporate stochastic ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor theory is developed showing large support methods are developed for hypothesis testing with posterior computation relying on a simple gibbs sampler frequentist properties are illustrated in a simulation study and an epidemiology application is considered

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

estimating derivatives for samples of sparsely observed functions with application to online auction dynamics it is often of interest to recover derivatives of a sample of random functions from sparse and noise contaminated measurements especially when the dynamics of underlying processes is of interest we propose a novel approach based on estimating derivatives of eigenfunctions and expansions of random functions into their eigenfunctions to obtain a representation for derivatives in combination with estimates for functional principal component scores for sparse data this leads to a viable solution of the challenging problem to recover derivatives for sparsely observed functions we establish consistency results and demonstrate in simulations that the method is superior to alternative approaches derivative estimation with random effects models based on b spline bases kernel smoothing smoothing splines or p splines our study is motivated by an analysis of bidding histories for ebay auctions for which bids are typically very sparse in the middle and somewhat more frequent near the beginning and end of a

direct regression models for longitudinal rates of change comparing rates of growth or rates of change across covariate defined subgroups is a primary objective for many longitudinal studies in the special case of a linear trend over time the interaction between a covariate and time will characterize differences in longitudinal rates of change however in the presence of a non linear longitudinal trajectory the standard mean regression approach does not permit parsimonious description or inference regarding differences in rates of change therefore we propose regression methodology for longitudinal data that allows a direct structured comparison of rates across subgroups even in the presence of a non linear trend over time our basic longitudinal rate regression method assumes a proportional difference across covariate groups in the rate of change across time but this assumption can be relaxed rates are compared relative to a generally specified time trend for which we discuss both parametric and non parametric estimating approaches we develop mixed model longitudinal methodology that explicitly characterizes subject to subject variation in rates as well as a marginal estimating equation based method in addition we detail a score test to detect violations of the proportionality assumption and we allow time varying rate effects as a natural generalization simulation results demonstrate potential gains in power for the longitudinal rate regression model relative to a linear mixed effects model in the presence of a non linear trend in time we apply our method to a study of growth among infants born to hiv infected mothers and conclude with a discussion of possible extensions for our methods

homogenization of rough boundaries and interfaces homogenization is used to analyze a partial differential equation in a domain with a very rough boundary or interface following the procedure of kohler papanicolaou and varadhan boundary and interface problems in regions with very rough boundaries in multiple scattering and waves in random media p chow w kohler and g papanicolaou eds north holland amsterdam 1981 pp 165 197 and brizzi and chalot homogeneisation de frontiere ph d thesis department of mathematics universite de nice nice france 1978 it is shown that such a boundary or interface can be replaced by an equivalent layer within which a modified differential equation holds the coefficients in this new equation are certain effective parameters such as the effective conductivity the effective dielectric constant the effective refractive index etc these coefficients are determined by the solutions of certain special problems which involve the detailed shape of the boundary or interface this analysis is applied to

bayesian nonparametric estimation of continuous monotone functions with applications to dose response analysis in this article we consider monotone nonparametric regression in a bayesian framework the monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions and a general random probability measure is assumed as the prior for the mixing distribution we investigate the choice of the underlying parametric distribution function and find that the two sided power distribution function is well suited both from a computational and mathematical point of view the model is motivated by traditional nonlinear models for dose response analysis and provides possibilities to elicitate informative prior distributions on different aspects of the curve the method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose response analysis

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

assessing nonsuperiority noninferiority or equivalence when comparing two regression models over a restricted covariate region in many scientific problems the purpose of the comparison of two regression models which describe the relationship between a same response variable and several same covariates for two different groups is to demonstrate that one model is no higher than the other by a negligible amount or to demonstrate that the models have only negligible differences and so they can be regarded as describing practically the same relationship between the response variable and the covariates in this article methods based on one sided pointwise confidence bands are proposed for assessing the nonsuperiority of one model to the other and for assessing the equivalence of two regression models examples from qt qtc study and from drug stability study are used to illustrate the methods

