positive radial solutions and non radial bifurcation for semilinear elliptic equations in annular domains abstract we discuss the existence and multiplicity of positive radial solutions and the non radial bifurcation of u f u 0 in and u 0 on where is an annular domain of r n n 2 we prove that if f u 0 for u 0 and lim u f u u then there exists 0 such that there are at least two positive radial solutions for each 0 at least one for and none for if f 0 0 lim u 0 f u u 1 and uf u 1 e f u for u 0 e 0 then there exists a variational solution for 0 1 where 1 is the least eigenvalue of if f 0 0 lim u 0 f u u 0 and lim u f u u then there exists at least one positive radial solution for any 0 we obtain some precise multiplicity results for narrow annulus and show that the non radial bifurcation occurs if the growth of f u is rapid enough as u

assessing normality in random effects models when one uses the unbalanced mixed linear model mathbf y i mathbf x i mathbf alpha mathbf z i mathbf beta i varepsilon i i 1 cdots n to analyze data from longitudinal experiments with continuous outcomes it is customary to assume varepsilon i sim operatorname ind mathscr n mathbf 0 sigma 2 mathbf i i independent of mathbf beta i sim operatorname iid mathscr n mathbf 0 delta where sigma 2 and the elements of an arbitrary mathbf delta are unknown variance and covariance components in this paper we describe a method for checking model adequacy and in particular the distributional assumption on the random effects mathbf beta i we generalize the weighted normal plot to accommodate dependent nonidentically distributed observations subject to multiple random effects for each individual unit under study one can detect various departures from the normality assumption by comparing the expected and empirical cumulative distribution functions of standardized linear combinations of estimated residuals for each of the individual units through application of distributional results for a certain class of estimators to our context we adjust the estimated covariance of the empirical cumulative distribution function to account for estimation of unknown parameters several examples of our method demonstrate its usefulness in the analysis of longitudinal data

existence of positive solutions for non positive higher order bvps abstract we shall provide conditions on non positive function f t u 1 u n 1 so that the boundary value problem has at least one positive solution then we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions

hilbert s projective metric and nonlinear elliptic problems abstract this paper deals with the eigenvalue problems for a class of positive nonlinear operators the projective metric technique is used to prove the existence of a unique fixed point of the operator we then show how to apply our results to the study of nonlinear elliptic problems

uniqueness of positive radial solutions for semilinear elliptic equations on annular domains where 5 5a b x rn 0iai x ib is an annular domain in rn n 3 it is well known that the uniqueness problems of solutions of 1 1 and 1 2 are both fundamental and often di8cult during the last decade there has been tremendous progress in studying these problems when 5 is a ball in rn or entire rn n 3 see e g 1 2 5 10 11 however very little was known concerning the annular domain until the work of ni and nussbaum 12 until very recently co man 3 showed that when n 3 f u u up 1ip 3 1 1 and 1 2 have unique positive radial solution for any annular domain see also 13 then it is of interest to extend co man s result to a more general situation for example we may ask the following question

positive solutions of difference equations with two point right focal boundary conditions abstract we consider the following boundary value problem formula formula where 1 p n 1 is fixed using a fixed point theorem for operators on a cone we develop criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are established for special cases we also include several examples to dwell upon the importance of the results obtained

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

on the existence of bounded positive solutions for a class of singular bvps abstract we investigate the existence and properties of solutions to a second order singular ode we base ourselves on the variational approach which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences

on prediction and the power transformation family summary the power transformation family is often used for transforming to a normal linear model the variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated compared to when the transformation parameter is known we consider prediction of future untransformed observations when the data can be transformed to a linear model when the transformation must be estimated the prediction error is not much larger than when the parameter is known

