nonparametric least squares estimation of a multivariate convex regression function this paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional we characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided we also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization computation and consistency of its least squares estimator

the efficiency factors of particular effects in designs with orthogonal factorial structure on etudie le confounding partiel qui n est pas necessairement orthogonal aux blocs on relie le facteur d efficacite d une interaction ou d un effet principaux aux nombres de chemins d un certain type dans le graphe de concurrence des traitements

circuits and efficiency in incomplete block designs summary this paper explains why numbers of circuits in the variety concurrence graph of a design provide an attractive measure of its efficiency it is conjectured that the search for designs with an optimal value of the harmonic mean efficiency factor can be restricted to those with minimal numbers of circuits of shorter lengths this conjecture is seen to be highly plausible to be a natural generalization of a conjecture that is already widely accepted and to offer significant savings in the construction of efficient designs

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

oracle estimation of parametric models under boundary constraints in many classical estimation problems the parameter space has a boundary in most cases the standard asymptotic properties of the estimator do not hold when some of the underlying true parameters lie on the boundary however without knowledge of the true parameter values confidence intervals constructed assuming that the parameters lie in the interior are generally over conservative a penalized estimation method is proposed in this article to address this issue an adaptive lasso procedure is employed to shrink the parameters to the boundary yielding oracle inference which adapt to whether or not the true parameters are on the boundary when the true parameters are on the boundary the inference is equivalent to that which would be achieved with a priori knowledge of the boundary while if the converse is true the inference is equivalent to that which is obtained in the interior of the parameter space the method is demonstrated under two practical scenarios namely the frailty survival model and linear regression with order restricted parameters simulation studies and real data analyses show that the method performs well with realistic sample sizes and exhibits certain advantages over standard methods

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

efficient estimation of semiparametric transformation models for counting processes summary a class of semiparametric transformation models is proposed to characterise the effects of possibly time varying covariates on the intensity functions of counting processes the class includes the proportional intensity model and linear transformation models as special cases nonparametric maximum likelihood estimators are developed for the regression parameters and cumulative intensity functions of these models based on censored data the estimators are shown to be consistent and asymptotically normal the limiting variances for the estimators of the regression parameters achieve the semi parametric efficient bounds and can be consistently estimated the limiting variances for the estimators of smooth functionals of the cumulative intensity function can also be consistently estimated simulation studies reveal that the proposed inference procedures perform well in practical settings two medical studies are provided

bayes factors and approximations for variance component models abstract in this article we consider tests of variance components using bayes factors such tests arise in many fields of application including medicine agriculture and engineering when using bayes factors the choice of prior distribution on the parameter of interest is of great importance we propose a unit information reference method for variance component models the calculation of bayes factors in this context is not straightforward there are well documented difficulties with markov chain monte carlo approaches such as gibbs sampling and the usual laplace approximation is not appropriate due to the boundary null hypothesis we describe both an importance sampling approach and an analytical approximation for calculating the numerator and denominator of the bayes factor the importance sampling approach is straightforward to implement and also forms the basis for a rejection algorithm that allows generation of samples from the posterior distributions under the null and alternative hypotheses

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

joint variable selection for fixed and random effects in linear mixed effects models it is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed effects lme model typical approaches perform selection separately on each of the fixed and random effect components however changing the structure of one set of effects can lead to different choices of variables for the other set of effects we propose simultaneous selection of the fixed and random factors in an lme model using a modified cholesky decomposition our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects it performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero a constrained expectation maximization algorithm is then used to obtain the final estimates it is further shown that the proposed penalized estimator enjoys the oracle property in that asymptotically it performs as well as if the true model was known beforehand we demonstrate the performance of our method based on a simulation study and a real data example

confidence bounds for normal means under order restrictions with application to dose response curves toxicology experiments and low dose extrapolation abstract suppose that y 1 yk are normal random variables with ordered means u 1 u 2 uk a confidence bound is found for each ui that takes advantage of the ordering the upper and lower bounds are the maximum and minimum values of x such that the hypotheses that x ui and ui x are accepted by their respective likelihood ratio tests these bounds are often more precise than the usual bounds and can be used to determine the safety of a toxin and to bound the virtual safe dose in a low dose extrapolation simultaneous intervals for u 1 uk are also derived

