c2 quadratic trigonometric polynomial curves with local bias quadratic trigonometric polynomial curves with local bias are presented in this paper the quadratic trigonometric polynomial curves have c 2 continuity with a non uniform knot vector and any value of the bias while the quadratic b spline curves have c 1 continuity the changes of a local bias parameter will only affect two curve segments with the bias parameters the quadratic trigonometric polynomial curves can move locally toward or against a control vertex a quadratic trigonometric bezier curve is also introduced as special case of the given trigonometric polynomial curves

bifurcation from stability to instability for a free boundary problem arising in a tumor model we consider a time dependent free boundary problem with radially symmetric initial data t 0 if open image in new window and r 0 0 r in r then the stationary solution is unstable

a class of αβγ bernstein bezier basis functions over triangular domain a class of email protected c bernstein bezier basis functions over triangular domain which include the cubic ball basis functions over triangular domain and the cubic bernstein bezier basis functions over triangular domain is constructed based on these new basis functions a kind of triangular bernstein bezier type patch with three exponential shape parameters is proposed the shapes of the triangular bernstein bezier type patch can be modified intuitively and foreseeable by changing the values of the three exponential shape parameters under the same control net the conditions for g 1 continuous smooth joining two triangular bernstein bezier type patches are given

on hotelling s formula for the volume of tubes and naiman s inequality abstract motivation by the question of testing for a nonlinear parameter in a regression model with independent homoscedastic normal residuals hotelling 1939 was led to consider the geometric problem of computing the volume of a tube of given radius around a curve in s to the n 1 power the unit sphere in ir to the nth power the answer involves only the arc length of the curve and not its curvature providing the radius of the tube is sufficiently small that there is no self overlap in the tube starting from a somewhat different statistical setting naiman 1986 arrived at the same geometric problem and showed that hotelling s result properly interpreted is an upper bound for the volume of a tube of arbitrary radius the purpose of this note is to give two new derivations of the hotelling naiman results the first involves differential inequalities the second is probabilistic using the concept of upcrossing borrowed from the theory of gaussian processes in the context of gaussian processes knowles 1987 has observed that approximations obtained from hotelling s result and bounds derived via upcrossings are related

distance for degree raising and reduction of triangular bezier surfaces the problem of degree reduction and degree raising of triangular bezier surfaces is considered the l 2 and l 2 measures of distance combined with the least squares method are used to get a formula for the bezier points the methods use the matrix representations of the degree reduction and degree raising

the g2 and c2 rational quadratic trigonometric bezier curve with two shape parameters with applications the rational quadratic trigonometric bezier curve with two shape parameters is presented in this paper which is new in literature the purposed curve inherits all the geometric properties of the traditional rational quadratic bezier curve the presence of shape parameters provides a control on the shape of the curve more than that of traditional bezier curve moreover the weight offers an additional control on the curve simple constraints for shape parameters are derived using the end points curvature so that their values always fall within the defined range the composition of two segments of curve using g 2 and c 2 continuity is given the new curves can accurately represent some conics and best approximates the traditional rational quadratic bezier curve

distances with rational triangular bezier surfaces in this paper we give the matrix form for the degree elevation of rational triangular bezier surfaces we use the l 2 measure to find a formula for the distance between two rational triangular bezier surfaces a polynomial triangular bezier surface approximation of a rational triangular bezier surface based on the least squares method is given the final formulas contain only bezier points and matrix of degree elevation

detection of random change point in one parameter exponential families abstract we consider a sequence x 1 x 2 x n of independent random variables which are susceptible to changing their distribution after the nt first observations where t is a random variable of a distribution known with support in 0 1 the object of this work is to detect the eventual change of distribution for that we study the performance of a test based on the statistic of log likelihood it shows that when the number of observations gets larger the distribution of the statistic log likelihood behaves like that of an affine function of the brownian motion this allows by using the concept of contiguity in the sense of lecam the evaluation of the asymptotic power function of the test

change point estimation using nonparametric regression we consider a regression model in which the mean function may have a discontinuity at an unknown point we propose an estimate of the location of the discontinuity based on one side nonparametric regression estimates of the mean function the change point estimate is shown to converge in probability at rate 0 n 1 and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models confidence regions for the location and size of the change are also discussed

