a note on the regression analysis of censored data maximum likelihood estimates of the parameters in linear models with censored normal responses may be simply obtained using the em algorithm the iterative computations required for the regression coefficients are identical to those described by schmee and hahn for least squares estimates but those for the variance estimates are different the biases of the two variance estimates are discussed

the analysis of a fractional factorial experiment with censored data using iterative least squares schmee and hahn 1979 suggested iterative least squares as a simple method for analyzing censored data the application of this method to the analysis of the results of a fractional factorial experiment with censored observations is described and illustrated in this paper

on the local well posedness of quasilinear schrodinger equations in arbitrary space dimension abstract a class of quasilinear schrodinger equations is studied which contain strongly singular nonlinearities including derivatives of second order such equations have been derived as models of several physical phenomena the results of this paper apply to the superfluid film equation in fluid mechanics the local well posedness for smooth solutions of the cauchy problem is proved in arbitrary space dimension without any smallness assumption on the initial value this improves results in the literature which cover the one dimensional case only almost global well posedness results are obtained as well the proof combines nash moser techniques on implicit function theorems in frechet spaces with hyperbolic semigroup theory including evolution systems using the intersection of all sobolev spaces as basic function space the nondissipativity is overcome by a transformation procedure yielding the evolution operator and a priori estimates of higher order sobolev norms for the linearized problem here a certain trace has to vanish in view of apparent integrability conditions the transformations and the regularity theory are substantially different from the easier one dimensional case in particular continuity estimates are proved for the operator norms of the linear evolution operator in negative sobolev spaces

maximal determinant over a certain class of matrices and its application to d optimality of designs it is known that some optimality criteria of experimental designs are functionals of the eigenvalues of their information matrices in this context we study the problem of maximizing the determinant of it p pt 2 over the class of t by t permutation matrices and the determinant of it p pt 2 5 over the class of t by t permutation matrices with zero diagonal derangement matrices the results are used to characterize d optimal complete block designs under an interference model

multiplicity results for some nonlinear schrodinger equations with potentials multiple semiclassical standing waves for a class of nonlinear schrodinger equations with potentials are found by means of a perturbative variational method

circular designs balanced for neighbours at distances one and two summary we define three types of neighbour balanced designs for experiments where the units are arranged in a circle or single line in space or time the designs are balanced with respect to neighbours at distance one and at distance two the variants come from allowing or forbidding self neighbours and from considering neighbours to be directed or undirected for two of the variants we give a method of constructing a design for all values of the number of treatments except for some small values where it is impossible in the third case we give a partial solution that covers all sizes likely to be used in practice

on the design of experiments under spatial correlation on considere tout d abord le cas ou les effets du traitement sont estimes par les moindres carres on considere ensuite le cas ou l analyse a utiliser est les moindres carres generalises utilisant une matrice de correlation connue

efficiency of nearest neighbour balanced block designs for correlated observations summary block designs for observations correlated in one dimension are investigated nearest neighbour balanced block designs turn out to be optimal for autoregressive correlation models when generalized least squares estimation is used performance of these designs for other correlation models is shown to be quite satisfactory the efficiency of the proposed designs in comparison to the randomized block designs is computed and tabulated for some cases

a catalogue of efficient neighbour designs with border plots we consider designs in linear blocks with border plots in which a treatment may affect the response on the two adjacent plots three series of designs are given i neighbour balanced designs in complete blocks ii neighbour balanced designs in blocks each of which lacks one treatment iii partially neighbour balanced designs in few complete blocks complete methods of construction and randomization are given optimality properties are discussed

analysis of censored data from fractionated experiments a bayesian approach abstract censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous categorical outcomes when censored data are observed from a fractionated experiment likelihood based estimates quite often do not exist especially when the opportunity for improvement is great to circumvent this problem we propose a bayesian analysis strategy that has a straightforward implementation using the data augmentation and monte carlo em algorithms for nonregular designs with complex aliasing patterns a modified analysis strategy is proposed that substantially reduces the computation needed for model selection the proposed strategy is illustrated using data from three real industrial experiments for these data sets the analysis results are fairly insensitive to the specification of the prior

neighbour balanced block designs for correlated errors summary the paper considers a simple block model and assumes that the errors within the blocks are correlated following a stationary first order autoregressive process gill shukla 1985 consider this model but they restrict the set of the competing designs to a small subset of the possible designs the binary and equireplicate designs in the present paper we show that the designs determined by gill shukla are optimal over all possible designs for positive correlations and that neighbour balanced designs in general are highly efficient

alternating subspace spanning resampling to accelerate markov chain monte carlo simulation this article provides a simple method to accelerate markov chain monte carlo sampling algorithms such as the data augmentation algorithm and the gibbs sampler via alternating subspace spanning resampling assr the assr algorithm often shares the simplicity of its parent sampler but has dramatically improved efficiency the methodology is illustrated with bayesian estimation for analysis of censored data from fractionated experiments the relationships between assr and existing methods are also discussed

bifurcations for quasilinear schrodinger equations i abstract this paper is concerned with bifurcation problems for quasilinear schrodinger type equations such as the modified nonlinear schrodinger equations which have appeared as several models from mathematical physics we give a new approach for dealing with bifurcation problems of nonlinear potential operators the novelty of our approach lies in establishing multiple bifurcations without making a reduction to finite dimensional problems the finite dimensional reduction procedures that have been used in the past work for semilinear problems but are not suitable for quasilinear problems we give a unified approach requiring much less regularity of the problems as applications we provide multiple bifurcation results for the modified nonlinear schrodinger equations

analysis of interval censored data from fractionated experiments using covariance adjustment censored data are commonly observed in industrial experiments such as for life testing and reliability improvement analyzing censored data from highly fractionated experiments presents a challenging problem to experimenters because many traditional methods become inadequate motivated by the data from a fluorescent lamp experiment we consider in this article analyzing censored data from highly fractionated experiments using covariance adjustment based on multivariate multiple regression models which make use of the joint distribution of multivariate response variables the bayesian approach is taken for the main statistical inference the posterior distribution of the parameters is obtained using the data augmentation algorithm we illustrate the methodology with the fluorescent lamp experiment data with the real example and a simulation study we show that covariance adjustment can lead to both dramatic variance reduction and possible bias reduction

