cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

assessment of stratum covariate interactions in cox s proportional hazards regression model we assess stratum e g treatment interactions with covariates and with the baseline hazard function in the proportional hazards ph regression model for lifetime data we consider models incorporating stratum interactions both with and without stratification of the risk sets in the likelihood function and describe likelihood ratio statistics for tests of the presence of these interactions we also present step down methods for building reduced models which include stratum specific parameters corresponding to covariates which interact with treatment we apply ph models with such interactions to a clinical trial of des in the treatment of prostate cancer to determine optimal treatment conditional on each patient s covariates

points of monotonicity in orlicz lorentz function spaces abstract in orlicz lorentz function space m 0 points of upper monotonicity lower monotonicity upper local uniform monotonicity and lower local uniform monotonicity are characterized as the corollary we can easily obtain the criteria for strict monotonicity upper local uniform monotonicity and lower local uniform monotonicity of m 0

non squareness properties of orlicz lorentz sequence spaces abstract in this paper criteria for non squareness properties non squareness local uniform non squareness and uniform non squareness of orlicz lorentz sequence spaces and of their n dimensional subspaces n n 2 as well as of the subspaces a of all order continuous elements in are given since degenerate orlicz functions and degenerate weight sequences are also admitted these investigations concern the most possible wide class of orlicz lorentz sequence spaces finally as immediate consequences criteria for all non squareness properties of orlicz sequence spaces which complete the results of sundaresan 1966 53 hudzik 1985 23 hudzik 1985 24 are deduced it is worth recalling that uniform non squareness is an important property because it implies super reflexivity as well as the fixed point property see james 1964 31 james 1972 33 and garcia falset et al 2006 19

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

rotundity properties in banach spaces via sublinear operators abstract conditions for extreme points strongly extreme points lur points su points points in direction of which the space is uniformly rotund and points with the kadec klee property with respect to the convergence almost everywhere for the space d e s generated by a kothe space e and a sublinear operator s defined on a linear space x and with values in l 0 are given as corollaries conditions for rotundity midpoint local uniform rotundity local uniform rotundity uniform rotundity in every direction and the kadec klee property for the convergence locally in measure of these spaces are deduced interpretations of the results in cases of kothe bochner spaces cesaro orlicz spaces and k interpolation spaces are presented

on some geometric properties of generalized orlicz lorentz function spaces in this article we continue investigations concerning generalized orlicz lorentz function spaces initiated in the papers foralewski 2011 29 30 cf also foralewski 2008 27 28 first it is shown that modular is orthogonally subadditive next monotonicity properties are considered in order to get sufficient conditions for uniform monotonicity of the space a strong condition of 2 type and the notion of regularity of the generated musielak orlicz function are introduced finally criteria for non squareness of are presented

another look at cesaro sequence spaces abstract we consider the cesaro sequence space ces p as a closed subspace of the infinite l p sum of finite dimensional spaces we easily obtain many known results for example ces p has property of rolewicz uniform opial property and weak uniform normal structure we also consider some generalized cesaro sequence spaces finally we compute the von neumann jordan and james constants of the two dimensional cesaro sequence space ces p 2 when 1 p 2

necessary and sufficient conditions of stability a multiloop generalization of the circle criterion a linear time invariant system with a vector output and a vector input is described this system is closed by an uncertain nonlinear time varying feedback the only information on this feedback is given by several integral quadratic inequalities i e the uncertainties under consideration generalize the so called conic nonlinearities necessary and sufficient frequency domain conditions of stability are obtained an advanced version of the s procedure losslessness theorem and some other tools of the absolute stability theory are used

monotonicity characteristic of kothe bochner spaces abstract estimates of the characteristic of monotonicity in kothe bochner function spaces e x with some consequences are given characterizations of strict and uniform monotonicity of the sequence lattice e x n n 1 are obtained

