estimation of the ratio of scale parameters in the two sample problem with arbitrary right censorship abstract a two sample version of the cramer von mises statistic for right censored observations is used to obtain an estimator of the ratio of scale parameters of two distributions it is shown that this estimator is consistent for small samples simulations are performed which show the superiority of the estimator over the maximum likelihood estimator for exponential distributions author

an existence result for non smooth vibro impact problems we are interested in mechanical systems with a finite number of degrees of freedom submitted to frictionless unilateral constraints we consider the case of a convex non smooth set of admissible positions given by k q mathbb r d phi alpha q geq 0 1 leq alpha leq v v geq 1 and we assume inelastic shocks at impacts we propose a time discretization of the measure differential inclusion which describes the dynamics and we prove the convergence of the approximate solutions to a limit motion which satisfies the constraints moreover if the geometric properties ensuring continuity on data hold at the limit we show that the transmission of velocities at impacts follows the inelastic shocks rule

a two sample comparison for multiple ordered event data summary a longitudinal study is conducted to compare the process of a particular disease between two groups the process of the disease is monitored according to which of several ordered events occur in the paper the sojourn time between two successive events is considered as the outcome of interest the group effects on the sojourn times of the multiple events are parameterized by scale changes in a semiparametric accelerated failure time model where the dependence structure among the multivariate sojourn times is unspecified suppose that the sojourn times are subject to dependent censoring and the censoring times are observed for all subjects a log rank type estimating approach by rescaling the sojourn times and the dependent censoring times into the same distribution is constructed to estimate the group effects and the corresponding estimators are consistent and asymptotically normal without the dependent censoring the independent censoring times in general are not available for the uncensored data in order to complete the censoring information pseudo censoring times are generated from the corresponding nonparametrically estimated survival function in each group and we can still obtained unbiased estimating functions for the group effects a real application and a simulation study are conducted to illustrate the proposed methods

time stepping approximation of rigid body dynamics with perfect unilateral constraints i the inelastic impact case we consider a discrete mechanical system with a non trivial mass matrix subjected to perfect unilateral constraints described by the geometrical inequalities f alpha q geqq 0 alpha in 1 dots nu nu geqq 1 we assume that the transmission of the velocities at impact is governed by newton s law with a coefficient of restitution e 0 so that the impact is inelastic we propose a time discretization of the second order differential inclusion describing the dynamics which generalizes the scheme proposed in paoli j differ equ 211 247 281 2005 and for any admissible data we prove the convergence of approximate motions to a solution of the initial value problem

distribution free methods of estimating location difference with censored paired data abstract nonparametric point and interval estimators of location difference in matched pairs data with arbitrary right censorship are proposed based on a generalized gehan gilbert test wei 1980 the point estimator is shown to be asymptotically normal and strongly consistent the limits of the corresponding interval estimator are readily computable an example is also provided to illustrate the techniques to problems in survival data analysis

bounds on net survival probabilities for dependent competing risks bounds on the marginal survival function based on data from a competing risks experiment are obtained these bounds require an investigator to specify a range of possible concordances for the times to occurrences of the competing risks these bounds are tighter than those of peterson 1976 proceedings of the national academy of sciences 73 11 13

on finite element approximation in the l norm of variational inequalities we are interested in the approximation in thel norm of variational inequalities with non linear operators and somewhat irregular obstacles we show that the order of convergence will be the same as that of the equation associated with the non linear operator if the discrete maximum principle is verified

