spatiospectral concentration on a sphere we pose and solve the analogue of slepian s time frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere or alternatively of strictly spacelimited functions that are optimally concentrated in the spherical harmonic domain such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications as well as in medical imaging computer science cosmology and numerical analysis the spherical slepian functions can be found by solving either an algebraic eigenvalue problem in the spectral domain or a fredholm integral equation in the spatial domain the associated eigenvalues are a measure of the spatiospectral concentration when the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a sturm liouville operator this enables the eigenfunctions to be computed extremely accurately and efficiently even when their area bandwidth product or shannon number is large in the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth the spherical concentration problem reduces to its planar equivalent which exhibits self similarity when the shannon number is kept invariant

sufficiency and duality in nonsmooth multiobjective optimization involving generalized f α π d type i functions in this paper new classes of generalized f a p d type i functions are introduced for a nonsmooth multiobjective programming problem based upon these generalized functions sufficient optimality conditions are established weak strong and strict converse duality theorems are also derived for wolfe and mond weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems

generalized morse wavelets this paper examines the class of generalized morse wavelets which are eigenfunction wavelets suitable for use in time varying spectrum estimation via averaging of time scale eigenscalograms generalized morse wavelets of order k the corresponding eigenvalue order depend on a doublet of parameters spl beta spl gamma we extend results derived for the special case spl beta spl gamma 1 and include a proof of the resolution of identity the wavelets are easy to compute using the discrete fourier transform dft and for spl beta spl gamma 2m 2 can be computed exactly a correction of a previously published eigenvalue formula is given this shows that for spl gamma 1 generalized morse wavelets can outperform the hermites in energy concentration contrary to a conclusion based on the spl gamma 1 case for complex signals scalogram analyses must be carried out using both the analytic and anti analytic complex wavelets or odd and even real wavelets whereas for real signals the analytic complex wavelet is sufficient

nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data the purpose of this paper is to derive confidence bands for quantile functions using a nonparametric likelihood ratio approach the method is easy to implement and has several appealing properties it applies to right censored and left truncated data and it does not involve density estimation or even require the existence of a density previous approaches e g bootstrap have imposed smoothness conditions on the density the performance of the proposed method is investigated in a monte carlo study and an application to real data is given

bivariate instantaneous frequency and bandwidth the generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived these are uniquely defined whether the signal is represented as a pair of real valued signals or as one analytic and one anti analytic signal a nonstationary but oscillatory bivariate signal has a natural representation as an ellipse whose properties evolve in time and this representation provides a simple geometric interpretation for the bivariate instantaneous moments the bivariate bandwidth is shown to consist of three terms measuring the degree of instability of the time varying ellipse amplitude modulation with fixed eccentricity eccentricity modulation and orientation modulation or precession an application to the analysis of data from a free drifting oceanographic float is presented and discussed

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

on generalized pseudoconvex functions abstract in this paper the concept of pseudoconvexity is generalized in three different ways and the interrelation of them is investigated for constrained optimization sufficiency of kuhn tucker optimality conditions is derived under some assumptions which do not require the generalized pseudoconvexity of the lagrangian itself

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

efficiency through variational like inequalities with lipschitz functions in this work first we introduce several notions of invexity and pseudoinvexity for a locally lipschitz function by means of the generalized jacobian we study relationships between these concepts in particular the implications between preinvexity and invexity next we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite dimensional non necessarily pareto vector optimization problems with locally lipschitz objective functions through solutions of vector variational like inequality problems these conditions are stated via the generalized jacobian and under pseudoinvexity hypotheses and they show that a vector optimization problem can be reformulated as a vector variational like inequality problem this work extends and improves several previous papers where the objective function of the vector optimization problem is assumed to be differentiable or being locally lipschitz the authors consider the componentwise subdifferential based on the clarke s generalized gradients of the components of the objective function throughout the paper some simple examples are given in order to illustrate the main concepts and results

a resampling method based on pivotal estimating functions summary suppose that under a semiparametric model setting one is interested in drawing inferences about a finite dimensi onal parameter vector based on an estimating function generally a consistent point estimator j for 0 the true value for j can be easily obtained by finding a root of the corresponding estimating equation to estimate the variance of ft however may involve complicated and subjective nonparametric functional estimates in this paper a general and simple resampling method for inferences about js0 based on pivotal estimating functions is proposed the new procedure is illustrated with the quantile and rank regression models for both cases our proposal can be easily and efficiently implemented with existing statistical software