extremity in kothe bochner function spaces abstract letebe a kothe function space over a complete measurable space andxa banach space recall an elementhineis said to beorder continuousif for any decreasing sequence gn inse ngn 0 andgn h implies limn gn 0 we show that every denting point of the unit ball ofeis order continuous using this result we prove thatfis a denting point of the unit ball ofe x if and only if is a denting point of the unit ball of for almost all supp is a denting point of the unit ball of suppose thateis order continuous we also prove that for any unit vectorfine x if f xis a strongly exposed point of the unit ball ofeand for almost allt supp f f t f t xis a strongly exposed point of the unit ball ofx thenfis a strongly exposed point of the unit ball ofe x

local monotonicity structure of symmetric spaces with applications abstract in this paper we discuss several monotonicity properties in banach lattices we start with several general results on local structure of symmetric banach function spaces discussing in particular whether a point x e has some local property if and only if its nonincreasing rearrangement x has the same property section 2 in that section we also prove some general facts for nonincreasing rearrangements which may be of independent interest next we apply these results to find complete criteria for local monotonicity structure of lorentz spaces p and orlicz lorentz spaces sections 3 local structure of lorentz spaces 4 1 local structure of orlicz lorentz spaces 4 2 local uniform structure of lorentz spaces we conclude with the description of global monotonicity structure of lorentz spaces p section 4 3 we finish with the applications of upper monotonicity and lower monotonicity points to local best dominated approximation problems in banach lattices section 5

criteria for monotonicity properties of musielak orlicz spaces equipped with the amemiya norm abstract criteria for strict monotonicity lower local uniform monotonicity upper local uniform monotonicity and uniform monotonicity of musielak orlicz spaces over any finite and complete measure space endowed with the amemiya norm are given the fact that the spaces are considered over arbitrary finite measure space is essential because as it is shown in example 3 the musielak orlicz spaces need not be strictly monotone even if their restrictions to the nonatomic part and the purely atomic part are strictly monotone

radon nikodym property for the projective tensor product of kothe function spaces abstract let e be an order continuous kothe function space or an order continuous banach lattice and x be a dual banach space then e x the projective tensor product of e and x has the radon nikodym property if and only if both e and x do

characterization and efficient computation of the structured singular value the concept of structured singular value was recently introduced by doyle 1 as a tool for the analysis and synthesis of feedback systems with structured uncertainties it is a key to the design of control systems under joint robustness and performance specifications and it very nicely complements the h infty approach to control system design in this paper it is shown that the structured singular value can be obtained as the solution of several smooth optimization problems properties of these optimization problems are exhibited leading to a fast algorithm that always yields the structured singular value for block structures of size no larger than 3 and often does for block structures of larger size

understanding cox s regression model a martingale approach abstract an informal discussion is given of how martingale techniques can be used to extend cox s regression model and to derive its large sample properties

structured fusion lasso penalized multi state models multi state models generalize survival or duration time analysis to the estimation of transition specific hazard rate functions for multiple transitions when each of the transition specific risk functions is parametrized with several distinct covariate effect coefficients this leads to a model of potentially high dimension to decrease the parameter space dimensionality and to work out a clear image of the underlying multi state model structure one can either aim at setting some coefficients to zero or to make coefficients for the same covariate but two different transitions equal the first issue can be approached by penalizing the absolute values of the covariate coefficients as in lasso regularization if instead absolute differences between coefficients of the same covariate on different transitions are penalized this leads to sparse competing risk relations within a multi state model that is equality of covariate effect coefficients in this paper a new estimation approach providing sparse multi state modelling by the aforementioned principles is established based on the estimation of multi state models and a simultaneous penalization of the l1 norm of covariate coefficients and their differences in a structured way the new multi state modelling approach is illustrated on peritoneal dialysis study data and implemented in the r package penmsm copyright 2016 john wiley sons ltd

