estimating the city block two dimensional scaling model with simulated annealing abstract two dimensional scaling is a technique to represent dissimilarities among n objects in a two dimensional space so that the interpoint distances can best approximate the observed dissimilarities between pairs of objects the coordinates are found by minimizing the stress function it is well known that the number of local minima of the stress function increase with n in this paper we present a new approach for finding the global minimum of the stress function for the city block two dimensional scaling model the proposed method consists of two stages while the least square regression is used to obtain the local minimum of the stress function in stage 1 simulated annealing is applied to search for the global minimum in stage 2 real and simulated examples n 30 50 70 are used to assess the performance of the proposed algorithm results show that the coordinates can be quite accurately recovered by the proposed method

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

a new heterogeneous multidimensional unfolding procedure a variety of joint space multidimensional scaling mds methods have been utilized for the spatial analysis of two or three way dominance data involving subjects preferences choices considerations intentions etc so as to provide a parsimonious spatial depiction of the underlying relevant dimensions attributes stimuli and or subjects utility structures in the same joint space representation we demonstrate that care must be taken with respect to a key assumption in existent joint space mds models such that all estimated dimensions are utilized by each and every subject in the sample as this assumption can lead to serious distortions with respect to the derived joint spaces we develop a new bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three way dominance data a consumer psychology application regarding the preference for over the counter otc analgesics is provided we conclude by discussing the practical implications of the results as well as directions for future research

minimum energy filtering for attitude estimation in this work we study minimum energy filtering for attitude kinematics with vectorial measurements using mortensen s approach the exact form of a minimum energy attitude observer is derived and is shown to depend on the hessian of the value function of an associated optimal control problem a suitably chosen matrix representation of the hessian operator leads to a riccati equation that approximates a minimum energy attitude filter an extended version of the proposed approximate filter is included for a situation where there is slowly time varying bias in the gyro measurements a unit quaternion version of the proposed filter is derived and shown to outperform the multiplicative extended kalman filter mekf for situations with large initialization errors or large measurement errors

local multidimensional scaling for nonlinear dimension reduction graph drawing and proximity analysis in the past decade there has been a resurgence of interest in nonlinear dimension reduction among new proposals are local linear embedding isomap and kernel principal components analysis which all construct global low dimensional embeddings from local affine or metric information we introduce a competing method called local multidimensional scaling lmds like lle isomap and kpca lmds constructs its global embedding from local information but it uses instead a combination of mds and force directed graph drawing we apply the force paradigm to create localized versions of mds stress functions with a tuning parameter to adjust the strength of nonlocal repulsive forces we solve the problem of tuning parameter selection with a meta criterion that measures how well the sets of k nearest neighbors agree between the data and the embedding tuned lmds seems to be able to outperform mds pca lle isomap and kpca as illustrated with two well known image datasets the meta criterion can also be

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

attitude observer on the special orthogonal group with earth velocity estimation abstract this paper proposes a new nonlinear attitude observer based on high grade rate gyros and single body fixed vector measurements of a constant inertial vector in contrast with typical solutions that require two of these vectors the structure is cascaded where in the first block a vector that is related to the angular velocity of the earth is estimated and in the second block the attitude itself is obtained the attitude is directly estimated on the special orthogonal group and the estimation error is shown to converge to zero with a region of convergence that is best described as semi global with local exponential convergence simulation results illustrate the achievable performance of the proposed solution and the robustness to sensor noise

latent space approaches to social network analysis network models are widely used to represent relational information among interacting units in studies of social networks recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors we develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved social space we make inference for the social space within maximum likelihood and bayesian frameworks and propose markov chain monte carlo procedures for making inference on latent positions and the effects of observed covariates we present analyses of three standard datasets from the social networks literature and compare the method to an alternative stochastic blockmodeling approach in addition to improving on model fit for these datasets our method provides a visual and interpretable model based spatial representation of social relationships and improv

methods for comparing cumulative hazard functions in a semi proportional hazard model graphical methods based on the analysis of differences between log cumulative hazard functions are considered for a two group semi proportional hazard model which allows for interaction between treatments and covariates confidence procedures and test statistics that can be used to test for interaction and for main effects are developed their use is illustrated by applying them to the analysis of kidney transplant data from the university of california san francisco