symmetry breaking bifurcation of analytic solutions to free boundary problems an application to a model of tumor growth in this paper we develop a general technique for establishing analyticity of solutions of partial differential equations which depend on a parameter e the technique is worked out primarily for a free boundary problem describing a model of a stationary tumor we prove the existence of infinitely many branches of symmetry breaking solutions which bifurcate from any given radially symmetric steady state these asymmetric solutions are analytic jointly in the spatial variables and in e 1 the model and main result in this paper we present a general technique for establishing analyticity of solutions of systems of partial differential equations which depend analytically on a parameter e the method works not only for boundary value problems but also for free boundary problems in this latter context it can be used to establish long time existence of transient solutions and also to study the existence of spatially asymmetric steady solutions since free boundary problems are typically more challenging than their boundary value counterparts we shall concentrate here on a free boundary problem from developmental biology namely a model of tumor growth to further exemplify the generality of our approach an instance of a boundary value problem in a fixed domain is presented in the last section of the paper a variety of other problems are amenable to the same analysis including in particular the hele shaw model of fluid flow 11 within the last several decades a number of mathematical models have been developed that aimed at describing the evolution of carcinomas see e g 1 5 6 8 12 13 and the references cited there the main objective of these models has been to qualitatively describe under various simplifying assumptions the growth and stability of tumor tissue analysis and simulations of such models are helping to assess the relative importance of various mechanisms affecting tumor growth as well as the efficacy of certain cancer treatments on the other hand the description of the stationary dormant configurations that arise from the models has only been addressed in the case of spherical tumors but otherwise it remains largely unexplored in this paper we develop a method for establishing analyticity of received by the editors august 17 1999 1991 mathematics subject classification primary 35b32 35r35 secondary 35b30 35b60 35c10 35j85 35q80 92c15 95c15

optimal multi degree reduction of triangular bezier surfaces with corners continuity in the norm l2 this paper derives an approximation algorithm for multi degree reduction of a degree n triangular bezier surface with corners continuity in the norm l 2 the new idea is to use orthonormality of triangular jacobi polynomials and the transformation relationship between bivariate jacobi and bernstein polynomials this algorithm has a very simple and explicit expression in matrix form i e the reduced matrix depends only on the degrees of the surfaces before and after degree reduction and the approximation error of this degree reduced surface is minimum and can get a precise expression before processing of degree reduction combined with surface subdivision the piecewise degree reduced patches possess global c 0 continuity finally several numerical examples are presented to validate the effectiveness of this algorithm

bifurcation from stability to instability for a free boundary problem modeling tumor growth by stokes equation we consider a free boundary problem modeling tumor growth in fluid like tissue the model equations include a diffusion equation for the nutrient concentration and the stokes equation with a source which represents the proliferation of tumor cells the proliferation rate and the cell to cell adhesiveness which keeps the tumor intact are two parameters which characterize the aggressiveness of the tumor for any positive radius r there exists a unique radially symmetric stationary solution with radius r r for a sequence mn r there exist symmetry breaking bifurcation branches of solutions with free boundary r r eyn 0 o e 2 n even 2 for small e w hereyn 0 is the spherical harmonic of mode n 0 furthermore the smallest mn r s aymn r is such that n n r as r in this paper we prove that the radially symmetric stationary solution with r rs is linearly stable if n rs w heren rs mn rs and we prove that strict inequality holds if is small or if is large the biological implications of these results are discussed at the end of the paper

confidence regions and tests for a change point in a sequence of exponential family random variables summary maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables with particular emphasis on the exponential distribution the exact null and alternative distributions of the test statistics are found and the power is compared with a test based on a linear trend statistic exact and approximate confidence regions for the change point are based on the values accepted by a level x likelihood ratio test and a modification of the method proposed by cox spj0tvoll 1982 the methods are applied to a classical data set on the time intervals between coal mine explosions and the change in variation of stock market returns in both cases the confidence regions for the change point cover historical events that may have caused the changes

tests for a change point summary the problem considered is that of testing a sequence of independent normal random variables with constant known or unknown variance for no change in mean versus alternatives with a single change point various tests such as those based on the likelihood ratio and recursive residuals are studied power approximations are developed by integrating approximations for conditional boundary crossing probabilities a comparison of several tests is made

conditional boundary crossing probabilities with applications to change point problems abstract for normal random walks s sub 1 s sub 2 formed from independent identically distributed random variables x sub 1 x sub 2 we determine the asymptotic behavior under regularity conditions of p s sdub n mg n m for some n m sub m mxi m lambda0 xi g 1 where u sub m x sub one to the 2nd power x sub m to the 2nd power the result is applied to a normal change point problem to approximate null distributions of test statistics and to obtain approximate confidence sets for the change point