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

an application of imputation to an estimation problem in grouped lifetime analysis tanner and wang in press have introduced the data augmentation algorithm for the analysis of parametric missing data problems in this article this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data this algorithm makes use of the notions of cross validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate a procedure for estimating the variance of the estimator is also proposed the nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study the algorithm is illustrated with a numerical example

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

analysis of censored data from highly fractionated experiments although censored including interval censored data may be easier or less costly to collect than complete data they contain less information and are harder to analyze existing methodology is inadequate for analyzing such data from highly fractionated experiments we propose an iterative method that provides a simple and flexible way to consider many models simultaneously the method s simplicity makes it easy to implement with existing software results in computational savings and promotes experimenter involvement we demonstrate the procedure by reanalyzing data from two real experiments a simulation study also demonstrates its superiority over some existing methods including taguchi s minute accumulating analysis

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

the cauchy problem for quasi linear schrodinger equations with x rn t r with x1 xn and summation convention one may think of the equation in 1 1 as a non linear schrodinger equation where the operator modeling the dispersion relation is non isotropic and depends also on the unknown function its conjugate and their gradients in the space variables under appropriate assumptions on the function f the method presented here extends to fully non linear schrodinger equations of the form

asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h 1 supercritical exponent in this paper we obtain the asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h1 supercritical exponent to this aim the uniqueness and the non degeneracy of positive solutions of the corresponding limit equation which is a zero mass problem play important roles thus we also show the uniqueness and non degeneracy result for a class of zero mass problems by applying ode techniques

valid restricted randomization for unbalanced designs sufficient conditions for strong validity of randomization are given for designs whose block structure corresponds to an association scheme these conditions generalize previous results for orthogonal designs and balanced designs applications to restricted randomization of neighbour balanced designs are discussed

e optimal designs when errors follow a conditional autonormal process this paper deals with e optimal incomplete block designs in blocks of size three when observations within each block are correlated according to a conditional autonormal process the optimality problem is addressed within various subclasses of connected designs under generalized least squares estimation of treatment contrasts

some aspects of analysis of covariance an account from first principles is given of a number of aspects of analysis of covariance six different meanings of analysis of covariance are outlined and the history of this technique is sketched briefly the development of the key formulae from the method of least squares is described and generalizations to other distributions in the exponential family are mentioned special problems of application in randomized experiments and in observational studies are discussed finally the decomposition of regression relations is considered along with components of covariance

a ground state solution for an asymptotically periodic quasilinear schrodinger equation abstract this article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear schrodinger equation by using a change of variables the quasilinear problem is transformed into a semilinear one then we use a nehari type constraint to get the existence result

multiple normalized solutions for quasi linear schrodinger equations abstract in this paper we prove the existence of two solutions having a prescribed l 2 norm for a quasi linear schrodinger equation one of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global to overcome the lack of differentiability of the associated functional we rely on a perturbation method developed in 25

uniqueness and nondegeneracy of the ground state for a quasilinear schrodinger equation with a small parameter abstract we study least energy solutions of a quasilinear schrodinger equation with a small parameter we prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density abstract a recursive extended natural conjugate prior density is proposed for systems of seemingly unrelated regression equations compared to other classes of extended natural conjugate prior densities it offers the advantage that analytical expressions are available for the prior covariance matrix of the regression coefficients the posterior analysis combines analytical and numerical techniques numerical integration is based on monte carlo importance sampling an application to a system of four wage equations for eec countries serves to evaluate different techniques discussed in the paper

standing waves with a critical frequency for nonlinear schrodinger equations this paper is concerned with the existence and qualitative property of standing wave solutions for the nonlinear schrodinger equation with e being a critical frequency in the sense that we show that there exists a standing wave which is trapped in a neighbourhood of isolated minimum points of v and whose amplitude goes to 0 as moreover depending upon the local behaviour of the potential function v x near the minimum points the limiting profile of the standing wave solutions will be shown to exhibit quite different characteristic features this is in striking contrast with the non critical frequency case which has been extensively studied in recent years

standing waves for nonlinear schrodinger equations with a general nonlinearity for elliptic equations e2 u v x u f u 0 x rn n 3 we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component of positive local minimum points of v as e 0 under conditions on f which we believe to be almost optimal

randomization for a balanced superimposition of one youden square on another some experimentation particularly on trees in orchards requires the superimposition of a new set of treatments on an existing experiment on the assumption that the effects of the new treatments do not interact with those of the old different approaches to the randomization of such new treatments were considered by preece bailey and patterson who investigated in detail the case when one latin square is superimposed on another to produce a graeco latin square for non orthogonal superimpositions the theory is in general much more complicated however this paper shows that fairly simple randomization results are obtainable for certain balanced superimpositions of one youden square on another i when each youden square is of size t 1 x t and ii when each youden square is of size k x t where t is a prime power of the form 4s 1 and k 2s 1 or k 2s in each case t is the number of treatments in each youden square the valid randomization procedure obtained for the second case is unlike any previously known randomization procedure and is unlikely to be acceptable in practice it is however an excellent indication of the difficulties that arise when randomization is attempted in unusual circumstances

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea