on the best constants in inequalities of the markov and wirtinger types for polynomials on the half line abstract the main topic of the paper is best constants in markov type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves the norm is the l 2 norm with laguerre weight the leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term which is the operator norm of a volterra operator are given for best constants in inequalities of the wirtinger type the limit is computed and an asymptotic formula for the error term is presented

inference for the median residual life function in sequential multiple assignment randomized trials in survival analysis median residual lifetime is often used as a summary measure to assess treatment effectiveness it is not clear however how such a quantity could be estimated for a given dynamic treatment regimen using data from sequential randomized clinical trials we propose a method to estimate a dynamic treatment regimen specific median residual life merl function from sequential multiple assignment randomized trials we present the merl estimator which is based on inverse probability weighting as well as two variance estimates for the merl estimator one variance estimate follows from lunceford davidian and tsiatis 2002 survival function based variance estimate and the other uses the sandwich estimator the merl estimator is evaluated and its two variance estimates are compared through simulation studies showing that the estimator and both variance estimates produce approximately unbiased results in large samples to demonstrate our methods the estimator has been applied to data from a sequentially randomized leukemia clinical trial

piecewise linear curve approximation using graph theory and geometrical concepts in this paper a new methodology for curve approximation is presented the method is suitable for both self intersected and non self intersected curves it combines elements from graph theory and from elementary geometry and it is fully automated more specifically graph theory tools are utilized in order 1 to remove the details that are irrelevant to the general shape of the curve under study and 2 to decompose the curve into non self intersecting smaller curves then each such smaller curve is processed via geometrical tools in order to approximate it efficiently with linear segments experimental results show that the proposed method compares well with several other methods of the same purpose

semiparametric efficient estimation of survival distributions in two stage randomisation designs in clinical trials with censored data summary two stage randomisation designs are useful in the evaluation of combination therapies where patients are initially randomised to an induction therapy and then depending upon their response and consent are randomised to a maintenance therapy in this paper we derive the best regular asymptotically linear estimator for the survival distribution and related quantities of treatment regimes we propose an estimator which is easily computable and is more efficient than existing estimators large sample properties of the proposed estimator are derived and comparisons with other estimators are made using simulation

an elementary approach to weak convergence for quantile processes with applications to censored survival data abstract let be a continuously differentiable function with positive derivative and let n be a sequence of right continuous increasing processes we show that if n 1 2 n w where w is continuous then n 1 2 1 n 1 w 1 1 this result is applied to classical processes such as the empirical distribution function the kaplan meier estimator and some other situations we also prove an analogous result for the bootstrapped version of n 1 2 n and show how this allows one to obtain confidence bands for the quantile function 1 based on the bootstrap several examples are given

examination of percentile residual life we initiate a nonparametric large sample estimation theory for the percentile residual lifetime we introduce the empirical percentile residual life process and determine its asymptotic distribution resulting in asymptotically distribution free confidence intervals and confidence bands for the percentile residual lifetime we illustrate the methods using strike duration data from the work of d c schmittlein and d g morrison

comparison of interpolating methods for image resampling when resampling an image to a new set of coordinates for example when rotating an image there is often a noticeable loss in image quality to preserve image quality the interpolating function used for the resampling should be an ideal low pass filter to determine which limited extent convolving functions would provide the best interpolation five functions were compared a nearest neighbor b linear c cubic b spline d high resolution cubic spline with edge enhancement a 1 and e high resolution cubic spline a 0 5 the functions which extend over four picture elements c d e were shown to have a better frequency response than those which extend over one a or two b pixels the nearest neighbor function shifted the image up to one half a pixel linear and cubic b spline interpolation tended to smooth the image the best response was obtained with the high resolution cubic spline functions the location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned and the response has the most smoothing when the resampled points are equidistant from the original coordinate points thus at the expense of some increase in computing time image quality can be improved by resampled using the high resolution cubic spline function as compared to the nearest neighbor linear or cubic b spline functions

percentile residual life functions the percentile 0 1 residual life function at time t is defined as the percentile of the remaining life given survival up to time t note that percentile is used in place of 100 percentile two classes of life distributions defined by the percentile residual life function are the decreasing percentile residual life dprl class and the new better than used with respect to the percentile nbup class these two classes are respectively analogous to the well known decreasing mean residual life dmrl class and the new better than used in expectation nbue class that involve the mean residual life function we obtain properties of the percentile residual life function and of the dprl nbup and their dual classes some results differ notably from corresponding results for the mean residual life function

eigenvalue estimates for symmetric matrices abstract we use the fact that the set of symmetric positive semidefinite matrices of order n form a cone with a special structure in order to find bounds for the eigenvalues of a symmetric matrix

on the eigenvalues of certain canonical higher order ordinary differential operators abstract we consider the operator of taking the 2pth derivative of a function with zero boundary conditions for the function and its first p 1 derivatives at two distinct points our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for p 1 and p 3

scale space derived from b splines this paper proposes a scale space theory based on b spline kernels our aim is twofold 1 present a general framework and show how b splines provide a flexible tool to design various scale space representations in particular we focus on the design of continuous scale space and dyadic scale space frame representations a general algorithm is presented for fast implementation of continuous scale space at rational scales in the dyadic case efficient frame algorithms are derived using b spline techniques to analyze the geometry of an image the relationship between several scale space approaches is explored the behavior of edge models the properties of completeness causality and other properties in such a scale space representation are examined in the framework of b splines it is shown that besides the good properties inherited from the gaussian kernel the b spline derived scale space exhibits many advantages for modeling visual mechanism including the efficiency compactness orientation feature and parallel structure

a note on cause specific residual life in medical research investigators often wish to characterize the distributions of remaining lifetimes while nonparametric analyses of residual life distributions have been widely studied with independently right censored data residual life analysis has not been examined in the competing risks setting with multiple potentially dependent failure types we define the cause specific residual life distribution as the residual cumulative incidence function conditionally on survival to a given time because of the improper form of the cause specific distribution the mean cause specific residual lifetime does not exist theoretically we develop nonparametric inferences for the cause specific residual life function and its corresponding quantiles which may exist theoretical justification including uniform consistency and weak convergence is established simulation studies and a breast cancer data analysis demonstrate the practical utility of the methods

bootstrapping empirical functions in our previous sections we have established weak convergence of mean residual life total time of test lorenz and goldie processes to appropriate gaussian processes apart from a few special cases cf section 8 these limiting processes are functions of the underlying distributions consequently when testing for statistical hypotheses for example one would have to compute the resulting limiting distribution for each f of interest the same is true when trying to use our results for constructing confidence bands for the theoretical functionals of the said empirical processes this type of problems can be solved by adapting the bootstrap method proposed by efron 1979 1982 to the present situation as we will see the bootstrap method is simply a monte carlo simulation determined by the given observations

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

two dimensional spline interpolation for image reconstruction a scheme of two dimensional 2 d spline interpolation for image reconstruction is presented it is aimed to be applied in image data compression an impulse response derived from 2 d quadratic spline functions is theoretically analysed then it is approximated to be a finite duration one fir for practical implementation with this scheme compression rate of greater than 12 is achieved for x ray left ventricular cineangiogram image data compression

estimating intensity variance due to noise in registered images applications to diffusion tensor mri image registration techniques which require image interpolation are widely used in neuroimaging research we show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space we describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images the spatial transformations computed by the registration procedure and the interpolation or approximation kernel chosen the method is general and could handle various sources of signal variability such as thermal noise and physiological noise provided that their effects can be assessed in the original images our approach is applied to diffusion tensor dt mri data assuming only thermal noise as the source of variability in the data we show that incorrect noise variance estimates in registered diffusion weighted images can affect dt parameters as well as indices of goodness of fit such as chi square maps in addition to dt mri we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data such as in relaxometry and functional mri studies

more estimates for eigenvalues and singular values abstract there is an interesting relation between the angle that a matrix forms with the identity and its eigenvalues then we show for symmetric matrices that some information about the matrix can be known if the angle is computed a lower bound for the maximum eigenvalue is obtained for symmetric positive semidefinite matrices this inequality and the upper bound for eigenvalues given in 5 provide us an interval in which must lie the maximum eigenvalue finally some results from 5 and the first part of this paper are generalized for the non symmetric case