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

fixed and random effects selection in mixed effects models summary we consider selecting both fixed and random effects in a general class of mixed effects models using maximum penalized likelihood mpl estimation along with the smoothly clipped absolute deviation scad and adaptive least absolute shrinkage and selection operator alasso penalty functions the mpl estimates are shown to possess consistency and sparsity properties and asymptotic normality a model selection criterion called the icq statistic is proposed for selecting the penalty parameters ibrahim zhu and tang 2008 journal of the american statistical association 103 1648 1658 the variable selection procedure based on icq is shown to consistently select important fixed and random effects the methodology is very general and can be applied to numerous situations involving random effects including generalized linear mixed models simulation studies and a real data set from a yale infant growth study are used to illustrate the proposed methodology

balance orthogonality and efficiency factors in factorial design on montre que 1 l equilibre general relativement a une structure factorielle et 2 la structure factorielle orthogonale sont essentiellement les memes pour des plans factoriels avec un systeme unique de blocs

an information criterion for parameters under a simple order restriction suppose we have independent random samples from each of k populations specified by scalar valued unknown parameters 1 k satisfying the simple order restriction 1 k our concern is to seek distinct parameters among 1 k based on the data to find a configuration of distinct parameters among the 0 s one may consider employing akaike s information criterion akaike 1973 however the criterion is not appropriate for the order restricted maximum likelihood estimator of 1 k since the normality or the asymptotic normality of the estimator is not valid in this paper an information criterion is proposed for detecting the configuration of the true parameters with the simple order restriction this method may also be applied for detecting a changepoint in a sequence of parameters with a monotone trend a monte carlo study indicates that our new criterion is effective compared to akaike s information criterion for detecting the configuration of normal means satisfying the simple order restriction

multiple testing of general contrasts using logical constraints and correlations abstract use of logical constraints among hypotheses and correlations among test statistics can greatly improve the power of step down tests an algorithm for uncovering these logically constrained subsets in a given dataset is described the multiple testing results are summarized using adjusted p values which incorporate the relevant dependence structures and logical constraints these adjusted p values are computed consistently and efficiently using a generalized least squares hybrid of simple and control variate monte carlo methods and the results are compared to alternative stepwise testing procedures

adaptive lasso for cox s proportional hazards model summary we investigate the variable selection problem for cox s proportional hazards model and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience the new method is based on a penalized log partial likelihood with the adaptively weighted l1 penalty on regression coefficients providing what we call the adaptive lasso estimator the method incorporates different penalties for different coefficients unimportant variables receive larger penalties than important ones so that important variables tend to be retained in the selection process whereas unimportant variables are more likely to be dropped theoretical properties such as consistency and rate of convergence of the estimator are studied we also show that with proper choice of regularization parameters the proposed estimator has the oracle properties the convex optimization nature of the method leads to an efficient algorithm both simulated and real examples show that the method performs competitively

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

linear model selection by cross validation abstract we consider the problem of selecting a model having the best predictive ability among a class of linear models the popular leave one out cross validation method which is asymptotically equivalent to many other model selection methods such as the akaike information criterion aic the c p and the bootstrap is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n we show that the inconsistency of the leave one out cross validation can be rectified by using a leave n v out cross validation with n v the number of observations reserved for validation satisfying n v n 1 as n this is a somewhat shocking discovery because nv n 1 is totally opposite to the popular leave one out recipe in cross validation motivations justifications and discussions of some practical aspects of the use of the leave n v out cross validation method are provided and results

numerical differentiation for local and global tangent operators in computational plasticity in this paper numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators the derivatives of the constitutive equations are approximated by means of difference schemes these derivatives are needed to achieve quadratic convergence in the integration at gauss point level and in the solution of the boundary value problem numerical differentiation is shown to be a simple robust and competitive alternative to analytical derivatives quadratic convergence is maintained provided that adequate schemes and stepsizes are chosen this point is illustrated by means of some numerical examples