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

estimation in covariance components models abstract estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes the estimation of fixed and random effects when the variances and covariances are known is presented in bayesian terms point estimates of the unknown variances and covariances are computed using the em algorithm for maximum likelihood estimation from incomplete data the techniques are illustrated with data on law schools field mice and professional football teams

analysis of positive radial solutions for singular superlinear p laplacian systems on the exterior of a ball abstract in this paper we study some well posedness properties of a positive radial solution pair u 1 u 2 to a singular boundary value problem in the form p u i k i x f i u j in r n b r 0 a i u i n c i u j u i u i 0 on b r 0 u i 0 as x where i j 1 2 i j p stands for the singular degenerate p laplacian p w div w p 2 w with 1 p n 0 a i 0 r 0 0 k i c r 0 0 and c i c 0 0 0 0 here the functions f i c 0 r i 1 2 satisfy a combined p superlinear growth at and possibly have singularities at 0 we establish an existence result for the case 0 multiplicity results of positive radial solutions for certain ranges of and nonexistence results of a positive radial solution for the case 1

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

reml estimation of covariance matrices with restricted parameter spaces abstract restricted parameter spaces for covariance matrices such as 2 i or i j are often used to simplify estimation in addition fixed upper and or lower bounds may be needed to ensure that estimates satisfy a priori hypotheses with multivariate variance components models several covariance matrices need to be simultaneously estimated and even with a reduced parameter space estimation can be difficult in earlier work we have discussed estimation for a widely used class of models where the variance components matrices need only be nonnegative definite in this article we extend these results to handle a wide class of restricted parameter spaces we state the conditions required for a parameterization to be a member of the class discuss the implementation of the results for several different members of the class and discuss estimation with both balanced and unbalanced data we give several examples to demonstrate the results

on non radially symmetric bifurcation in the annulus we discuss the radially symmetric solutions and the non radially symmetric bifurcation of the semilinear elliptic equation u 2 eu 0 in and u 0 on where x r2 a2 0 a the upper branch of radial solutions has a non radially symmetric bifurcation symmetry breaking at each k a k 1 as a 0 the radial solutions will tend to the radial solutions on the disk and 0 a 1 the critical number on the disk

the three solutions theorem for p laplacian boundary value problems abstract the three solutions theorem is established for p laplacian boundary value problems in the presence of two pairs of lower and upper solutions which are well ordered by the relationship between the lower and upper solutions and degree theory in addition an application of the three solutions theorem is given

on radial solutions for singular combined superlinear elliptic systems on annular domains abstract we prove the existence of a large positive solution to the system r n 1 1 u r n 1 f 1 v a r b r n 1 2 v r n 1 f 2 u a r b u a 0 u b v a 0 v b where a 0 is a small positive parameter f i 0 r are continuous and lim z 1 1 f 1 c 2 1 f 2 z z for all c 0

uniqueness of positive radial solutions for dirichlet problems on annular domains abstract this paper deals with the uniqueness of positive radial solutions to dirichlet problems on annular domains in r n n 3 as an application we can obtain the results to equation u u p 1 u 0 0 where p 1 1 0 0 0 and 1 0 0

goodness of fit tests for mixed model diagnostics a simple goodness of fit test is proposed for checking distributional assumptions involved in a mixed linear model an estimated critical value of the test statistic is derived and is shown to be asymptotically correct under mild conditions as a special case the test may be applied to linear regression models to formally check distribution of the errors finite sample performance of the proposed test is examined and compared with that of a previously proposed test by simulations

existence of positive nonradial solutions for nonlinear elliptic equations in annular domains we study the existence of positive nonradial solutions of equation a f u 0 in sia u 0 on d la where s x 6 w a 2 and is positive and superlinear at both 0 and oo we use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak 0 1 for any positive integer k if is subcritical and for large k if is supercritical when is subcritical then a nehari type variational method can be used to prove that there exists a e 0 1 such that for any a e a 1 the equation has a nonradial solution on 0 a

transformations to symmetry and homoscedasticity abstract this article considers transformations in regression to eliminate skewness and heteroscedasticity of the response we work with the transform both sides model where the relationship between the median response and the independent variables has been identified at least tentatively to preserve this relationship the response and the regression model are transformed in the same way extending the work of others for the location parameter case we propose an estimator that eliminates skewness we also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity both and appear new by comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity we study the question when does the estimator of behave in terms of asymptotic variance as if the regression parameter were known and vice versa the results are of use for telling when the optimal estimator of do