recursive regularization filters design properties and applications least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed for each problem there is a family of discrete regularization filters r filters which allow an efficient determination of the solutions these operators are stable symmetric lowpass filters with an adjustable scale factor two decomposition theorems for the z transform of such systems are presented one facilitates the determination of their impulse response while the other allows an efficient implementation through successive causal and anticausal recursive filtering a case of special interest is the design of r filters for the first and second order difference operators these results are extended for two dimensional signals and for illustration purposes are applied to the problem of edge detection this leads to a very efficient implementation 8 multiplies 10 adds per pixel of the optimal canny edge detector based on the use of a separable second order r filter

the rate of strong uniform consistency for the product limit estimator the maximal deviation of the product limit estimate from the estimated distribution function is investigated as a consequence of a functional law of the iterated logarithm the log log law is proved for this deviation on appropriate half lines with the precise constants this result implies that the log log law need not hold in general for the maximal deviation on the whole line then a general asymptotic order of magnitude is determined for the latter deviation this order depends on the joint behaviour of the censoring and censored distributions in a well defined way corresponding to specific joint behaviours several limsup results are deduced as consequence including all the previously known log log type laws in improved form the results are also extended to the variable censoring model

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

multiscale curvature based shape representation using b spline wavelets this paper presents a new multiscale curvature based shape representation technique with application to curve data compression using b spline wavelets the evolution of the curve is implemented in the b spline scale space which enjoys a number of advantages over the classical gaussian scale space for instance the availability of fast algorithms the b spline wavelet transforms are used to efficiently estimate the multiscale curvature functions based on the curvature scale space image we introduce a coarse to fine matching algorithm which automatically detects the dominant points and uses them as knots for curve interpolation

testing for normality in arbitrary dimension on etend le theoreme de convergence faible univariable de murota et takeuchi 1981 pour la transformee de mahalanobis de la fonction caracteristique empirique a d variables d 1

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

simple algorithms and architectures for b spline interpolation it is proved that the toeplitz binary value matrix inversion associated with mth order b spline interpolation can be implemented using only 2 m 1 additions pipelined architectures are developed for real time b spline interpolation based on simple running average filters it is shown that an ideal interpolating function which is approximated by a truncated sinc function with m half cycles can be implemented using b splines with m 2 multiplies with insignificant loss of performance the coefficients at the knots of the truncated sinc function can be approximated using coefficients which are powers of two the resulting implementation requires only m 4m 6 additions it is believed that the truncated sinc function approximated by zero order b spline functions actually achieves the best visual performance

technical note when does the βth percentile residual life function determine the distribution knowledge of the th percentile residual life function does not uniquely determine the underlying distribution additional information about the tail behavior of the distribution is needed knowledge of both the 1 and 2 percentile residual life functions does uniquely determine the distribution provided that 1 and 2 are noncommensurate this corrects and extends the results of schmittlein and morrison schmittlein d c d g morrison 1981 the median residual lifetime a characterization theorem and an application opns res 29 392 399

asymptotically sharp inequalities for polynomials involving mixed laguerre norms abstract the paper concerns best constants in markov type inequalities between the norm of a higher derivative of a polynomial and the norm of the polynomial itself the norm of the polynomial and its derivative is taken in l 2 on the half line with the weight t e t and t e t respectively under the assumption that is larger than the order of the derivative we determine the leading term of the asymptotics of the constants as the degree of the polynomial goes to infinity thus proving a conjecture raised by bottcher and dorfler in 2010 4