unbiased testing in exponential family regression let x ij z i i 1 2 k j 1 2 n i be independent observations such that z i is a fixed r x 1 vector r can be 0 no z s observed or 1 2 k 1 and x ij is distributed according to a one parameter exponential family which is log concave with natural parameter i we test the hypothesis that z where 1 k z is the matrix whose ith row is z i and 1 r is a vector of parameters we focus on r 2 and z i 1 z i i 1 2 k z i z i 1 the null hypothesis on hand is thus of the form i 1 2 z i in such a case the model under the null hypothesis becomes logistic regression in the binomial case poisson regression in the poisson case and linear regression in the normal case we consider mostly the one sided alternative that the second order differences of the natural parameters are nonnegative such testing problems test goodness of fit vs alternatives in which the natural parameters behave in a convex way we find classes of tests that are unbiased and that lie in a complete class we also note that every admissible test of constant size is unbiased in some discrete situations we find the minimal complete class of unbiased admissible tests generalizations and examples are given

inferences for the linear errors in variables with changepoint models abstract a new linear structural errors in variables regression with changepoint model is considered in this model we consider the likelihood ratio test based on the maximum hotelling t 2 for the test of no change against the alternative of exactly one change if there is a change either known a priori or by testing then we estimate the unknown changepoint parameter and some other related parameters by maximum likelihood the limiting distribution of the changepoint estimator is investigated and it is shown that the asymptotic efficiency increases as the absolute regression slope coefficient increases a monte carlo study shows that the proposed estimator performs satisfactorily

the power of likelihood ratio and cumulative sum tests for a change in a binomial probability summary a simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables it is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence but that the likelihood ratio test is much more powerful near the ends an example from epidemiology is used to illustrate the results under certain conditions the cumulative sum test is identical to a two sample kolmogorov smirnov test and so the iterative procedure can be used to find the null distribution of kolmogorov smirnov and related statistics

robustness of the likelihood ratio test for a change in simple linear regression abstract this article examines the robustness of the likelihood ratio tests for a change point in simple linear regression we first summarize the normal theory of kim and siegmund who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope we then discuss the robustness of these tests using the convergence theory of stochastic processes we show that the test statistics converge to the same limiting distributions regardless of the underlying distribution we perform simulations to assess the distributional insensitivity of the test statistics to a weibull a lognormal and a contaminated normal distribution in two different cases fixed and random independent variables numerical examples illustrate that the test has a correct size and retains its power when the distribution is nonnormal we also study the effects of the independent variable s configuration with the

maximally selected chi square statistics two samples can be compared by selecting a cut point and then forming a 2 x 2 table of the numbers of observations above and below the cut point in each sample when the cut point is selected so as to maximize the standard chi square statistic the chi square percentile points are inappropriate actual significance levels are computed for large samples and correct percentile poillts are tabulated

iterative process for g2 multi degree reduction of bezier curves 2 continuity abstract in this paper the issue of multi degree reduction of bezier curves with c 1 and g 2 continu ity at the end points of the curve is considered an iterative method which is the first of this type is derived it is shown that this algorithm converges and can be applied itera tively to get the required accuracy some examples and figures are given to demonstrate the efficiency of this method

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

quasi static motion of a capillary drop ii the three dimensional case abstract a theory is presented to analyze the nonlinear stability of a drop of incompressible viscous fluid with negligible inertia the theory is developed here on the three dimensional version of the relevant free boundary model for stokes equations within this context we show that if the free boundary initiates close to a sphere r 1 e 0 e small then there exists a global in time solution with free boundary r 1 t e 1 n 1 n t e n which approaches a sphere exponentially fast as t moreover we prove that if 0 is analytic resp c in then the velocity u x t e the pressure p x t e and the free boundary are all jointly analytic resp c in x e in an earlier paper we considered the analogous problem for a two dimensional drop although the three dimensional problem proceeds along similar lines the analysis is more complicated due to the fact that we work here with spherical harmonics and vector spherical harmonics

stability and instability of liapunov schmidt and hopf bifurcation for a free boundary problem arising in a tumor model first published in transactions of the american mathematical society in volume 360 issue 10 published by the american mathematical society

construction of triangular dp surface and its application in this paper a new type of bivariate basis on a triangle is presented which is constructed by extending the univariate ntp basis proposed by delgado and pena some algebraic properties and its recursive formulae are given then a new type of surfaces that is called triangular dp surface is defined and its recursive evaluation algorithm is obtained also in the case of low degree its subdivision algorithm and degree elevation algorithm are derived it is shown that this type of surfaces is obviously more advantageous than triangular bezier surface and hence extremely useful for geometric design especially for the situation in which the surface needs to be evaluated quickly