positive solutions for a higher order four point boundary value problem with a p laplacian in this paper we study the existence of positive solutions of the following nth order four point boundary value problem with one dimensional p laplacian f p u n 1 h t f t u t u t u n 2 t 0 0 3 u i 0 0 0 i n 3 u n 1 0 au n 2 x 0 n 3 u n 1 1 bu n 2 h 0 n 3 where f p s s p 2s p 1 0 a 1 x 0 b 11 h 0 x h 1 by using a fixed point theorem in cones the existence of a positive solution and multiple positive solutions is obtained also at the end of this paper we present a generalization of this problem

positive solutions of systems of singular hammerstein integral equations with applications to semilinear elliptic equations in annuli abstract the existence of multiple positive solutions of systems of singular hammerstein integral equations is studied where the nonlinearities involved are allowed to have singularities in their second variables and satisfy weaker conditions involving the first eigenvalues of the corresponding linear hammerstein integral operators such systems contain some mathematical models arising in science and engineering applications are given to the existence of multiple positive radial solutions of systems of semilinear singular elliptic equations in annuli on which to the best of our knowledge there has been little study

power transformations to symmetry summary power transformations for achieving distributional symmetry are discussed estimates of the transformation power are based on general measures of symmetry they are shown to be consistent and asymptotically normal use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case the methods are compared to the likelihood methods of box cox 1964 and alternative methods of hinkley 1975 1977 the box cox method or a robust adaptation of it carroll 1980 bickel doksum 1981 is found to be the generally most suitable method

the effect of covariance structure on variance estimation in balanced growth curve models with random parameters abstract intuition suggests that altering the covariance structure of a parametric model for repeated measures data alters the variances of the model s estimated mean parameters the purpose of this article is to sharpen such intuition for a family of growth curve models with differing numbers of random effects for the individual sampling units and with a fixed structure on the mean for every member of this family the maximum likelihood ml estimator of the fixed effects is identical to the ordinary least squares ols estimator in addition simple closed form ml and restricted maximum likelihood estimators for the variance and covariance parameters exist for every member as a consequence closed form expressions for the estimated variance covariance matrix of the ols estimator of the fixed effects also exist for the entire family we derive explicit relationships between the variance and covariance parameter estimators from different members of the family and thereby extend some familiar results fo

least squares estimation of covariance matrices in balanced multivariate variance components models abstract the problem of estimating covariance matrices in balanced multivariate variance components models is discussed as with univariate models it is possible for the traditional estimators based on differences of the mean square matrices to produce estimates that are outside the parameter space in fact in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite nnd in this article we develop an iterative estimation procedure satisfying a least squares criterion that is guaranteed to produce nnd estimates of the covariance matrices discuss the speed of convergence and provide an example to show how the estimates change

the minimal number of characters over a normal p subgroup abstract if n is a normal p subgroup of a finite group g and irr n is a g invariant irreducible character of n then the number irr g of irreducible characters of g over is always greater than or equal to the number k p g n of conjugacy classes of g n consisting of p elements in this paper we investigate when there is equality

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

counting characters above invariant characters in solvable groups abstract this paper discusses two related questions first given a g invariant character of a normal subgroup n of a solvable group what can we say if the number of characters of g above is in some sense as small as possible isaacs and navarro 5 have shown that under certain assumptions about primes dividing the order of the group one can show that g n must have a very particular structure here we show that these assumptions can be weakened to obtain results about all solvable groups we also discuss a related question about blocks for a prime p and a p block b of g we let k b denote the number of ordinary characters in b it is relatively easy to show that k b is bounded below by k g d which is the number of conjugacy classes of g that intersect the defect group d of b in this paper we ask what can be said if equality is achieved we show that for p solvable groups if k b k g d then b is nilpotent and thus k b irr d in addition we show that this result holds for many blocks of arbitrary finite groups including all blocks of the symmetric groups we also extend a result on fully ramified coprime actions in 5