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

multiple multidimensional morse wavelets this paper defines a set of operators that localize a radial image in space and radial frequency simultaneously the eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found the eigenfunctions are optimally concentrated over a given region of radial space and scale space defined via a triplet of parameters analytic forms for the energy concentration of the functions over the region are given the radial function localization operator can be generalised to an operator localizing any l2 ropf2 function it is demonstrated that the latter operator given an appropriate choice of localization region approximately has the same radial eigenfunctions as the radial operator based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude orientation and phase structure of locally oscillatory signals the full set of quaternionic wavelet functions are component by component orthogonal their statistical properties are tractable and forms for the variability of the estimators of the local phase and orientation are given as well as the local energy of the image by averaging estimators across wavelets a substantial reduction in the variance is achieved

element analysis a wavelet based method for analysing time localized events in noisy time series a method is derived for the quantitative analysis of signals that are composed of superpositions of isolated time localized events here these events are taken to be well represented as rescaled and phase rotated versions of generalized morse wavelets a broad family of continuous analytic functions analysing a signal composed of replicates of such a function using another morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima the distribution of events in general power law noise is determined in order to establish significance based on an expected false detection rate finally an expression for an event s region of influence within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events signals can then be reconstructed based on a small number of isolated points on the time scale plane this method termed element analysis is applied to the identification of long lived eddy structures in ocean currents as observed by along track measurements of sea surface elevation from satellite altimetry

a small sample study of the stepp approach to assessing treatment covariate interactions in survival data a new intuitive method has recently been proposed to explore treatment covariate interactions in survival data arising from two treatment arms of a clinical trial the method is based on constructing overlapping subpopulations of patients with respect to one or more covariates of interest and in observing the pattern of the treatment effects estimated across the subpopulations a plot of these treatment effects is called a subpopulation treatment effect pattern plot here we explore the small sample characteristics of the asymptotic results associated with the method and develop an alternative permutation distribution based approach to inference that should be preferred for smaller sample sizes we then describe an extension of the method to the case in which the pattern of estimated quantiles of survivor functions is of interest

a note on invex problems with nonnegative variable we provide sufficient optimality conditions involving invexity for mathematical programming problems with nonnegative variable we also show that upon certain assumptions on the scaling function these problems are convex transformable hence certain associated convex problems should be solved some applications are shown

estimating the median survival time summary two methods are proposed for setting confidence intervals for the median survival time it is shown how these are related to bootstrap methods for censored data and some numerical comparisons are presented in many medical follow up studies the survival experience of a group of patients is summarized by the product limit or kaplan meier estimate of the survival distribution this may follow an analysis of the relation between survival time and some explanatory variables by for example the proportional hazards model the median of the estimated survival distribution is sometimes a convenient summary statistic and may be preferred to the mean because it is less sensitive to long tails in the estimated survival distribution this paper is concerned with estimating the distribution of the estimated median and providing confidence intervals for the true median two methods are considered in 2 they are both based in different ways on generalizations of the solution for the uncensored case these methods turn out to be connected to two ways of extending bootstrap methods for use with censored data this connexion is discussed in 3 thinking about extensions of the bootstrap to censored data highlights the need for careful consideration of the role of the censoring mechanism and how it should be incorporated into the data analysis section 4 provides some examples and monte carlo simulations the work is closely related to that of efron 1981 and emerson 1981

analysis of modulated multivariate oscillations the concept of a common modulated oscillation spanning multiple time series is formalized a method for the recovery of such a signal from potentially noisy observations is proposed and the time varying bias properties of the recovery method are derived the method an extension of wavelet ridge analysis to the multivariate case identifies the common oscillation by seeking at each point in time a frequency for which a bandpassed version of the signal obtains a local maximum in power the lowest order bias is shown to involve a quantity termed the instantaneous curvature which measures the strength of local quadratic modulation of the signal after demodulation by the common oscillation frequency the bias can be made to be small if the analysis filter or wavelet can be chosen such that the signal s instantaneous curvature changes little over the filter time scale an application is presented to the detection of vortex motions in a set of freely drifting oceanographic instruments tracking the ocean currents

group sequential tests with censored survival data adjusting for covariates summary group sequential tests for the analysis of survival data that compare two treatments and allow for the adjustment of other concomitant variables are discussed these methods allow early termination of a study if large treatment differences occur based on simulation results we compare the operating characteristics of these adjusted tests with the unadjusted sequentially computed log rank test