dynamical systems with active singularities of elastic type a modeling and controller synthesis framework a new class of systems characterized by admitting impulsive control action within their singular motion phases such as dimension changes state discontinuities and other irregularities is introduced this class termed dynamical systems with active or controlled singularities encompasses various applications with sensing and or actuation ultra fast in comparison with the natural system time scale including mechanisms with impact induced motion power and sensor networks under faults fast positioning devices smart skins and switching electronic circuits the present work focuses on systems with impact type singularities induced through system interaction with controlled or active state constraints the latter are assumed to be characterized by parameter dependent elastic type constraint violation that vanishes in the limit as the parameter value tends to infinity a physically well justified representation of this class of systems is proposed but found to be not well suited for controller synthesis in the singular phase to address this problem two equations are derived one describing controlled rigid impacts in auxiliary stretched time and compatible with the regular control design techniques termed controlled infinitesimal dynamics equation and another incorporating controlled impact dynamics in the infinitesimal form in terms of the shift operator along the trajectories of the first equation termed the limit model the latter is demonstrated to generate a unique isolated discontinuous system motion i e to provide a tight and well behaved description of the collision with rigid constraint it is then shown that the corresponding paths generated by the original physically based and the limit representations can be made arbitrarily close to each other uniformly except possibly in the vicinities of the jump points by the appropriate choice of the value of the constraint violation parameter this is shown to permit enforcing for sufficiently large values of the parameter the desired limit system behavior onto the original system by simply taking the control signals found through the limit representation time rescaling them and inserting the resulting signals directly into the original system these features show that the procedure developed in fact provides a well posed controller synthesis framework for the class of systems considered using this framework a ball racket rotationally controlled impact representation is developed and on its basis a singular phase control signal in the form of racket rotation velocity is designed demonstrating that the soft racket provides the specified bounce off angle increment under a noticeably lower racket rotation velocity and a longer rotation phase than the hard racket

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

nonparametric estimation for a scale change with censored observations abstract nonparametric point and interval estimators of the ratio of two scale parameters are given for arbitrarily right censored data based on the idea of hodges and lehmann 1963 these estimators are defined in terms of rank test statistics for testing the equality of two survival distributions the asymptotic properties and efficiencies of estimators corresponding to the tests studied by gill 1980 are investigated

nonparametric inference in factorial designs with censored data a method is proposed for testing the hypotheses of no main effects and no interaction in factorial designs with several observations per cell the method uses the fact that these hypotheses can be expressed in terms of a vector of contrasts it is based on the observation that nonparametric estimation of these contrasts is no more difficult than estimation of the location difference in the two sample problem to implement the method with censored data a new extension of the hodges lehmann estimator is proposed the estimator is simple to compute and its variance is easily evaluated a simulation study examines the performance of the proposed estimation and testing method in the context of a two by two design and a real data set from a three way layout with heavy censoring is analyzed

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

quantile regression for doubly censored data double censoring often occurs in registry studies when left censoring is present in addition to right censoring in this work we propose a new analysis strategy for such doubly censored data by adopting a quantile regression model we develop computationally simple estimation and inference procedures by appropriately using the embedded martingale structure asymptotic properties including the uniform consistency and weak convergence are established for the resulting estimators moreover we propose conditional inference to address the special identifiability issues attached to the double censoring setting we further show that the proposed method can be readily adapted to handle left truncation simulation studies demonstrate good finite sample performance of the new inferential procedures the practical utility of our method is illustrated by an analysis of the onset of the most commonly investigated respiratory infection pseudomonas aeruginosa in children with cystic fibrosis through the use of the u s cystic fibrosis registry

randomization based interval estimation in randomized clinical trials randomization based interval estimation takes into account the particular randomization procedure in the analysis and preserves the confidence level even in the presence of heterogeneity it is distinguished from population based confidence intervals with respect to three aspects definition computation and interpretation the article contributes to the discussion of how to construct a confidence interval for a treatment difference from randomization tests when analyzing data from randomized clinical trials the discussion covers i the definition of a confidence interval for a treatment difference in randomization based inference ii computational algorithms for efficiently approximating the endpoints of an interval and iii evaluation of statistical properties ie coverage probability and interval length of randomization based and population based confidence intervals under a selected set of randomization procedures when assuming heterogeneity in patient outcomes the method is illustrated with a case study