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

joint estimation of location dispersion and random effects in robust design this article presents a methodology for simultaneously modeling three components of a general mixed model approach to robust design location fixed effects dispersion effects and random effects control noise and random factors can be accommodated with this approach parameters associated with all three are estimated jointly using residual maximum likelihood and assuming normality simulated and real datasets illustrate the key concepts and advantages over previously proposed approaches

an extension of partial likelihood methods for proportional hazard models to general transformation models on utilise un schema de reechantillonnage appele echantillonneur de vraisemblance pour calculer la vraisemblance partielle et les estimateurs de vraisemblance partielle maximum

on tests applied to residuals abstract the null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals it might be expected however that the dependence decreases as the sample size increases so that the limiting null distribution is the same as if the test were based on independent observations the author investigates whether this large sample equivalence holds for tests of correlation scale difference regression and location difference particular emphasis is placed on showing when rank tests based on residuals have a strongly asymptotically distribution free property u statistic theorems are used to investigate these issues

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

on the existence of positive radial solutions for nonlinear elliptic equations in annular domains abstract we study the existence of positive radially symmetric solutions of u g x f u 0 in annulus with dirichlet dirichlet neumann boundary conditions we show that the equation has a positive radial solution on any annulus if f and f are positive and f is superlinear at 0 and

bayesian inference for finite population parameters in multistage cluster sampling abstract assuming a model appropriate for many multistage sample surveys bayesian predictive inference for a general linear function of the finite population elements is described in a broad class of linear estimators of the posterior mean e of is shown to have the optimal frequentist property of minimal bounded mean squared error for the special case of three stage sampling e is described in detail also presented are the results of an investigation of the effect on inferences of alteration of the values of some parameters in the prior distribution

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

variance component estimation with model based diagnostics the problem of estimating variance components in mixed linear models has no satisfactory solution for the unbalanced data case further there has been little work on diagnostic methods for assessing the data and the model in this article we propose a new class of unbiased estimators these estimators have simple closed form expressions allowing for smallsample analysis and easy computations the structure of the estimators reveals natural diagnostics for examining the data and the model assumptions the source of negative estimates of variance components is revealed limited efficiency studies indicate that these estimators are comparable to existing estimators the estimators are illustrated by two numerical examples that reveal the importance of the diagnostic analysis

existence uniqueness and nondegeneracy of positive solutions of semilinear elliptic equations we study positive solutions of the dirichlet problem a u x f u x 0 x d u x o x e ad where d is an n ball we find necessary and sufficient conditions for solutions to be nondegenerate we also give some new existence and uniqueness theorems in this paper we study positive solutions of the dirichlet problem au x f u x o x f2

on the existence of positive solutions and their continuous dependence on functional parameters for some class of elliptic problems we discuss the existence and the dependence on functional parameters of solutions of the dirichlet problem for a kind of the generalization of the balance of a membrane equation since we shall propose an approach based on variational methods we treat our equation as the euler lagrange equation for a certain integral functional j we will not impose either convexity or coercivity of the functional we develop a duality theory which relates the infimum on a special set x of the energy functional associated with the problem to the infimum of the dual functional on a corresponding set xd the links between minimizers of both functionals give a variational principle and in consequence their relation to our boundary value problem we also present the numerical version of the variational principle it enables the numerical characterization of approximate solutions and gives a measure of a duality gap between primal and dual functional for approximate solutions of our problem

nonlinear component of variance models summary general aspects of nonlinearity in the context of component of variance models are discussed and two special topics are examined in detail firstly simple procedures both formal and informal are proposed for describing departures from normal theory linear models transformation models are shown to be a special case of a more general formulation and data on blood pressure are analyzed in illustration secondly an approximate likelihood is proposed and its accurate performance is examined numerically using examples of exponential regression and the analysis of several related 2 x 2 tables in the latter example the approximate score test has improved power over the mantelhaenszel test

double positive solutions of n p boundary value problems for higher order difference equations abstract we shall provide existence criteria for double positive solutions of the n p boundary value problem n y f k y y n 2 y g k y y n 1 y n 1 k n i y 0 0 0 i n 2 p y n n p 0 where n 2 and 0 p n 1 is fixed upper and lower bounds for the two positive solutions are also established for a particular boundary value problem when n 2 several examples are included to dwell upon the importance of the results obtained

positive solutions of quasilinear boundary value problems abstract this paper deals with the existence of positive solutions for the boundary value problem formula formula where f is either superlinear or sublinear at and f t 0 may be negative and p is a positive continuous function the results extend several known results for semilinear equations our approach is based on fixed point theory for completely continuous operators which leave invariant a suitable cone in a banach space of continuous functions