approximate case influence for the proportional hazards regression model with censored data a method is presented for approximating the influence of individual cases upon regression coefficient estimates obtained from the cox proportional hazards model observations can thus be identified which may greatly influence statistical inferences regarding the effects of prognostic factors upon survival time an example from a cancer clinical trial is given

pose estimation using line based dynamic vision and inertial sensors an observer problem from a computer vision application is studied rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation orientation estimation is formulated as an observer problem with implicit output where the states evolve on so 3 a careful observability study reveals interesting group theoretic structures tied to the underlying system structure a locally convergent observer where the states evolve on so 3 is proposed and numerical estimates of the domain of attraction is given further it is shown that given convergent orientation estimates position estimation can be formulated as a linear implicit output problem from an applications perspective it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates this is consistent with real time constraints due to the complementary characteristics of the sensors which are fused in a multirate way

singular value decomposition in additive multiplicative and logistic forms singular value decomposition svd is widely used in data processing reduction and visualization applied to a positive matrix the regular additive svd by the first several dual vectors can yield irrelevant negative elements of the approximated matrix we consider a multiplicative svd modification that corresponds to minimizing the relative errors and produces always positive matrices at any approximation step another logistic svd modification can be used for decomposition of the matrices of proportions when a regular svd can yield the elements beyond the zero one range while the modified svd decomposition produces all the elements within the correct range at any step of approximation several additional modifications of matrix approximation are also considered

global optimal attitude estimation using uncertainty ellipsoids a deterministic attitude estimation problem for a rigid body in a potential field with bounded attitude and angular velocity measurement errors is considered an attitude estimation algorithm that globally minimizes the attitude estimation error is obtained assuming that the initial attitude the initial angular velocity and measurement noise lie within given ellipsoidal bounds an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained the center of the uncertainty ellipsoid provides point estimates and the size of the uncertainty ellipsoid measures the accuracy of the estimates the point estimates and the uncertainty ellipsoids are propagated using a lie group variational integrator and its linearization respectively the attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized

probabilistic non linear principal component analysis with gaussian process latent variable models summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure in this paper we provide an overview of some existing techniques for discovering such embeddings we then introduce a novel probabilistic interpretation of principal component analysis pca that we term dual probabilistic pca dppca the dppca model has the additional advantage that the linear mappings from the embedded space can easily be non linearised through gaussian processes we refer to this model as a gaussian process latent variable model gp lvm through analysis of the gp lvm objective function we relate the model to popular spectral techniques such as kernel pca and multidimensional scaling we then review a practical algorithm for gp lvms in the context of large data sets and develop it to also handle discrete valued data and missing attributes we demonstrate the model on a range of real world and artificially generated data sets

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

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

adaptive compensation of gyro bias in rigid body attitude estimation using a single vector measurement the presence of bias in measurement of rate gyros is a performance limiting factor for satellite attitude determination systems gyro bias is usually handled by kalman filtering methods which are mostly based on linearization approaches and lack global convergence properties on the other hand the existing asymptotically convergent nonlinear observers take into account the gyro bias only when multiple vector measurements are available we present an asymptotically convergent attitude estimator which uses only one vector measurement and a rate gyro whose output is contaminated with an unknown and constant bias the effect of unknown bias is compensated by means of a parameter adaptation law an explicit condition on the reference vectors for ensuring observability of the system is introduced a realistic simulation is presented to illustrate the performance of the proposed attitude estimator in face of significant bias in gyro measurement and when a magnetometer is used to provide the single vector measurement

attitude estimation using biased gyro and vector measurements with time varying reference vectors we present two results on attitude estimation using vector and rate gyro measurements the first result concerns an observer previously presented by hamel mahony and pflimlin with proven stability results when i the reference vectors are stationary or ii the gyro measurements are unbiased we prove semiglobal stability without either of these assumptions when a parameter projection is added and convergence from all initial attitudes when using a resetting strategy the second result is an algorithm for estimation of bias in the body fixed vector measurements which is analyzed in combination with the attitude and gyro bias observer