comparing two failure time distributions in the presence of dependent censoring summary in a randomised clinical trial to compare two groups of patients suppose that the time to disease occurrence the major response variable may be subject to dependent censoring by death or selective patient withdrawal while the patients who have reached the disease endpoint are followed for their secondary endpoints or survival information to adjust for the dependent censoring in assessing the group difference in disease occurrence we assume that on a logarithmic scale the times to disease occurrence and dependent censoring for the two groups satisfy a bivariate location shift model with a completely unspecified underlying distribution rank based procedures are constructed for making inferences about the location shift parameter model checking techniques are also developed numerical studies show that the proposed methods are appropriate for practical use an illustration with data taken from a recent aids clinical trial is provided

nonparametric analysis of an accelerated failure time model summary survival distributions can be characterized by and compared through their hazard functions tests using a proportional hazards model have good power if the two hazards do not cross but without time dependent covariates can have low power if they do the method contained herein is designed to provide a complement to the proportional hazards model differences in survival distributions are parameterized by a scale change and the log rank statistic is used to generate an estimate of the change and a confidence interval based test this approach is fully efficient for the weibull family with no censoring in general it compares favourably with the proportional hazards approach although neither method dominates

a general estimator of the treatment effect when the data are heavily censored summary a generalized hodges lehmann type estimator for the treatment effect in the twosample problem with right censoring is proposed based on an inverse quantile type idea using truncated versions of the kaplan meier estimators over the subspace where they are consistent its strong consistency and asymptotic normality can be obtained under no conditions on the uninformative censorings and the resulting variance is easily estimable from the data in simulation studies the proposed estimator is superior to existing procedures in the presence of heavy unequal censoring

a fixed point approximation method for some noncoercive variational problems abstract this paper deals with the finite element approximation of some variational problems namely linear elliptic boundary value problems variational inequalities and quasi variational inequalities with noncoercive operators to prove optimal l error estimates we introduce a simple and direct argument combining continuous piecewise linear finite elements with the banach fixedpoint theorem

penalty approximation for non smooth constraints in vibroimpact abstract we examine the penalty approximation of the free motion of a material point in an angular domain we choose an over damped penalty approximation and we prove that if the first impact point is not at the vertex then the limit of the approximation exists and is described by moreau s rule for inelastic impacts the proofs rely on validated asymptotics and use some classical tools of the theory of dynamical systems

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

nonparametric methods for analyzing incomplete nondecreasing repeated measurements in comparing the effectiveness of two treatments suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject a class of univariate one sided global asymptotically distribution free tests is proposed to test the equality of the two treatments the test procedures allow different patterns of missing observations in the two groups to be compared although the missing data mechanism is required to be independent of the observations in each treatment group test based point and interval estimators of the global treatment difference are given multiple inference procedures are also provided to examine the time trend of treatment differences over the entire study the proposed methods are illustrated by an example from a bladder cancer study

the noncoercive quasi variational inequalities related to impulse control problems abstract this paper deals with the numerical analysis of noncoercive quasi variational inequalities of impulse control problems optimally l error estimates are derived using qualitative properties of both the continuous and finite element approximation solutions and the notion of subsolutions

estimations in homoscedastic linear regression models with censored data an empirical process approach pertaining to the estimating equations proposed by tsiatis based on the linear rank test we show the existence of local confounding between the baseline hazard function and the covariates due to the local confounding an estimating equation in tsiatis family with a larger time point of truncation could contain less information about the regression parameter than the estimating equation with a smaller time point of truncation this phenomenon further indicates significant loss of efficiency of tsiatis estimating equations as well as the power loss of log rank type tests when the baseline hazard function goes up and down along the time scale to take care of this local confounding without using nonparametric estimates of the derivative of the baseline hazard function we propose the empirical process approach epa based on an empirical process constructed from tsiatis log rank estimating equation by varying its truncating time point the epa will provide very tractable estimations of the regression parameters as well as pearson s chi squared statistics for testing the model s assumptions specifically the performance of the epa estimator is shown to be very close to the best estimator in tsiatis family

optimal control problems in hybrid systems with active singularities abstract the optimal control problem for systems with controlled unilateral phase constraints is considered the definition of the generalized solutions is introduced the transformation method for the original optimal control problem within the class of generalized solution to a standard optimal control problem is proposed and the necessary optimality conditions are found