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

weighted normal plots abstract weighted normal plots are proposed as graphical checks on the normality of random effects in gaussian linear models the technique is illustrated using the one way comparisons model yi i i where the i i are independent pairs with i and i independent n 0 2 and n 0 2 i respectively for i 1 n when the variance components 2 and 2 i are known an unweighted normal plot of the standardized zi yi 2 2 i 1 2 provides a check of the overall adequacy of the model weighted normal plots involve a modification that gives the ith observation a sample weight of wi 2 2 i 1 under the null hypothesis the sample size must be larger by a factor of 1 v m 2 where m and v are the mean and variance of the weights to produce a weighted plot with approximately the same sampling variance as an unweighted normal plot despite this higher variability we show that weighted plots are more sensitive than unweighted plots to several departures from the assume

positive solutions and nonlinear eigenvalue problems for third order difference equations first solutions that lie in a cone intersected with an annular type region are obtained for the third order difference equation 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 in the cases that f is either superlinear or sublinear the second part is devoted to determining values of for which there exist positive solutions of 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 when both limx 0 f x x and limx f x x exist as positive real numbers

positive solutions of semipositone higher order differential equations on time scales abstract in this paper we are concerned with the following 2 n th order differential equations on time scales 1 n y 2 n t g t f t y t t a b y 2 i a i 1 y 2 i 1 a i 1 y 2 i i 1 y 2 i y 2 i b 0 i n 1 where a b n 1 i 0 1 i b a i a i 0 i b i i 1 a i b i 1 2 n the functions g a b 0 and f a b 0 are continuous or g is singular at t a and or t b we obtain some properties and sharp estimates of the corresponding green s function and investigate the existence of positive solutions of the semipositone problems for 2 n order differential equations by the use of the property of green s function variable transformation and the fixed point index theorem

on the existence of multiple solutions of the boundary value problem for nonlinear second order differential equations abstract we consider the boundary value problem for nonlinear second order differential equations of the form u a x f u 0 0 u 0 u 1 0 we establish the precise condition concerning the behavior of the ratio f s s at infinity and zero for the existence of solutions with prescribed nodal properties then we derive the existence and the multiplicity of nodal solutions to the problem our argument is based on the shooting method together with the strum s comparison theorem the results obtained here can be applied to the study of radially symmetric solutions of the dirichlet problem for semilinear elliptic equations in annular domains

existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains au f x u 0 in s u 0 on xj when n is some annulus and the above conditions in 4 29 are not necessarily satisfied in fact in our main result theorem 2 4 f is not necessarily c lim f t u u may not exist or may be u rn finite and f t u could be zero for u in some finite interval 0 p we also allow lim f t u u 0 corollary 2 6 and lim f t u u may not exist in example 2 3 below u o u 0 neither lim f u u nor lim f u u exists on the other hand we show that u 0 u m

the cost of generalizing logistic regression abstract binary response regression models in which the link function is a family defined by one or more unknown shape parameters are considered detailed attention is given to the two single parameter families proposed by aranda ordaz 1981 that incorporate the logistic linear and complementary log log link functions as special cases one model is a symmetric family of alternatives to the logistic shape and the second model is an asymmetric family the increase in variance of quantities of interest due to the addition of an extra parameter is calculated using asymptotic methods this inflation in variance is interpreted as the cost of adding an additional parameter to the model in considering the seriousness of this cost the reduction in bias due to the estimation of the additional parameter should also be taken into account three quantities of interest predicted probabilities for a fixed value of the explanatory variable predicted value of the explanatory variable to obtain a specific probability