minimum area confidence set optimality for confidence bands in simple linear regression the average width of a simultaneous confidence band has been used by several authors e g naiman and piegorsch as a criterion for the comparison of different confidence bands in this article the area of the confidence set that corresponds to a confidence band is used as a new criterion for simple linear regression comparisons have been carried out under this new criterion between hyperbolic bands two segment bands and three segment bands which include constant width bands as special cases it is found that if one requires a confidence band over the whole range of the covariate then the best confidence band is given by the working and hotelling hyperbolic band furthermore if one needs a confidence band over a finite interval of the covariate then a restricted hyperbolic band can again be recommended although a three segment band may be very slightly superior in certain cases

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

irreducible affine varieties over a free group i irreducibility of quadratic equations and nullstellensatz the object of this paper which consists of two parts is to describe irreducible varieties over free groups and to characterize finitely generated fully residually free groups we prove that any variety over a free group f can be defined by a finite number of systems of equations s 1 in triangular form where quadratic words play the role of leading terms algebraically irreducible varieties are exactly the varieties whose coordinate groups are fully residually f the crucial point of the classification of fully residually free groups is to prove that the coordinate groups of irreducible varieties are embeddable into lyndon s free z x group f since every finitely generated fully residually free group is a free factor of the coordinate group of an irreducible variety and the group f is fully residually f we obtain a characterization of finitely generated fully residually free groups as subgroups of f the group f and its subgroups have been studied extensively during the last several years in particular every finitely generated subgroup of f hence every finitely generated fully residually free group can be obtained from free abelian groups of finite rank by finitely many free products with amalgamation and hnn extensions of the type where amalgamated and associated subgroups are free abelian of finite rank in particular this implies that every finitely generated fully residually free group is finitely presented there are three parts to this paper algebraic geometry over free groups the theory of free exponential groups and makanin razborov s machinery to deal with equations over free groups 11 14 13 the algebraic geometry approach has been shown to be very usefull in dealing with equations over groups it provides necessary topological means and a method to transcribe geometric notions into pure group theoretic language following baumslag myasnikov remeslennikov 1 we use the standard algebraic geometry notions such as variety zariski topology irreducibility of varieties radicals and coordinate groups some of the ideas of the algebraic geometry approach go back to r lyndon 9 e rips j stallings 16

effective contact angle for rough boundary abstract we provide rigorous justification for the classical wenzel equation for the roughness enhanced effective contact angle the minimization of the total surface energy is reformulated into a variational problem as the size of the roughness becomes small we show convergence of the minimizer the limiting minimizer and effective contact angle are explicitly calculated to verify the wenzel equation

irreducible affine varieties over a free group ii systems in triangular quasi quadratic form and description of residually free groups abstract we shall prove the conjecture of myasnikov and remeslennikov 4 which states that a finitely generated group is fully residually free every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group if and only if it is embeddable in the lyndon s exponential groupfz x which is thez x completion of the free group herez x is the ring of polynomials of one variable with integer coefficients historically lyndon s attempts to solve tarski s famous problem concerning the elementary equivalence of free groups of different ranks led him to introducefz x an free group is a groupgsuch that the class of formulas true ing is the same as the class of formulas true in a nonabelian free group a finitely generated group is free if and only if it is fully residually free 22 our result gives an algebraic description of free groups we shall give an algorithm to represent a solution set of an arbitrary system of equations overfas a union of finite number of irreducible components in the zariski topology onfn the solution set for every system is contained in the solution set of a finite number of systems in triangular form with quadratic words as leading terms the possibility of such a decomposition for a solution set was conjectured by razborov in 20 and also by rips we shall give a description of systems of equations determining irreducible components using methods developed in 13 19 it is possible to find some of these methods in 18 we are thankful to e rips for attracting our attention to these techniques

monotone smoothing with application to dose response curves and the assessment of synergism a spline based procedure for monotone curve smoothing is proposed and is illustrated by application to dose response curves it is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs

pooling batches in drug stability study by using constant width simultaneous confidence bands one important study objective in drug stability studies is to estimate the shelf life of a drug a key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf life for the drug in this paper constant width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches with a particular view to establish the practical equivalence of different batches this approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal it is shown how constant width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models in particular it is shown that constant width simultaneous confidence bands have a better chance to establish the equivalence than and so are preferable to the hyperbola shaped simultaneous confidence bands considered j am stat assoc 2004 99 395 403

subgroups of direct products of limit groups if ti tn are limit groups and s c t x x tn is of type fp q then s contains a subgroup of finite index that is itself a direct product of at most n limit groups this answers a question of sela

monotone b spline smoothing abstract estimation of growth curves or item response curves often involves monotone data smoothing methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated built on the ideas of koenker ng and portnoy and ramsay we propose monotone b spline smoothing based on l 1 optimization this method inherits the desirable properties of spline approximations and the computational efficiency of linear programs the constrained fit is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence through applications to some real and simulated data we show that the method is useful in a variety of applications the basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems

inferring stochastic dynamics from functional data in most current data modelling for time dynamic systems one works with a prespecified differential equation and attempts to estimate its parameters in contrast we demonstrate that in the case of functional data the equation itself can be inferred assuming only that the dynamics are described by a first order nonlinear differential equation with a random component we obtain data adaptive dynamic equations from the observed data via a simple smoothing based procedure we prove consistency and introduce diagnostics to ascertain the fraction of variance that is explained by the deterministic part of the equation this approach is shown to yield useful insights into the time dynamic nature of human growth copyright 2012 oxford university press

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

a functional data analytic approach to signal discrimination motivated by specific problems involving radar range profiles we suggest techniques for real time discrimination in the context of signal analysis the key to our approach is to regard the signals as curves in the continuum and employ a functional data analytic fda method for dimension reduction based on the fda technique for principal coordinates analysis this has the advantage relative to competing methods such as canonical variates analysis of providing a signal approximation that is best possible in an l2 sense for a given dimension as a result it produces particularly good discrimination we explore the use of both nonparametric and gaussian based discriminators applied to the dimensionreduced data

the mordell lang conjecture for function fields we give a proof of the geometric mordell lang conjecture in any characteristic our method involves a model theoretic analysis of the kernel of manin s homomorphism and of a certain analog in characteristic p department of mathematics massachusetts institute of technology 2 277 cambridge massachusetts 02139 current address department of mathematics hebrew university jerusalem israel e mail address ehud math mit edu

elementary theory of free non abelian groups we prove that any two non abelian free groups have the same elementary theory and that this theory is decidable these results solve two questions that were raised by tarski in 1945

krull dimension of solvable groups in this paper we prove that free solvable groups have finite krull dimension in fact this is true for much wider class of solvable groups termed rigid groups along the way we study the algebraic structure of the limit solvable groups fully residually free solvable groups

wetting of rough surfaces a homogenization approach the contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests we study the roughness induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory by relying on a variational formulation of the problem we show that the macroscopic contact angle is associated with the solution of two cell problems giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase our results are valid for both chemically heterogeneous and homogeneous surfaces in the latter case a very transparent structure emerges from the variational approach the classical laws of wenzel and cassie baxter give bounds for the optimal energy and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case to the largest one in the hydrophilic case

dynamics of layered interfaces arising from phase boundaries the dynamics of a material in two phases is studied in the context of phase field models based on a landau ginzburg free energy functional they consist of a system of two nonlinear diffusion equat

an integral equation method for the cahn hilliard equation in the wetting problem abstract we present an integral equation approach to solving the cahn hilliard equation equipped with boundary conditions that model solid surfaces with prescribed young s angles the discretization of the system in time using convex splitting leads to a modified biharmonic equation at each time step to solve it we split the solution into a volume potential computed with free space kernels plus the solution to a second kind integral equation skie the volume potential is evaluated with the help of a box based volume fmm method for non box domains the source density is extended by solving a biharmonic dirichlet problem the near singular boundary integrals are computed using quadrature by expansion qbx with fmm acceleration our method has linear complexity in the number of surface volume degrees of freedom and can achieve high order convergence in space with adaptive refinement to manage error from function extension