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

thresholded multivariate principal component analysis for phase i multichannel profile monitoring abstractmonitoring multichannel profiles has important applications in manufacturing systems improvement but it is nontrivial to develop efficient statistical methods because profiles are high dim

detecting relevant changes in time series models summary most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form h0 1 2versush1 1 2 where 1 and 2 denote parameters of the process before and after a change point the paper takes a different perspective and investigates the null hypotheses of no relevant changes i e h0 1 2 where is an appropriate norm this formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary if the difference between the parameters before and after the change point is small a general approach to problems of this type is developed which is based on the cumulative sum principle for the asymptotic analysis weak convergence of the sequential empirical process must be established under the alternative of non stationarity and it is shown that the resulting test statistic is asymptotically normally distributed the results can also be used to establish similarity of the parameters i e h1 1 2 at a controlled type 1 error and to estimate the magnitude 1 2 of the change with a corresponding confidence interval several applications of the methodology are given including tests for relevant changes in the mean variance parameter in a linear regression model and distribution function among others the finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analysing a data example from portfolio management

bifurcation for a free boundary problem modeling the growth of tumors with a drug induced nonlinear proliferation rate abstract in this paper we study a free boundary model describing growth of tumors under action of drugs to our knowledge in theoretical discussion for free boundary problems the proliferation rate in tumor models discussed in previous bifurcation results is a linear function of nutrients and inhibitors whereas in this paper we consider the net proliferation rate as a nonlinear function depending on both nutrients and drugs first the existence and the uniqueness of radially symmetric stationary solutions are obtained second we prove that symmetry breaking solutions bifurcate from the radially symmetric stationary solutions when the concentration of drug on the boundary of tumor is less than one in the rescaled model

nonparametric inference on structural breaks this paper proposes estimators of location and size of structural breaks in a possibly dynamic nonparametric regression model the structural breaks can be located at given periods of time and or they can be explained by the values taken by some regressor as in threshold models no previous knowledge of the underlying regression function is required the paper also studies the case in which several regressors explain the breaks we derive the rate of convergence and provide central limit theorems for the estimators of the location s and size s a monte carlo experiment illustrates the performance of our estimators in small samples

the effect of serial correlation on tests for parameter change at unknown time it is shown that serial correlation can produce striking effects in distributions of change point statistics failure to account for these effects is shown to invalidate change point tests either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process or through diminution of the power of the tests when high frequency mass predominates these effects are characterized by the expression 2i f o fjr f a da where f is the spectral density of the noise process in sample survey work this is known as the design effect or deff simple precise adjustments to change point test statistics which account for serial correlation are provided the same adjustment applies to all commonly used regression models residual processes are derived for both stationary time series satisfying a moment condition and for general linear regression models with stationary error structure 1 introduction stochastic models for time sequenced data are generally characterized by several unknown parameters these parameters may change over time and if the changes when they occur do so unannounced and at unknown time points then the associated inferential problem is referred to as the change point problem various important application areas of statistics involve change detection in a central way two of these areas are quality assurance and environmental monitoring most of the statistics commonly applied to the change point problem involve cumulative sums or partial sums of regression residuals the distribution theory for these statistics has been computed under the assumption that the error process for the regression model is white noise in this paper we consider linear regression of a random variable against general nonstochastic functions of time but with error variables that form a serially correlated time series we then examine the large sample properties of the stochastic processes defined by the partial sums of the regression residuals large sample distribution theory for fixed sample size statistics used to detect changes in regression parameters is usually derived by computing the distributions of various functionals on

approximating tensor product bezier surfaces with tangent plane continuity we present a simple method for degree reduction of tensor product bezier surfaces with tangent plane continuity in l 2 norm continuity constraints at the four corners of surfaces are considered so that the boundary curves preserve endpoints continuity of any order a we obtain matrix representations for the control points of the degree reduced surfaces by the least squares method a simple optimization scheme that minimizes the perturbations of some related control points is proposed and the surface patches after adjustment are c continuous in the interior and g 1 continuous at the common boundaries we show that this scheme is applicable to surface patches defined on chessboard like domains

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

asymptotic stability for a free boundary problem arising in a tumor model abstract we consider a tumor model in which all cells are proliferating at a rate and their density is proportional to the nutrient concentration the model consists of a coupled system of an elliptic equation and a parabolic equation with the tumor boundary as a free boundary it is known that for an appropriate choice of parameters there exists a unique spherically symmetric stationary solution with radius r s which is independent of it was recently proved that there is a function r s such that the spherical stationary solution is linearly stable if r s and linearly unstable if r s in this paper we prove that the spherical stationary solution is nonlinearly stable or asymptotically stable if r s