generalized morse wavelets as a superfamily of analytic wavelets the generalized morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets subsuming eight apparently distinct types of analysis filters into a single common form this superfamily of analytic wavelets provides a framework for systematically investigating wavelet suitability for various applications in addition to a parameter controlling the time domain duration or fourier domain bandwidth the wavelet shape with fixed bandwidth may be modified by varying a second parameter called for integer values of the most symmetric most nearly gaussian and generally most time frequency concentrated member of the superfamily is found to occur for 3 these wavelets known as airy wavelets capture the essential idea of popular morlet wavelet while avoiding its deficiencies they may be recommended as an ideal starting point for general purpose use

sufficiency and duality in nondifferentiable multiobjective programming involving generalized type i functions abstract recently hachimi and aghezzaf defined generalized f d type i functions a new class of functions that unifies several concepts of generalized type i functions in this paper the generalized f d type i functions are extended to nondifferentiable functions by utilizing the new concepts we obtain several sufficient optimality conditions and prove mixed type and mond weir type duality results for the nondifferentiable multiobjective programming problem

interim analyses based on median survival times summary for a typical two arm survival study analyses are usually performed periodically to evaluate for example the treatment difference in this paper we propose to use differences or ratios of estimated median survival times repeatedly during a study to evaluate the relative merit of two treatment groups this new procedure provides quantitative assessments of the treatment difference and is completely model free our method is illustrated with a recent aids clinical study which evaluates the efficacy of a reduced dose of azt

nonsmooth invex functions and sufficient optimality conditions in this paper the various definitions of nonsmooth invex functions are gathered in a general scheme by means of the concept of k directional derivative characterizations of nonsmooth k invexity are derived as well as results concerning constrained optimization without any assumption of convexity of the k directional derivatives

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

nondifferentiable multiobjective programming under generalized d univexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex strong pseudoinvex weak quasi invex weak pseudoinvex and strong quasi invex functions in aghezzaf and hachimi numer funct anal optim 22 2001 775 d invex functions in antczak europ j oper res 137 2002 28 and univex functions in bector et al univex functions and univex nonlinear programming proc admin sci assoc canada 1992 p 115 by utilizing the new concepts we derive a karush kuhn tucker sufficient optimality condition and establish mond weir type and general mond weir type duality results for the nondifferentiable multiobjective programming problem

repeated confidence intervals for the median survival time summary we describe methods for the construction of a confidence interval for median survival time based on right censored data these methods are extended to the construction of repeated confidence intervals for the median based on accumulating data here the overall probability that all intervals contain the true median is guaranteed at a fixed level the use of repeated confidence intervals for median survival time in post marketing surveillance is discussed a confidence interval for median survival time provides a useful summary of the survival experience of a group of patients if confidence intervals are calculated repeatedly as data accumulates the probability that at least one interval fails to contain the median may be much higher than the error rate for a single interval and if these confidence intervals are used in a decision making process the probability of an incorrect decision increases accordingly jennison turnbull 1984 have proposed methods for calculating repeated confidence intervals appropriate to such situations similar ideas have also been discussed by lai 1984 in 2 we propose a new form of single sample nonparametric confidence interval this interval has asymptotically correct coverage probability and monte carlo simulations suggest it is superior to its competitors for small sample sizes repeated confidence intervals for the median are presented in 3 and their stnall sample size performance is assessed by monte carlo simulation an example of their use is given in 4 all the methods considered can easily be modified to give confidence intervals for other quantiles or for the survival probability at a fixed time

mse estimates for multitaper spectral estimation and off grid compressive sensing we obtain estimates for the mean squared error mse for the multitaper spectral estimator and certain compressive acquisition methods for multi band signals we confirm a fact discovered by thomson spectrum estimation and harmonic analysis proc ieee 1982 assuming bandwidth w and n time domain observations the average of the square of the first k lfloor 2nw rfloor slepian functions approaches as k grows an ideal bandpass kernel for the interval w w we provide an analytic proof of this fact and measure the corresponding rate of convergence in l 1 norm this validates a heuristic approximation used to control the mse of the multitaper estimator the estimates have also consequences for the method of compressive acquisition of multi band signals introduced by davenport and wakin giving mse approximation bounds for the dictionary formed by modulation of the critical number of prolates

multi objective infinite programming using the theory of abstract optimization problems in infinite dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi objective infinite programming problem sufficient conditions are given under invexity assumptions we generalize the notion of kkt invexity for the multi objective infinite problem and show that this notion is a necessary and sufficient condition for every vector kkt solution to be a weakly efficient solution moreover we develop a theorem of the alternative useful for proving some of our results

generalized proper efficiency and duality for a class of nondifferentiable multiobjective variational problems withv invexity abstract a mond weir type dual for a class of nondifferentiable multiobjective variational problems in which every component of the objective function contains a term involving the square root of a certain positive semidefinite quadratic form is considered and various duality results viz weak strong and converse duality theorems are developed for conditionally properly efficient solutions these results are obtained under v invexity assumptions and its generalizations on objective and constraint functions this work extends many results on variational problems established earlier