functional components of variation in handwriting abstract functional data analysis techniques are used to analyze a sample of handwriting in chinese the goals are a to identify a differential equation that satisfactorily models the data s dynamics and b to use the model to classify handwriting samples taken from differential individuals after preliminary smoothing and registration steps a second order linear differential equation for which the forcing function is small is found to provide a good reconstruction of the original script records the equation is also able to capture a substantial amount of the variation in the scripts across replication the cross validated classification process is 100 effective for the samples analyzed

nonparametric state price density estimation using constrained least squares and the bootstrap the economic theory of option pricing imposes constraints on the structure of call functions and state price densities except in a few polar cases it does not prescribe functional forms this paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions such as monotonicity and convexity within a single least squares procedure the bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints we apply the techniques to option pricing data on the dax

nonparametric conditional density estimation using piecewise linear solution path of kernel quantile regression the goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y this can be achieved by estimating the entire conditional density p y x in this letter we present a new approach for nonparametric conditional density estimation we develop a piecewise linear path following method for kernel based quantile regression it enables us to estimate the cumulative distribution function of p y x in piecewise linear form for all x in the input domain theoretical analyses and experimental results are presented to show the effectiveness of the approach

functional data analysis of the dynamics of the monthly index of nondurable goods production functional data analysis techniques pioneered by ramsay and bernard silverman are used to analyze the dynamics of a monthly nonseasonally adjusted index of production after determining the order three of the ordinary differential equation that describes the data and estimating its coefficients the time variation of each vector of coefficients is examined in detail to determine the evolutionary dynamics of each series over a 70 year span the dynamical properties of the solution paths are also analyzed for their qualitative dynamics the resulting models are used to examine the interaction between seasonal dynamics dynamics at business cycle frequencies and long term growth

algebraic geometry over groups i algebraic sets and ideal theory abstract the object of this paper which is the first in a series of three is to lay the foundations of the theory of ideals and algebraic sets over groups

constructing wall laws with domain decomposition or asymptotic expansion techniques abstract this paper is concerned with the numerical simulation of flows of viscous fluids over rough surfaces the proposed methodology introduces consistant equivalent wall laws using domain decomposition techniques with nonmatching grids and local periodicity assumptions the paper describes this approach with its theoretical background studies its limitations and its potential applicability and compares its results to the boundary conditions that are obtained by alternative asymptotic strategies

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

semiparametric curve alignment and shift density estimation for biological data we observe a large number of signals all of them with identical although unknown shape but with a different random shift the objective is to estimate the individual time shifts and their distribution such an objective appears in several biological applications like neuroscience or ecg signal processing in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal noise ratio and without a knowledge of the pulse shape is of interest we suggest an m estimator leading to a three stage algorithm we first split our data set in blocks then the shift estimation in each block is done by minimizing a cost function based on the periodogram the estimated shifts are eventually plugged into a standard density estimator we show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution the theory is applied both to simulations and to alignment of real ecg signals the proposed approach outperforms the standard methods for curve alignment and shift density estimation even in the case of low signal to noise ratio and is robust to numerous perturbations common in ecg signals

monotonic calibrated interpolated look up tables real world machine learning applications may have requirements beyond accuracy such as fast evaluation times and interpretability in particular guaranteed monotonicity of the learned function with respect to some of the inputs can be critical for user confidence we propose meeting these goals for low dimensional machine learning problems by learning flexible monotonic functions using calibrated interpolated look up tables we extend the structural risk minimization framework of lattice regression to monotonic functions by adding linear inequality constraints in addition we propose jointly learning interpretable calibrations of each feature to normalize continuous features and handle categorical or missing data at the cost of making the objective non convex we address large scale learning through parallelization mini batching and random sampling of additive regularizer terms case studies on real world problems with up to sixteen features and up to hundreds of millions of training samples demonstrate the proposed monotonic functions can achieve state of the art accuracy in practice while providing greater transparency to users