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

boundary crossing probabilities and statistical applications abstract this paper surveys recent results involving boundary crossing probabilities and related statistical applications the first part is concerned with problems of sequential analysis especially repeated significance tests and their application to sequential clinical trials involving survival data the second part develops the probability theory motivated by the problems of part 1 a method for computing first passage distributions of brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries the third part is concerned with fixed sample statistical problems especially change point problems which involve boundary crossing probabilities examples are given of problems for which methods of part 2 appear adequate and of problems which require new methods

constrained multi degree reduction of triangular bezier surfaces using dual bernstein polynomials we propose a novel approach to the problem of multi degree reduction of bezier triangular patches with prescribed boundary control points we observe that the solution can be given in terms of bivariate dual discrete bernstein polynomials the algorithm is very efficient thanks to using the recursive properties of these polynomials the complexity of the method is o n 2m 2 n and m being the degrees of the input and output bezier surfaces respectively if the approximation with appropriate boundary constraints is performed for each patch of several smoothly joined triangular bezier surfaces the result is a composite surface of global c r continuity with a prescribed order r some illustrative examples are given

sequential analysis of the proportional hazards model abstract for the proportional hazards model of survival analysis an appropriate large sample theory is developed for cases of staggered entry and sequential analysis the principal techniques involve an approximation of the score process by a suitable martingale and a random rescaling of time based on the observed fisher information as a result we show that the maximum partial likelihood estimator behaves asymptotically like brownian motion author

quasi bernstein bezier polynomials over triangular domain with multiple shape parameters abstract based on a new developed recursive relation a class of quasi bernstein bezier polynomials over triangular domain with multiple shape parameters which includes the classical bernstein bezier polynomials and the cubic and quartic said ball polynomials over triangular domain as special cases is constructed the given polynomials have some important and good properties for surface modeling such as partition of unity non negativity linear independence and so on the shapes of the corresponding triangular quasi bernstein bezier patch can be modified intuitively and foreseeable by altering the values of the shape parameters without changing the control points in order to compute the patch stably and efficiently a new de casteljau type algorithm is developed moreover the conditions for g 1 continuous smooth joining two triangular quasi bernstein bezier patches are derived

brownian approximations to first passage probabilities by direct probabilistic argument one term of an edgeworth type asymptotic expansion is obtained for certain first passage distributions for random walks these results provide partial justification for and extensions of approximations suggested earlier as a heuristic consequence of laplace transform calculations

computing steady state solutions for a free boundary problem modeling tumor growth by stokes equation we consider a free boundary problem modeling tumor growth where the model equations include a diffusion equation for the nutrient concentration and the stokes equation for the proliferation of tumor cells for any positive radius r it is known that there exists a unique radially symmetric stationary solution the proliferation rate m and the cell to cell adhesiveness c are two parameters for characterizing aggressiveness of the tumor we compute symmetry breaking bifurcation branches of solutions by studying a polynomial discretization of the system by tracking the discretized system we numerically verified a sequence of m c symmetry breaking bifurcation branches furthermore we study the stability of both radially symmetric and radially asymmetric stationary solutions

morphological stability of an elastic tumor host interface abstract the ability of tumors to metastasize is preceded by morphological instabilities such as chains or fingers that invade the host environment therefore parameters that control the morphology of the tumor may also contribute to its invasive ability previous analyses on morphological changes were performed using surface energy of the tumor host interface in an effort to understand the role the interface stiffness plays on tumor evolution here we model the tumor host interface as an elastic membrane governed by the helfrich bending energy using an energy variation approach we derive a modified laplace young condition for the stress jump across the interface in the stokes equation we then perform a linear stability analysis and investigate how physical parameters such as viscosity bending rigidity and apoptosis affect the morphological instability results show that increased bending rigidity versus mitosis rate contributes to a more stable morphological tumor behavior on the other hand increasing tumor viscosity or apoptosis may lead to invasive fingering morphologies comparison with experimental data on glioblastoma spheroids shows good agreement especially for tumors with high adhesion and low proliferation

a novel extension to the polynomial basis functions describing bezier curves and surfaces of degree n with multiple shape parameters the construction of bezier curves using shape control parameters is one of the most popular areas of research in computer aided geometric design cagd a class of new polynomial basis functions with n 1 local shape control parameters is presented here to allow the construction of bezier curves with n local shape control parameters which is an extension to the classical bernstein basis functions of degree n the properties of the proposed basis functions and the corresponding piecewise polynomial curve with n 1 local shape control parameters are analyzed this analysis shows that the new class of polynomial functions meets the conditions required for both c 0 c 1 and c 2 continuity as well as g 0 g 1 and g 2 continuity some curve design applications are then discussed and an extended application for surface design is also presented the modeling examples illustrate that the new extension provides not only a better approximation and mathematical description of bezier curves but allows the shape parameters to be altered making it a valuable method for the design of curves and surfaces

an extension of the bezier model abstract in this paper we first construct a new kind of basis functions by a recursive approach based on these basis functions we define the bezier like curve and rectangular bezier like surface then we extend the new basis functions to the triangular domain and define the bernstein bezier like surface over the triangular domain the new curve and surfaces have most properties of the corresponding classical bezier curve and surfaces moreover the shape parameter can adjust the shape of the new curve and surfaces without changing the control points along with the increase of the shape parameter the new curve and surfaces approach the control polygon or control net in addition the evaluation algorithm for the new curve and triangular surface are provided

shape analysis of cubic trigonometric bezier curves with a shape parameter abstract for the cubic trigonometric polynomial curves with a shape parameter tb curves for short the effects of the shape parameter on the tb curve are made clear the shape features of the tb curve are analyzed the necessary and sufficient conditions are derived for these curves having single or double inflection points a loop or a cusp or be locally or globally convex the results are summarized in a shape diagram of tb curves which is useful when using tb curves for curve and surface modeling furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples respectively

modeling distortion product otoacoustic emission input output functions using segmented regression distortion product otoacoustic emissions dpoaes are low level acoustic signals the detection of which involves extraction from a background of noise boege and janssen j acoust soc am 111 1810 1818 2002 described a method for modeling the presence and growth of these responses while improving growth function parameter estimation this technique excludes a significant fraction of the data especially low level responses and relies on ad hoc model fit acceptance criteria the statistical difficulties associated with these limitations are described and a weighted segmented linear regression model that avoids them is proposed a simple test is presented for the presence of dpoae growth this technique is compared to that of boege and janssen in a dataset of 9 556 input output i o functions collected over 4years on 866 ears from 379 construction apprentices and 63 age matched controls comparisons are made on the entire dataset and within audiometric hearing loss categories segmented regress

regularity of solutions to a free boundary problem modeling tumor growth by stokes equation in this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid like tissues the model equations include a quasi stationary diffusion equation for the nutrient concentration and a stokes equation with a source representing the proliferation density of the tumor cells subject to a boundary condition with stress tensor effected by surface tension this problem is a fully nonlinear problem involving nonlocal terms based on the employment of the functional analytic method and the theory of maximal regularity we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity

curve construction based on four αβ bernstein like basis functions a b s t r a c t four new bernstein like basis functions with two exponential shape parameters are constructed in this paper which include the cubic said ball basis functions and the cubic bernstein basis functions within the general framework of quasi extended chebyshev space we prove that the proposed bernstein like basis is an optimal normalized totally positive basis in order to compute the corresponding bezier like curves stably and efficiently a new corner cutting algorithm is developed necessary and sufficient conditions are derived for the planar bezier like curve having single or double inflection points a loop or a cusp or be locally or globally convex in terms of the relative position of its control polygons side vectors based on the new proposed bernstein like basis a class of b spline like basis functions with two local exponential shape parameters is constructed their totally positive property is also proved the associated b splinelike curves have c 2 continuity at single knots and include the cubic non uniform b spline

approximate tail probabilities for the maxima of some random fields abstract hogan and siegmund 1986 adapt the method developed by pickands 1969 qualls and watanabe 1973 and bickel and rosenblatt 1973 to obtain explicit large deviation approximations for the maxima of several gaussian random fields arising in statistics using a special argument for one particular case they suggest a heuristic second order approximation for that case and they show by a monte carlo experiment that the second order approximation frequently gives considerably better numerical results the purpose of this paper is to show that the method developed by woodroofe 1976 1982 for problems in one dimensional time can be adapted to study maxima of random fields overall it involves simpler computations than the previous method and consequently seems potentially capable of delivering a genuine second order approximation should one seem desirable

on the degree elevation of bernstein polynomial representation the polynomials determined in the bernstein bezier basis enjoy considerable popularity in computer aided design cad applications the common situation in these applications is that polynomials given in the basis of degree n have to be represented in the basis of higher degree the corresponding transformation algorithms are called algorithms for degree elevation of bernstein polynomial representations these algorithms are only then of practical importance if they do not require the ill conditioned conversion between the bernstein and the power basis we discuss all the algorithms of this kind known in the literature and compare them to the new ones we establish some among the latter are better conditioned and not more expensive than the currently used ones all these algorithms can be applied componentwise to vector valued polynomial bezier representations of curves or surfaces

testing for parameter constancy in linear regressions an empirical distribution function approach this paper proposes some tests for parameter constancy in linear regressions the tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free the local power analysis reveals that the proposed tests have nontrivial local power against a wide range of alternatives in particular the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances the model allows for both dynamic and trending regressors the residuals may be obtained based on any root n consistent estimator under the null of regression parameters as an intermediate result some weak convergence for stochastically weighted sequential empirical processes is established

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

the cusum test of homogeneity with an application in spontaneous abortion epidemiology we test the hypothesis of homogeneity over time in the rate of an event with a modification of page s cumulative sum cusum procedure the modification draws on an indifference zone approach to testing that is well suited to the epidemiologic study of retrospective data we provide procedures for evaluating the significance level of the largest observed cusum value occurring in a sequence of fixed length we draw inferences unconditionally with a known baseline rate of the event and conditionally on observed margins with unknown baseline rate data collected over a five year period from one new york city hospital serve to illustrate the modified cusum test in a study of fluctuations in the proportions of chromosomally normal trisomic x monosomic and triploid spontaneous abortions

identifying optimal risk windows for self controlled case series studies of vaccine safety in vaccine safety studies subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window to our knowledge risk windows for vaccine safety studies have tended to be pre defined and not to use information from the current study inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period which can introduce bias we propose a data based approach for identifying the optimal risk windows for self controlled case series studies of vaccine safety the approach involves fitting conditional poisson regression models to obtain incidence rate ratio estimates for different risk window lengths for a specified risk window length l the average time at risk t l is calculated when the specified risk window is shorter than the true the incidence rate ratio decreases with 1 t l increasing but there is no explicit relationship when the specified risk window is longer than the true the incidence rate ratio increases linearly with 1 t l increasing theoretically the risk window with the maximum incidence ratio is the optimal risk window because of sparse data problem we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long risk windows

multi degree reduction of tensor product bezier surfaces with general boundary constraints abstract we propose an efficient approach to the problem of multi degree reduction of rectangular bezier patches with prescribed boundary control points we observe that the solution can be given in terms of constrained bivariate dual bernstein polynomials the complexity of the method is o mn 1 n 2 with m min m1 m2 where n1 n2 and m1 m2 is the degree of the input and output bezier surface respectively if the approximation with appropriate boundary constraints is performed for each patch of several smoothly joined rectangular bezier surfaces the result is a composite surface of global cr continuity with a prescribed r 0 in the detailed discussion we restrict ourselves to r 0 1 which is the most important case in practical application some illustrative examples are given

testing for a two phase multiple regression maximum likelihood methods are used to estimate the parameters of two separate multiple regressions that switch at an unknown point in the data normal errors with constant variance are assumed and likelihood ratio statistics are used to test for the presence of two separate regressions our main result is a conservative bound on the null distribution function of the test statistic this bound is based on an improved bonferroni inequality and a simple power series approximation is provided similar bounds are given for likelihood ratio statistics that test for a shift in the constant term of the regression only the accuracies of the bounds and approximations are evaluated on a number of examples

first exit densities of brownian motion through one sided moving boundaries let a a e be a sequence of curved boundaries which tend to infinity as a increases let t a inf t 0 w t geqq psi a t where w t denotes the standard brownian motion under regularity conditions on the boundaries uniform approximations for the first exit densities of ta are derived the consequences for upper and lower class functions are discussed the approximations for the first exit densities of brownian motion with drift which are also derived lead to uniform approximations for the power functions of sequential tests the quality of the approximations is demonstrated by some figures

dynamic linear models with markov switching abstract in this paper hamilton s 1988 1989 markov switching model is extended to a general state space model this paper also complements shumway and stoffer s 1991 dynamic linear models with switching by introducing dependence in the switching process and by allowing switching in both measurement and transition equations building upon ideas in hamilton 1989 cosslett and lee 1985 and harrison and stevens 1976 a basic filtering and smoothing algorithm is presented the algorithm and the maximum likelihood estimation procedure is applied in estimating lam s 1990 generalized hamilton model with a general autoregressive component the estimation results show that the approximation employed in this paper performs an excellent job with a considerable advantage in computation time a state space representation is a very flexible form and the approach taken in this paper therefore allows a broad class of models to be estimated that could not be handled before in addition the algorithm for calculating smoothed inferences on the unobserved states is a vastly more efficient one than that in the literature