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

generalized pseudoconvex functions and multiobjective programming abstract in a recent work cited in the introduction a concept of generalized pseudoconvexity was used to obtain optimality results in nonlinear programming in the present work we give sufficient optimality conditions in the context of the multiobjective programming problem under the assumptions of generalized pseudoconvexity on objective and constraint functions an application of such a result is given for fractional programming also

higher order properties of analytic wavelets the influence of higher order wavelet properties on the analytic wavelet transform behavior is investigated and wavelet functions offering advantageous performance are identified this is accomplished through detailed investigation of the generalized morse wavelets a two parameter family of exactly analytic continuous wavelets the degree of time frequency localization the existence of a mapping between scale and frequency and the bias involved in estimating properties of modulated oscillatory signals are proposed as important considerations wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain as quantified by the third central moments a particular subset of the generalized morse wavelets recognized as deriving from an inhomogeneous airy function emerge as having particularly desirable properties these ldquoairy waveletsrdquo substantially outperform the only approximately analytic morlet wavelets for high time localization special cases of the generalized morse wavelets are examined revealing a broad range of behaviors which can be matched to the characteristics of a signal

on the analytic wavelet transform an exact and general expression for the analytic wavelet transform of a real valued signal is constructed resolving the time dependent effects of nonnegligible amplitude and frequency modulation the analytic signal is first locally represented as a modulated oscillation demodulated by its own instantaneous frequency and then taylor expanded at each point in time the terms in this expansion called the instantaneous modulation functions are time varying functions which quantify at increasingly higher orders the local departures of the signal from a uniform sinusoidal oscillation closed form expressions for these functions are found in terms of bell polynomials and derivatives of the signal s instantaneous frequency and bandwidth the analytic wavelet transform is shown to depend upon the interaction between the signal s instantaneous modulation functions and frequency domain derivatives of the wavelet inducing a hierarchy of departures of the transform away from a perfect representation of the signal the form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal in which case our expressions simplify considerably one may then quantify the time varying bias associated with signal estimation via wavelet ridge analysis and choose wavelets to minimize this bias

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

a statistical analysis of morse wavelet coherence wavelet coherence computed from two time series has been widely applied in hypothesis testing situations but has proven resistant to analytic study with resort to simulations for statistical properties as part of the null hypothesis being tested such simulations invariably assume joint stationarity of the series if estimated using multiple orthogonal morse wavelets wavelet coherence is in fact amenable to statistical study since the wavelets are complex valued we consider the case of wavelet coherence calculated from discrete time complex valued and stationary time series under gaussianity the goodman distribution is for large samples appropriate for wavelet coherence the true wavelet coherence value is identified in terms of its frequency domain equivalent theoretical results are illustrated and verified via simulations

two sample quantile tests under general conditions summary a simple nonparametric two sample test for equality of a given collection of quantiles is developed which can be applied to a variety of empirical distribution functions including the kaplan meier estimator a self consistent estimator for doubly censored data and an estimator for repeated measures data the null hypothesis tested is that the quantiles are equal but other aspects of the distributions may diver between the two samples this procedure can also be applied to quantile testing in group sequential clinical trials with staggered patient entry a simple simulation study demonstrates that the moderate sample size properties of this procedure are reasonable

comparison of median survival times with adjustment for covariates brookmeyer and crowley derived a non parametric confidence interval for the median survival time of a homogeneous population by inverting a generalization of the sign test for censored data the 1 alpha confidence interval for the median is essentially the set of all values t such that the kaplan meier estimate of the survival curve at time t does not differ significantly from one half at the two sided alpha level su and wei extended this approach to the two sample problem and derived a confidence interval for the difference in median survival times based on the kaplan meier estimates of the individual survival curves and a minimum dispersion test statistic here i incorporate covariates into the analysis by assuming a proportional hazards model for the covariate effects while leaving the two underlying survival curves virtually unconstrained i generate a simultaneous confidence region for the two median survival times adjusted to any selected value z of the covariate vector using a test based approach analogous to brookmeyer and crowley s for the one sample case this region is in turn used to derive a confidence interval for the difference in median survival times between the two treatment groups at the selected value of z employment of a procedure suggested by aitchison sets the level of the simultaneous region to a value that should yield at least approximately the desired confidence coefficient for the difference in medians simulation studies indicate that the method provides reasonably accurate coverage probabilities