the monotone smoothing of scatterplots we consider the problem of summarizing a scatterplot with a smooth monotone curve a solution that combines local averaging and isotonic regression is proposed and we demonstrate its use with two examples in the second example the procedure is applied in a regression setting to some data from box and cox 1964 and it is shown how this new procedure generalizes box and cox s well known family of transformations in the same example the bootstrap is applied to obtain a measure of the variability of the procedure

principal differential analysis data reduction by differential operators functional data are observations that are either themselves functions or are naturally representable as functions when these functions can be considered smooth it is natural to use their derivatives in exploring their variation principal differential analysis pda identifies a linear differential operator l w 0 i w 1 d w m 1 d m 1 d m that comes as close as possible to annihilating a sample of functions convenient procedures for estimating the m weighting functions w j are developed the estimated differential operator l is analogous to the projection operator used as the data annihilator in principal components analysis and thus can be viewed as a type of data reduction or exploration tool the corresponding linear differential equation may also have a useful substantive interpretation modelling and regularization features can also be incorporated into pda

exact confidence bounds for all contrasts of three or more regression lines abstract it is desired to compare 3 treatments under the assumption of iid normal errors it is well known that the scheffe method produces exact simultaneous confidence bounds for all contrasts of the treatment means furthermore it is known that the scheffe method is conservative when one desires confidence bounds for a specific subset of contrasts of means exact methods such as those due to tukey and dunnett yield tighter bounds than the scheffe method for specific subsets of contrasts of means in this article multiple comparisons of the treatments are done not in terms of their means but rather in terms of a parametric function the parametric function of interest is the simple linear regression model e y x it is desired to find simultaneous confidence bounds for all contrasts of the simple linear regression models although the scheffe method can be used to find such bounds this is extremely conservative the union intersection method is used to develop simultaneous confidence bou

tests for monotonicity of a regression mean with guaranteed level in this paper a nonparametric procedure for testing for monotonicity of a regression mean with guaranteed level is proposed the procedure is based on signs of differences of observations from the response variable the test is calibrated against the most difficult null hypothesis when the regression function is constant and produces an exact test in this context in general the test is conservative the power of the test is good and comparable with that of other nonparametric tests it is shown that the testing procedure has asymptotic power 1 against certain local alternatives the method is also robust against heavy tailed error distributions and even maintains good power when the errors are for example cauchy distributed a simulation study is provided to demonstrate finite sample behaviour of the testing procedure

bayesian multivariate isotonic regression splines in many applications interest focuses on assessing the relationship between a predictor and a multivariate outcome variable and there may be prior knowledge about the shape of the regression curves for example regression functions that relate dose of a possible risk factor to different adverse outcomes can often be assumed to be nondecreasing in such cases interest focuses on 1 assessing evidence of an overall adverse effect 2 determining which outcomes are most affected and 3 estimating outcome specific regression curves this article proposes a bayesian approach for addressing this problem motivated by multisite tumor data from carcinogenicity experiments a multivariate smoothing spline model is specified that accommodates dependency in the multiple curves through a hierarchical markov random field prior for the basis coefficients while also allowing for residual correlation a gibbs sampler is proposed for posterior computation and the approach is applied to data on body weight and t

bayesian inference for non gaussian ornstein uhlenbeck stochastic volatility processes we develop markov chain monte carlo methodology for bayesian inference for non gaussian ornstein uhlenbeck stochastic volatility processes the approach introduced involves expressing the unobserved stochastic volatility process in terms of a suitable marked poisson process we introduce two specific classes of metropolis hastings algorithms which correspond to different ways of jointly parameterizing the marked point process and the model parameters the performance of the methods is investigated for different types of simulated data the approach is extended to consider the case where the volatility process is expressed as a superposition of ornstein uhlenbeck processes we apply our methodology to the us dollar deutschmark exchange rate

algebraic geometry over groups ii logical foundations abstract the object of this paper which is the second in a series of three is to lay the logical foundations of the algebraic geometry over groups exploiting links between the algebraic geometry over groups and model theory we solve two problems on geometrical equivalence of groups which are due to b plotkin