empirical bayes estimation for the finite population mean on the current occasion abstract many finite populations which are sampled repeatedly change slowly over time then estimation of finite population characteristics for the current occasion l may be improved by the use of data from previous surveys in this article we investigate the use of empirical bayes procedures based on two superpopulation models each model has the same first stage the values of the population units on the ith occasion are a random sample from the normal distribution with mean i and variance 2 i at the second stage we assume that either a 1 l are a random sample from the normal distribution with mean and variance 2 or b given 2 i and i has the normal distribution with mean and variance 2 i independently for each i whereas the 2 i are a random sample from the inverse gamma distribution with parameters 2 and 2 in a the 2 i and 2 are assumed to be unknown whereas in b and are unknown we develop empirical bayes point estimators and confide

the retransformed mean after a fitted power transformation abstract an approximate method is given to estimate the mean of a dependent variable after a linear model is fitted to the box cox power transformation of this variable the estimate is accurate except when the transformation power parameter is near zero the properties of the estimate in the one sample and regression cases are considered by both asymptotic calculations and monte carlo simulations and comparisons are made with the smearing estimate duan 1983 it is shown that there can be some cost due to estimating the power transformation as opposed to assuming it is known however this cost is not severe

reml estimation in unbalanced multivariate variance components models using an em algorithm estimation of covariance matrices when data are missing is a difficult problem in the multivariate mixed model setting problems can arise either because the data are unbalanced or because the response vectors are incomplete jennrich and schluchter 1986 biometrics 42 805 820 and laird lange and stram 1987 journal of the american statistical association 82 97 105 have proposed em algorithms for estimating the parameters associated with longitudinal data models in this paper a new em algorithm is proposed for the general multivariate mixed model the algorithm is derivativefree and based on an algorithm for balanced data proposed by calvin and dykstra 1991 annals qf statistics 19 850 869 once the algorithm is described it is used to produce estimates of the variance components matrices associated with a completely random two factor nested model for a bivariate response vector the data for this example come from calvin and sedransk 1991 journal of the american statistical association 86 36 48 who analyze a study of the quality of care received by cancer patients receiving radiation therapy

elliptic equations of order 2m in annular domains in this paper we study the existence of positive radial solutions for some semilinear elliptic problems of order 2m in an annulus with dirichlet boundary conditions we consider a nonlinearity which is either sublinear or the sum of a sublinear and a superlinear term

orthogonality and transformations in variance components models summary we consider variance components and other models for repeated measures in which a general transformation is applied to the response variable using cox reid s 1987 concept of parameter orthogonality and some approximations to the information matrix we show that the intraclass correlation coefficient in the one way model is robust to the choice of transformation this robustness result generalises to a vector of parameters determining the correlation structure to more complex variance components models to multivariate normal models to some longitudinal models and models involving linear regression functions for which we show that ratios of regression parameters are robustly estimated the results suggest that a natural way to parameterise the covariance structure in repeated measures models may be in terms of the variance and the correlation determined by separate sets of parameters

bayesian and frequentist predictive inference for the patterns of care studies abstract the patterns of care studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy in this article we propose and evaluate models which if acceptable permit bayesian and frequentist model based predictive inference for the desired finite population parameters using both hierarchical bayesian and frequentist mixed linear models we describe methodology for making the desired inferences emphasizing the use of transformed random variables finally we compare the frequentist bayes and empirical bayes approaches using data from one of the surveys all three methods produce essentially the same value for the finite population mean the standard empirical bayes and frequentist measures of variability are very much smaller than those derived from the bayesian approach the latter reflecting uncertainty about the values of the scale parameters in the model

estimates and confidence intervals for median and mean life in the proportional hazard model summary estimation procedures and confidence intervals are given for the median and mean survival time in the proportional hazard regression model for median survival the methods apply to censored data the procedures are based on cox s partial likelihood estimates of the linear model parameters in the log linear proportional hazard model and on breslow s estimate of the baseline hazard function the asymptotic properties of these semiparametric estimates are developed and they are compared with the optimal parametric estimates for the weibull regression model for the parameter values considered the more generally valid semiparametric estimate of mean survival loses little efficiency relative to the optimal parametric estimates in this model unless the weibull shape parameter is close to zero the efficiency loss for the semiparametric estimate of median survival is greater but not severe unless censoring is heavy we also compare the optimal parametric estimates of mean and median survival with the weibull shape parameter known and unknown and find that the efficiency loss for the unknown shape estimate is small

an application of topological transversality to non positive higher order difference equations in this paper we shall provide sufficient conditions on the non positive function i u 1 u n 1 so that the boundary value problem bvp given by e d nu i m i u i du i d n 2 i 0 and bc d mu 0 0 0 m n 3 a d n 2 0 b d n 1u 0 0 c d n 2u t 1 d d n 1u t 1 0 has at least one positive solution

transformations for components of variance and covariance summary variance component models make various independence assumptions and typically assume effects are normally distributed here we assume that the data possibly after suitable transformation satisfy such a model an analysis of transformations for balanced variance component models is presented components of covariance being incorporated in the multivariate case an analysis of some blood pressure data is discussed transformations of data are often applied in the analysis of variance of linear models with fixed effects little or no investigation has been done on transformations for component of variance models the formal analysis for finding a transformation which maximizes the log likelihood for fixed effects models box cox 1964 requires modification for components of variance models in 2 we consider the simplest nontrivial case namely the balanced one way classification we note extensions to more complex univariate balanced models in 3 we deal only with cases where all the variance components are appreciable and the possibility that the maximum likelihood estimates occur on the boundary of the parameter space can be disregarded we examine in 4 an analysis of transformations for the multivariate balanced one way classification components of covariance thus being incorporated in the model in 5 we describe an analysis of some bivariate blood pressure data components of covariance are an important contribution to the analysis

existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains abstract this paper is concerned with the problem of elliptic equations in annular domains involving derivative terms using nonlinear analysis methods some results regarding existence of solutions are established more precisely at least one radial solution is obtained basing on schauder s fixed point theorem and contraction mapping theorem respectively some iterative technique is also applied which allows us to overcome difficulties that the nonlinearity is related to derivative terms

existence of positive solutions for boundary value problem of second order fde abstract we use a fixed point theorem in cones to investigate the existence of positive solutions for boundary value problem of a second order functional differential equation fde with the form y t r t y t 0 0 y t y t t r t 0 y t y t n t 1 t 1 a where y t y t for a we allow that r t has the singularity at the endpoints t 0 and t 1 of 0 1 our results include the situations that f is either superlinear or sublinear

the cost of adding parameters to a model summary for a general regression model with n independent observations we consider the variance of the estimate of a quantity of interest under two scenarios one scenario is where all the parameters are estimated from the data the other scenario is where a subset of the parameters is assumed known at their true values and the remaining parameters are estimated we focus on quantities of interest which are defined on the scale of the response variable we show that under certain conditions the ratio of a weighted sum across the design points of the variance of the quantity of interest is given by q p where q and p are the number of free parameters in the two scenarios thus in this average sense the inflation in variance associated with adding parameters also interpreted as the cost of adding parameters to a model is directly proportional to the number of parameters we study models involving power transformations non linear models and exponential family models

the existence of positive solutions for the sturm liouville boundary value problems abstract for the sturm liouville boundary value problem p t u t f t u t 0 0 t 1 1 u 0 1 p 0 u 0 0 2 u 1 2 p 1 u 1 0 where 0 we shall use a fixed point theorem in a cone to obtain the existence of positive solutions for on a suitable interval

genotype by environment variance heterogeneity in a two stage analysis the analysis of a series of crop variety trials often proceeds using a mixed model in which the data are the combined means from individual trials the residual variation for this model consists of genotype by environment g e interactions and within trial error variation the latter is regarded as known from the analyses of individual trials and any associated heterogeneity can be accounted for in the overall mixed model by the use of weights the g e interactions may also have nonconstant variance and since the variances themselves are often of interest we propose that heterogeneity arising from these sources be accommodated by modelling the g e variances as a log linear function of explanatory variables we present a residual maximum likelihood estimation method and develop a diagnostic technique for detecting dependence the approach is demonstrated using a large unbalanced set of crop variety testing data the methodology is easily generalized to residual variance modelling in any mixed model application

measures of location of skew distributions obtained through box cox transformations abstract box cox power transformations are used to transform a set of observations to symmetry a measure of location of the original data is obtained by applying the inverse transformation to the center of the transformed data its properties are discussed and it is compared with other measures of location