the unobserved heterogeneity distribution in duration analysis jabbringgfeweb vu nl gberggfeweb vu nl summary in a large class of hazard models with proportional unobserved heterogeneity the distribution of the heterogeneity among survivors converges to a gamma distribution this convergence is often rapid we derive this result as a general result for exponential mixtures and explore its implications for the specification and empirical analysis of univariate and multivariate duration models

a bayesian vector multidimensional scaling procedure for the analysis of ordered preference data multidimensional scaling mds comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data in this paper we develop a new bayesian vector mds model to analyze ordered successive categories preference dominance data commonly collected in many social science and business studies a joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data unlike classical deterministic mds procedures the bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest also our procedure models the raw integer successive categories data which ameliorates the need of any data preproce

a bayesian multidimensional scaling procedure for the spatial analysis of revealed choice data we present a new bayesian formulation of a vector multidimensional scaling procedure for the spatial analysis of binary choice data the gibbs sampler is gainfully employed to estimate the posterior distribution of the specified scalar products bilinear model parameters the computational procedure allows for the explicit estimation of a covariance matrix which can accommodate violations of iia due to context effects in addition posterior standard errors can be estimated which reflect differential degrees of consumer choice uncertainty and or brand position instability a marketing application concerning the analysis of consumers consideration sets for luxury automobiles is provided to illustrate the use of the proposed methodology

graphical methods for assessing violations of the proportional hazards assumption in cox regression a major assumption of the cox proportional hazards model is that the effect of a given covariate does not change over time if this assumption is violated the simple cox model is invalid and more sophisticated analyses are required this paper describes eight graphical methods for detecting violations of the proportional hazards assumption and demonstrates each on three published datasets with a single binary covariate i discuss the relative merits of these methods smoothed plots of the scaled schoenfeld residuals are recommended for assessing ph violations because they provide precise usable information about the time dependence of the covariate effects

brief paper a ges attitude observer with single vector observations this paper proposes a globally exponentially stable ges observer for attitude estimation based on a single time varying reference vector in inertial coordinates and corresponding vector in body fixed coordinates in addition to angular velocity readings the proposed solution is computationally efficient and in spite of the fact that the observer does not evolve on the special orthogonal group so 3 an explicit solution on so 3 is also provided whose error is shown to converge exponentially fast to zero for all initial conditions the distinct roles of the inertial and the corresponding body fixed vectors on the observability of the system are also examined and simulation results are shown that illustrate the performance of the proposed attitude observer in the presence of low grade sensor specifications

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

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

bayesian multidimensional scaling and choice of dimension multidimensional scaling is widely used to handle data that consist of similarity or dissimilarity measures between pairs of objects we deal with two major problems in metric multidimensional scaling configuration of objects and determination of the dimension of object configuration within a bayesian framework a markov chain monte carlo algorithm is proposed for object configuration along with a simple bayesian criterion called mdsic for choosing their dimension simulation results are presented as are real data our method provides better results than does classical multidimensional scaling and alscal for object configuration and mdsic seems to work well for dimension choice in the examples considered

graphical comparison of cumulative hazards for two populations summary we consider graphs confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group in particular we consider the relative change a t in a cumulative rate function which is used to define a generalized proportional hazard model this model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model we introduce an estimate a t or a t based on the kaplan meier and nelson aalen estimates and obtain the asymptotic distribution of the process a t a t appropriately scaled this result is used to construct asymptotic pointwise confidence intervals for a t under the proportional hazard model assumption doob s transformation of gaussian processes is used to derive asymptotic simultaneous confidence bands for a t from a general class of test statistics defined as sup norms of weighted differences between a t and its estimate a t we also consider procedures based on estimates r u of the relative trend function r u between cumulative hazards the methods are illustrated on a data set from a study of the effect of radiation on mice and on a data set from a study of the effect of tumour size on the survival of cancer patients

nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities a maximum likelihood estimation procedure is developed for multidimensional scaling when dis similarity measures are taken by ranking procedures such as the method of conditional rank orders or the method of triadic combinations the central feature of these procedures may be termed directionality of ranking processes that is rank orderings are performed in a prescribed order by successive first choices those data have conventionally been analyzed by shepard kruskal type of nonmetric multidimensional scaling procedures we propose as a more appropriate alternative a maximum likelihood method specifically designed for this type of data a broader perspective on the present approach is given which encompasses a wide variety of experimental methods for collecting dissimilarity data including pair comparison methods such as the method of tetrads and the pick m method of similarities an example is given to illustrate various advantages of nonmetric maximum likelihood multidimensional scaling as a statistical method at the moment the approach is limited to the case of one mode two way proximity data but could be extended in a relatively straightforward way to two mode two way two mode three way or even three mode three way data under the assumption of such models as indscal or the two or three way unfolding models

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

inference for shift functions in the two sample problem with right censored data with applications abstract for two distribution functions f and g the shift function is defined by t g 1 f t t the shift function is the distance from the 45 line and the quantity plotted in q q plots in the analysis of lifetime data a represents the difference between two treatments the shift function can also be used to find crossing points of two distribution functions the large sample distribution theory for estimates of is studied for right censored data it turns out that the asymptotic covariance function depends on the unknown distribution functions f and g hence simultaneous confidence bands cannot be directly constructed a construction of simultaneous confidence bands for is developed via the bootstrap construction and application of such bands are explored for the q q plot

estimating cumulative treatment effects in the presence of nonproportional hazards often in medical studies of time to an event the treatment effect is not constant over time in the context of cox regression modeling the most frequent solution is to apply a model that assumes the treatment effect is either piecewise constant or varies smoothly over time i e the cox nonproportional hazards model this approach has at least two major limitations first it is generally difficult to assess whether the parametric form chosen for the treatment effect is correct second in the presence of nonproportional hazards investigators are usually more interested in the cumulative than the instantaneous treatment effect e g determining if and when the survival functions cross therefore we propose an estimator for the aggregate treatment effect in the presence of nonproportional hazards our estimator is based on the treatment specific baseline cumulative hazards estimated under a stratified cox model no functional form for the nonproportionality need be assumed asymptotic properties of the proposed estimators are derived and the finite sample properties are assessed in simulation studies pointwise and simultaneous confidence bands of the estimator can be computed the proposed method is applied to data from a national organ failure registry

multiclus a new method for simultaneously performing multidimensional scaling and cluster analysis this paper develops a maximum likelihood based method for simultaneously performing multidimensional scaling and cluster analysis on two way dominance or profile data this multiclus procedure utilizes mixtures of multivariate conditional normal distributions to estimate a joint space of stimulus coordinates andk vectors one for each cluster or group in at dimensional space the conditional mixture maximum likelihood method is introduced together with an e m algorithm for parameter estimation a monte carlo analysis is presented to investigate the performance of the algorithm as a number of data parameter and error factors are experimentally manipulated finally a consumer psychology application is discussed involving consumer expertise experience with microcomputers

analysis of non linear attitude observers for time varying reference measurements this paper provides a comprehensive stability analysis of a suite of nonlinear attitude observers that have been developed over the last few years the observers considered are based on vectorial measurements of an a priori known reference direction by treating the reference direction and the measurement in the same analysis framework and allowing time variation of either we are able to define general persistency of excitation criteria that incorporate and generalize convergence criteria used in prior work a key outcome is conditions that ensure almost global asymptotic and local exponential stability of attitude observers based on a single vector measurement as long as the excitation conditions are met on the reference and system trajectory the approach generalizes stability results provided in prior work based on rank conditions that required at least two or more vector measurements