a return to the hardy littlewood integral inequality this paper is concerned with the extension and generalization of a classic integral inequality first considered by hardy and littlewood in 1932 the integral inequality is big int b a p f 2 q f 2 big 2 leqslant k int b a w f 2 int b a w w 1 pf qf 2 f in delta where k is a positive number the coefficients p q and w are real valued and w 0 on the interval a b infty a b leqslant infty and p 1 q w in l loc a b delta is the maximal linear manifold of functions f for which the two integrals on the right hand side are both finite the hardy littlewood inequality is the special case a 0 b infty p w 1 and q 0 on 0 infty here k 4 and all the cases of equality can be identified in this paper the results of everitt in 1971 connecting the above inequality with the titchmarsh weyl m coefficient of the associated differential equation py qy lambda wy on a b are restated in an improved form and are shown to hold under the above minimal conditions on the coefficients p q and w it is proved that the best possible value for the number k satisfies 1 k leqslant infty and that within these bounds all values of k can be realized in the course of establishing these results new information of independent interest is obtained about the behaviour of the m coefficient near the real axis examples are given to exhibit the wide range of possibilities for the integral inequality recent results on the asymptotic form of the m coefficient and on the transformation theory of the associated differential equation are shown to have applications for the general properties of the inequality all recent contributions to this general integral inequality are listed in the references and their content is surveyed during the course of the paper

b spline snakes a flexible tool for parametric contour detection we present a novel formulation for b spline snakes that can be used as a tool for fast and intuitive contour outlining we start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal curvature constrained snake is a cubic spline irrespective of the form of the external energy field unfortunately such regularized snakes suffer from slow convergence speed because of a large number of control points as well as from difficulties in determining the weight factors associated to the internal energies of the curve we therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies i e the regularization term in other words we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots the theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments validation results are presented comparing the traditional snake using internal energies and the proposed approach without internal energies showing the similar performance of the latter several biomedical examples of applications are included to illustrate the versatility of the method

a new flexible dependence measure for semi competing risks semi competing risks data are often encountered in chronic disease follow up studies that record both nonterminal events e g disease landmark events and terminal events e g death studying the relationship between the nonterminal event and the terminal event can provide insightful information on disease progression in this article we propose a new sensible dependence measure tailored to addressing such an interest we develop a nonparametric estimator which is general enough to handle both independent right censoring and left truncation our strategy of connecting the new dependence measure with quantile regression enables a natural extension to adjust for covariates with minor additional assumptions imposed we establish the asymptotic properties of the proposed estimators and develop inferences accordingly simulation studies suggest good finite sample performance of the proposed methods our proposals are illustrated via an application to denmark diabetes registry data

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

the median residual lifetime a characterization theorem and an application the concept of the median residual lifetime for a probability distribution is outlined and shown to have several advantages over its more common counterpart the mean residual lifetime a characterization theorem shows that a pareto distribution of the second kind or equivalently a gamma mixture of exponentials is the unique distribution with a linearly increasing median residual lifetime an empirical example from the literature on strike durations is presented

a unified curvature definition for regular polygonal and digital planar curves in this paper we propose a new definition of curvature called visual curvature it is based on statistics of the extreme points of the height functions computed over all directions by gradually ignoring relatively small heights a multi scale curvature is obtained the theoretical properties and the experiments presented demonstrate that multi scale visual curvature is stable even in the presence of significant noise to our best knowledge the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves moreover it yields stable curvature estimates of curves in digital images even under sever distortions we also show a relation between multi scale visual curvature and convexity of simple closed curves

regression on quantile residual life a time specific log linear regression method on quantile residual lifetime is proposed under the proposed regression model any quantile of a time to event distribution among survivors beyond a certain time point is associated with selected covariates under right censoring consistency and asymptotic normality of the regression estimator are established an asymptotic test statistic is proposed to evaluate the covariate effects on the quantile residual lifetimes at a specific time point evaluation of the test statistic does not require estimation of the variance covariance matrix of the regression estimators which involves the probability density function of the survival distribution with censoring simulation studies are performed to assess finite sample properties of the regression parameter estimator and test statistic the new regression method is applied to a breast cancer data set with long term follow up to estimate the patients median residual lifetimes adjusting for important prognostic factors