bifurcation for a free boundary tumor model with extracellular matrix and matrix degrading enzymes abstract we study a free boundary problem modeling solid tumor growth with ecm and mde interactions the production rate of mde by tumor cells is a nonlinear function depending on nutrients and mde this nonlinear term is more complicated for this model we can not give the explicit expressions or integral expressions for mde terms while we only get the existence and uniqueness at first we show the existence and the uniqueness of radially symmetric stationary solutions then the existence of symmetry breaking solutions bifurcating from the radially symmetric stationary solutions is obtained

the likelihood ratio test for a change point in simple linear regression summary we consider likelihood ratio tests to detect a change point in simple linear regression a when the alternative specifies that only the intercept changes and b when the alternative permits the intercept and the slope to change approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable the approximations are compared with simulations in order to assess their accuracy for the model in which only the intercept is allowed to change a confidence region for the change point and an approximate joint confidence region for the change point the difference in intercepts and the slope are obtained by inversion of the appropriate likelihood ratio tests

a general regression changepoint test for time series data abstractthis article develops a test for a single changepoint in a general setting that allows for correlated time series regression errors a seasonal cycle time varying regression factors and covariate information within a changepoint statistic is constructed from likelihood ratio principles and its asymptotic distribution is derived the asymptotic distribution of the changepoint statistic is shown to be invariant of the seasonal cycle and the covariates should the latter obey some simple limit laws however the limit distribution depends on any time varying factors a new test based on arma residuals is developed and is shown to have favorable properties with finite samples driving our work is a changepoint analysis of the mauna loa record of monthly carbon dioxide concentrations this series has a pronounced seasonal cycle a nonlinear trend heavily correlated regression errors and covariate information in the form of climate oscillations in the end we find a prominent changepoint in the ea

change points in nonparametric regression analysis an otherwise smooth regression model are proposed the assumptions needed are much weaker than those made in parametric models the proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change points of slope and of higher order curvature the proposed estimators are based on a comparison of left and right one sided kernel smoothers weak convergence of a stochastic process in local differences to a gaussian process is established for properly scaled versions of estimators of the location of a change point the continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change point estimators these rates are typically faster than n 1 2 rates of global lp convergence of curve estimates with appropriate kernel modifications adapting to estimated change points are derived as a consequence it is shown that these rates of convergence are the same as if the location of the change point was known the methods are illustrated by means of the well known data on the annual flow volume of the nile river between 1871 and 1970 1 introduction nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions sometimes a generally smooth curve might contain an isolated discontinuity or change point in the curve or in a possibly higher order derivative and in many cases interest focuses on the occurrence of such change points in parametric approaches to the regression change point problem simple linear regressions before and after a possible change point are assumed and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative or equivalently a slope change is incorporated into the model see for instance hinkley 1969 and brown durbin and evans 1975 the analysis of change points which describe sudden localized changes typically occurring in economics medicine and the physical sciences has recently found increasing interest general smoothness assumptions allowing for a large class of regression functions to be considered seem to be more appropriate in a variety of applied problems than parametric modelling an

a novel generalization of bezier curve and surface a new formulation for the representation and designing of curves and surfaces is presented it is a novel generalization of bezier curves and surfaces firstly a class of polynomial basis functions with n adjustable shape parameters is present it is a natural extension to classical bernstein basis functions the corresponding bezier curves and surfaces the so called quasi bezier i e q bezier for short curves and surfaces are also constructed and their properties studied it has been shown that the main advantage compared to the ordinary bezier curves and surfaces is that after inputting a set of control points and values of newly introduced n shape parameters the desired curve or surface can be flexibly chosen from a set of curves or surfaces which differ either locally or globally by suitably modifying the values of the shape parameters when the control polygon is maintained the q bezier curve and surface inherit the most properties of bezier curve and surface and can be more approximated to the control polygon it is visible that the properties of end points on q bezier curve and surface can be locally controlled by these shape parameters some examples are given by figures

large deviations for boundary crossing probabilities abstract for random walsk s sub n n 1 2 whose distribution can be imbedded in an exponential family a method is described for determining the asymptotic behavior as m goes to infinity of p s sub n m c n m for some n m such that s sub m m micron sub o micron sub 0 c 1 applications are given to the distribution of the smirnov statistic and to modified repeated significance tests author