the rank one mixed m problem and kharitonov type analysis the general mixed problem has been shown to be np hard so that the exact solution of the general problem is computationally intractable except for small problems in this paper we consider not the general problem but a particular special case of this problem the rank one mixed problem we show that for this case the mixed problem is equivalent to its upper bound which is convex and it can in fact be computed easily and exactly this special case is shown to be equivalent to the so called affine parameter variation problem for a polynomial with perturbed coefficients which has been examined in detail in the literature and for which several celebrated kharitonov type results have been proven

robust stability with time varying structured uncertainty considers the problem of assessing robust stability in the presence of block diagonally structured time varying dynamic uncertainty it is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition the notion of stability here is finite gain stability over finite energy signals in sharp contrast to the case of time invariant dynamic uncertainty this result is not limited by the number uncertainty blocks these results parallel previous results regarding finite gain stability over persistent bounded signals

optimal constant i o similarity scaling for full information and state feedback control problems abstract in robust control problems capturing all robustness and performance objectives in a single h norm cost function is impossible an alternative approach still untilizing the h norm involves diagonal similarity scaling of certain closed loop transfer functions the set of allowable diagonal scalings is problem dependent and reflects assumptions about the uncertainty and desired performance objectives the scaling set considered here is a prescribed convex set of positive definite matrices we consider the optimal constant scaling problem for the full information h control problem the solution is obtained by transforming the original problem into a convex feasibility problem specifically a structured linear matrix inequality in special cases solvability of the full information problem is equivalent to solvability of the state feedback problem

monotonicity properties in banach spaces via sublinear operators and corrigendum to rotundity properties in banach spaces via sublinear operators nonlinear analysis 64 2006 1171 1188 abstract various kinds of monotone points namely lower and upper strictly monotone lower and upper locally uniformly monotone points are studied in the space d e s generated by a kothe space e and a sublinear operator s defined on a banach lattice x and with values in e some results on global monotonicity properties are easily deduced from those results interpretations of the result in three different classes of the space d e s are given at the end a small corrigendum to our paper rotundity properties in banach spaces via sublinear operators published in nonlinear analysis 64 2006 1171 1188 is given

monotonicity and best approximation in orlicz sobolev spaces with the luxemburg norm abstract criteria for strict monotonicity upper lower locally uniform monotonicity and uniform monotonicity of orlicz sobolev spaces with the luxemburg norm are given some applications to best approximation are presented

hierarchical proportional hazards regression models for highly stratified data summary in clinical trials conducted over several data collection centers the most common statistically defensible analytic method a stratified cox model analysis suffers from two important defects first identification of units that are outlying with respect to the baseline hazard is awkward since this hazard is implicit rather than explicit in the cox partial likelihood second and more seriously identification of modest treatment effects is often difficult since the model fails to acknowledge any similarity across the strata we consider a number of hierarchical modeling approaches that preserve the integrity of the stratified design while offering a middle ground between traditional stratified and unstratified analyses we investigate both fully parametric weibull and semiparametric models the latter based not on the cox model but on an extension of an idea by gelfand and mallick 1995 biometrics51 843 852 which models the integrated baseline hazard as a mixture of monotone functions we illustrate the methods using data from a recent multicenter aids clinical trial comparing their ease of use interpretation and degree of robustness with respect to estimates of both the unit specific baseline hazards and the treatment effect

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

a convex parameterization of robustly stabilizing controllers this paper treats synthesis of robust controllers for linear time invariant systems uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial the main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations with the new parameterization certain robust performance problems can be stated in terms of quasi convex optimization

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

computational complexity reduction in scaled h synthesis abstract the h control problem with constant scaling is considered this problem is known to reduce to a search for matrices satisfying linear matrix inequalities lmis and an additional nonconvex constraint recently globally convergent algorithms to solve this nonconvex feasibility problem have been proposed a major factor that determines the computational complexity is the number of nonconvex constraints this paper gives verifiable conditions on the plant under which the reduction of nonconvex constraints is possible the conditions appear to be a strong requirement but in fact they are nautrally satisfied in certain problems 1997 elsevier science ltd