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

a graphical method for assessing goodness of fit in cox s proportional hazards model abstract suggested here is a simple graphical method for studying the goodness of fit in cox s regression model for survival data the method is easy to use as it does not require the estimation of alternative models and only involves quantities similar to those already appearing in the partial likelihood expression that is needed in the parameter estimation the rationale behind the graphs is very intuitive they make a direct comparison between observed and expected failure frequencies as estimated from the model in a correctly specified model one anticipates an approximate balance between such frequencies otherwise there will typically be groups of individuals for which the expected frequencies are systematically too high or too low to match with the data and this shows in the graphs introduced here in the concrete applications of the method the individuals are stratified in a way that depends on what aspect of the model is being checked against data there is always one graph for each stratum s

martingale difference residuals as a diagnostic tool for the cox model the proportional hazards model makes two major assumptions the hazard ratio is constant over time and the relationship between the hazard and continuous covariates is log linear methods exist for checking and relaxing each of these assumptions but in both cases the methods rely on the other assumption being true problems can occur if neither of the assumptions is appropriate or even if only one of the assumptions is appropriate but it is not known which we propose a new kind of residual for checking the two assumptions simultaneously the smoothed residuals provide a flexible estimate of the hazard ratio which may deviate from the standard proportional hazards model by having a time dependent hazard ratio transformed covariates or both the methods are illustrated using data from the medical research council s myeloma trials

a bayesian vector multidimensional scaling procedure incorporating dimension reparameterization with variable selection we propose a two way bayesian vector spatial procedure incorporating dimension reparameterization with a variable selection option to determine the dimensionality and simultaneously identify the significant covariates that help interpret the derived dimensions in the joint space map we discuss how we solve identifiability problems in a bayesian context that are associated with the two way vector spatial model and demonstrate through a simulation study how our proposed model outperforms a popular benchmark model in addition an empirical application dealing with consumers ratings of large sport utility vehicles is presented to illustrate the proposed methodology we are able to obtain interpretable and managerially insightful results from our proposed model with variable selection in comparison with the benchmark model

the invariant extended kalman filter as a stable observer we analyze the convergence aspects of the invariant extended kalman filter iekf when the latter is used as a deterministic nonlinear observer on lie groups for continuous time systems with discrete observations one of the main features of invariant observers for left invariant systems on lie groups is that the estimation error is autonomous in this paper we first generalize this result by characterizing the much broader class of systems for which this property holds for those systems the lie logarithm of the error turns out to obey a linear differential equation then we leverage this log linear property of the error evolution to prove for those systems the local stability of the iekf around any trajectory under the standard conditions of the linear case one mobile robotics example and one inertial navigation example illustrate the interest of the approach simulations evidence the fact that the ekf is capable of diverging in some challenging situations where the iekf with identical tuning keeps converging

nonlinear complementary filters on the special orthogonal group this paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units the outputs of such systems are characterized by high noise levels and time varying additive biases we formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group so 3 driven by reconstructed attitude and angular velocity measurements lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error the approach taken leads to an observer that we term the direct complementary filter by exploiting the geometry of the special orthogonal group a related observer termed the passive complementary filter is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs both the direct and passive filters can be extended to estimate gyro bias online the passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude this leads to an observer on so 3 termed the explicit complementary filter that requires only accelerometer and gyro outputs is suitable for implementation on embedded hardware and provides good attitude estimates as well as estimating the gyro biases online the performance of the observers are demonstrated with a set of experiments performed on a robotic test bed and a radio controlled unmanned aerial vehicle

on graphical tests for proportionality of hazards in two samples in this paper we present a class of graphical tests of the proportional hazards hypothesis for two sample censored survival data the proposed tests are improvements over some existing tests based on asymptotic confidence bands of certain functions of the estimated cumulative hazard functions the new methods are based on the comparison of unrestricted estimates of the said functions and their restricted versions under the hypothesis they combine the rigour of analytical tests with the descriptive value of plots monte carlo simulations suggest that the proposed asymptotic procedures have reasonable small sample properties the power is much higher than existing graphical tests and comparable with existing analytical tests the method is then illustrated through the analysis of a data set on bone marrow transplantation for leukemia patients

estimating durbin s approximation summary some statistical procedures involve boundary crossing probabilities for processes that converge weakly to continuous gaussian limits when carrying out these procedures boundary crossing probabilities associated with the limit processes may sometimes be substituted for the probabilities of interest an approach to estimating durbin s approximation to boundary crossing probabilities for continuous gaussian processes is described here when the covariance of the limit process satisfies a certain condition the approach may be used to estimate the boundary crossing probabilities associated with the limit processes two examples illustrate the applicability of the approach and the results of some simulation experiments are described