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

shape representation and recognition through morphological curvature scale spaces a multiscale morphological method for the purpose of shape based object recognition is presented a connected operator similar to the morphological hat transform is defined and two scale space representations are built using the curvature function as the underlying one dimensional signal each peak and valley of the curvature is extracted and described by its maximum and average heights and by its extent and represents an entry in the top or bottom hat transform scale spaces we demonstrate object recognition based on hat transform scale spaces for three large data sets a set of diatom contours the set of silhouettes from the mpeg 7 database and the set of two dimensional views of three dimensional objects from the coil 20 database our approach outperforms other methods for which comparative results exist

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

b spline design of maximally flat and prolate spheroidal type fir filters a digital fir filter is described that offers excellent passband and stopband characteristics for general applications design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of hermann 1971 and kaiser 1975 1979 to one having characteristics like the minimum sidelobe energy approximations of kaiser and saramaki 1989 the impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances unlike fir filters designed by window or frequency sampling methods the filter coefficients are determined from the inverse fourier transform in closed form once b splines have been used to replace sharp transition edges of the magnitude response although the filters are developed in the frequency domain a convergence window is identified in the convolution series and compared with windows of popular fir filters by means of example adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs the design technique is extended to create additional transitional filters from prototype window functions such as the transitional hann window filter the filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors

phase vector incompressible registration algorithm for motion estimation from tagged magnetic resonance images tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue it is challenging to obtain 3 d motion estimates due to a tradeoff between image slice density and acquisition time typically interpolation methods are used either to combine 2 d motion extracted from sparse slice acquisitions into 3 d motion or to construct a dense volume from sparse acquisitions before image registration methods are applied this paper proposes a new phase based 3 d motion estimation technique that first computes harmonic phase volumes from interpolated tagged slices and then matches them using an image registration framework the approach uses several concepts from diffeomorphic image registration with a key novelty that defines a symmetric similarity metric on harmonic phase volumes from multiple orientations the material property of harmonic phase solves the aperture problem of optical flow and intensity based methods and is robust to tag fading a harmonic magnitude volume is used in enforcing incompressibility in the tissue regions the estimated motion fields are dense incompressible diffeomorphic and inverse consistent at a 3 d voxel level the method was evaluated using simulated phantoms human brain data in mild head accelerations human tongue data during speech and an open cardiac data set the method shows comparable accuracy to three existing methods while demonstrating low computation time and robustness to tag fading and noise

an exact method for computing the area moments of wavelet and spline curves we present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis using green s theorem we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product the multidimensional filter coefficients are precomputed exactly as the solution of a two scale relation to demonstrate the performance improvement of the new method we compare it with existing methods such as pixel based approaches and approximation of the region by a polygon we also propose an alternate scheme when the scaling function is sinc x

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

on least squares regression with censored data summary the semiparametric accelerated failure time model relates the logarithm of the failure time linearly to the covariates while leaving the error distribution unspecified the present paper describes simple and reliable inference procedures based on the least squares principle for this model with right censored data the proposed estimator of the vector valued regression parameter is an iterative solution to the buckley james estimating equation with a preliminary consistent estimator as the starting value the estimator is shown to be consistent and asymptotically normal a novel resampling procedure is developed for the estimation of the limiting covariance matrix extensions to marginal models for multivariate failure time data are considered the performance of the new inference procedures is assessed through simulation studies illustrations with medical studies are provided

on inequalities for powers of linear operators and for quadratic forms let h be a hilbert space in which a symmetric operator s with a dense domain d s is given and let s have a finite deficiency index r s this paper contains a necessary and sufficient condition for validity of the following inequalities of kolmogorov type and a method for calculating the best possible constants c n m s moreover let be a symmetric bilinear functional with a dense domain d such that d s d and f g sf g for all f d s g d a necessary and sufficient condition for validity of the inequality as well as a method for calculating the best possible constant k are obtained then an analogous approach is worked out in order to obtain the best possible additive inequalities of the form the paper is concluded by establishing the best possible constants in the inequalities where t is an arbitrary dissipative operator the theorems are extensions of the results of ju i ljubic w n everitt and t kato

on discrete wirtinger northcott problems abstract some discrete wirtinger northcott inequalities are established in this paper let dx and x be the periodic difference and non periodic difference of a vector x r n respectively for 1 p we give the maximum and the minimum of d x x d x and x in the l p ball b p 0 n in particular we prove that for p the result min b 0 n d x 4 n n is even 4 n n 2 1 n is odd is equivalent to the well known discrete first northcott inequality established by fan taussky and todd

on an inequality of the kolmogorov type for a second order differential expression in this paper we discuss an integro differential inequality formed from the square of a second order differential expression a connection between the existence of the inequality and the titchmarsh weyl m function is established and it is shown that the best constant in the inequality is determined by the behaviour of the m function analytic results are established for specific classes of problems a numerical treatment of the inequality is also discussed and estimates of the best constant in specific examples are given

nonparametric estimation for the difference or ratio of median failure times a simple and purely nonparametric confidence interval procedure for the difference or ratio of two median failure times is proposed with censored observations the new proposal does not involve unstable and complicated nonparametric density estimates and is valid asymptotically even when the two underlying distribution functions differ in shape extensive numerical studies are carried out to examine the appropriateness of the new procedure for practical sample sizes

biorthogonal partners and applications two digital filters h z and f z are said to be biorthogonal partners of each other if their cascade h z f z satisfies the nyquist or zero crossing property biorthogonal partners arise in many different contexts such as filterbank theory exact and least squares digital interpolation and multiresolution theory they also play a central role in the theory of equalization especially fractionally spaced equalizers in digital communications we first develop several theoretical properties of biorthogonal partners we also develop conditions for the existence of biorthogonal partners and fir biorthogonal pairs and establish the connections to the riesz basis property we then explain how these results play a role in many of the above mentioned applications

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

mean residual life models with time dependent coefficients under right censoring the mean residual life provides the remaining life expectancy of a subject who has survived to a certain time point when covariates are present regression models are needed to study the association between the mean residual life function and potential regression covariates in this paper we propose a flexible class of semiparametric mean residual life models where some effects may be time varying and some may be constant over time in the presence of right censoring we use the inverse probability of censoring weighting approach and develop inference procedures for estimating the model parameters in addition we provide graphical and numerical methods for model checking and tests for examining whether or not the covariate effects vary with time asymptotic and finite sample properties of the proposed estimators are established and the approach is applied to real life datasets collected from clinical trials copyright 2012 oxford university press

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

on causal estimation from bandlimited stationary sequences this paper considers the problem of estimating a stationary sequence y from the observation of a stationary correlated sequence x by means of a causal linear filter thereby it is assumed that the spectral density x of x vanishes on a subset of the unit circle of positive lebesgue measure such that the classical derivation of the estimation filter based on the spectral factorization of x can not be applied the paper derives the transfer function of such an estimation filter discusses its stability behavior and applies the result to the causal reconstruction of deterministic signals from its samples

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

chromosome image enhancement using multiscale differential operators chromosome banding patterns are very important features for karyotyping based on which cytogenetic diagnosis procedures are conducted due to cell culture staining and imaging conditions image enhancement is a desirable preprocessing step before performing chromosome classification in this paper we apply a family of differential wavelet transforms wang and lee 1998 wang 1999 for this purpose the proposed differential filters facilitate the extraction of multiscale geometric features of chromosome images moreover desirable fast computation can be realized we study the behavior of both banding edge pattern and noise in the wavelet transform domain based on the fact that image geometrical features like edges are correlated across different scales in the wavelet representation a multiscale point wise product mpp is used to characterize the correlation of the image features in the scale space a novel algorithm is proposed for the enhancement of banding patterns in a chromosome image in order to compare objectively the performance of the proposed algorithm against several existing image enhancement techniques a quantitative criteria the contrast improvement ratio cir has been adopted to evaluate the enhancement results the experimental results indicate that the proposed method consistently outperforms existing techniques in terms of the cir measure as well as in visual effect the effect of enhancement on cytogenetic diagnosis is further investigated by classification tests conducted prior to and following the chromosome image enhancement in comparison with conventional techniques the proposed method leads to better classification results thereby benefiting the subsequent cytogenetic diagnosis

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed