large time behavior of solutions to the compressible navier stokes equations around a parallel flow in a cylindrical domain abstract stability of parallel flow of the compressible navier stokes equation in a cylindrical domain is studied it is shown that if the reynolds and mach numbers are sufficiently small then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous burgers equation

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

global existence of solutions to the compressible navier stokes equation around parallel flows abstract the initial boundary value problem for the compressible navier stokes equation is considered in an infinite layer of r n it is proved that if n 3 then strong solutions to the compressible navier stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations provided that the reynolds and mach numbers are sufficiently small the proof is given by a variant of the matsumura nishida energy method based on a decomposition of solutions associated with a spectral property of the linearized operator

nonparametric estimation of mean squared prediction error in nested error regression models nested error regression models are widely used for analyzing clustered data for example they are often applied to two stage sample surveys and in biology and econometrics prediction is usually the main goal of such analyses and mean squared prediction error is the main way in which prediction performance is measured in this paper we suggest a new approach to estimating mean squared prediction error we introduce a matched moment double bootstrap algorithm enabling the notorious underestimation of the naive mean squared error estimator to be substantially reduced our approach does not require specific assumptions about the distributions of errors additionally it is simple and easy to apply this is achieved through using monte carlo simulation to implicitly develop formulae which in a more conventional approach would be derived laboriously by mathematical arguments

some majorization inequalities in multivariate statistical analysis this paper contains a review of certain majorization inequalities in multivariate statistical analysis the results apply to a large class of distributions including the multivariate normal distribution and have implications in estimation hypothesis testing and other related problems in statistics

some recent developments on majorization inequalities in probability and statistics abstract we review some recent developments on majorization inequalities in probability and statistics in section 2 we describe some related generalizations including majorization in an integral form multivariate majorization stochastic majorization and other related orderings include the lorentz ordering and arrangement increasing ordering and state some results section 3 concerns partial orderings of probability contents of certain classes of geometric regions in r n via a majorization ordering of their parameter vectors section 4 deals with some applications of majorization theory to dependence and peakedness orderings of random variables in most cases the described results have become available since the publication of marshall and olkin s book 1979 and are directly or indirectly inspired by it

the large time behavior of solutions in the critical l p framework for compressible viscous and heat conductive gas flows in this paper we are concerned with non isentropic navier stokes equations governing compressible viscous and heat conductive gases we formulate an additional regularity assumption of low frequencies in rd d 3 and then establish the sharp time weighted inequality which allows us to get the time decay estimates of global strong solutions in the lp critical besov spaces precisely it is shown that if the initial data belong to some besov space b2 s1 with s1 1 d2 s0 s0 2dp d2 then the lp norm of the critical global solutions admits the time decay t s12 d2 12 1p in particular t d2p if s1 s0 which coincides with that of the heat kernel in the lp framework in comparison with the work of danchin and xu j math fluid mech 20 1641 1665 2018 the low frequency assumption is improved such that the regularity s1 belongs to the whole range 1 d2 s0

the pointwise estimates of diffusion wave for the navier stokes systems in odd multi dimensions we study the dissipation of solutions of the isentropic navier stokes equations in odd multi dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygen s principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

on some decay properties of stokes semigroup of compressible viscous fluid flow in a 2 dimensional exterior domain in this paper we proved the local energy decay and some lp lq decay properties of solutions to the initial boundary value problem for the stokes equations of compressible viscous fluid flow in a 2 dimensional exterior domain kobayashi 1997 19 and kobayashi and shibata 1999 21 treated the same problem in a 3 dimensional exterior domain and our results obtained in this paper are an extension of results in kobayashi 1997 19 and kobayashi and shibata 1999 21 to the 2 dimensional case the fundamental solution to the resolvent equations for the stokes equations in r2 has a logarithmical singularity at 0 being a resolvent parameter while it is continuous up to 0 in r3 this difference requires us a new idea to prove the local energy decay estimate once getting the local energy decay estimate the required lp lq decay estimates in the exterior domain are obtained by combining the local energy estimate and the lp lq estimates in r2 by a cut off technique

asymptotic behavior of solutions to the compressible navier stokes equation around a parallel flow the initial boundary value problem for the compressible navier stokes equation is considered in an infinite layer of mathbf r 2 it is proved that if the reynolds and mach numbers are sufficiently small then strong solutions to the compressible navier stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations the large time behavior of the solution is described by a solution of a one dimensional viscous burgers equation the proof is given by a combination of spectral analysis of the linearized operator and a variant of the matsumura nishida energy method

on large time behavior of solutions to the compressible navier stokes equations in the half space in r3 the navier stokes equation for compressible viscous fluid is considered on the half space in r3 under the zero dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum time decay properties in l2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in l2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in some lower bounds are derived for solutions to the linearized problem one of which indicates a nonlinear phenomenon not appearing in the case of the cauchy problem on the whole space

rate of convergence of non stationary flow to the steady flow of compressible viscous fluid we consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in r 3 in shibata and tanaka y shibata k tanaka on the steady flow of compressible viscous fluid and its stability with respect to initial disturbance j math soc japan 55 2003 797 826 we proved the unique existence and some regularity of the steady flow and its globally in time stability with respect to a small initial disturbance in the h 3 framework in this paper we investigate the rate of the convergence of the non stationary flow to the corresponding steady flow when the initial data are small enough in the h 3 and also belong to l 6 5

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

small area estimation with uncertain random effects random effects models play an important role in model based small area estimation random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables in a recent article datta hall and mandal showed that if the random effects can be dispensed with via a suitable test then the model parameters and the small area means may be estimated with substantially higher accuracy the work of datta hall and mandal is most useful when the number of small areas m is moderately large for large m the null hypothesis of no random effects will likely be rejected rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator as a flexible alternative to the fay herriot random effects model and the approach in datta hall and mandal in this article we consider a mixture model for random effects it is reasonably expected that small areas wit

bayesian versus frequentist measures of error in small area estimation summary this paper compares analytically and empirically the frequentist and bayesian measures of error in small area estimation the model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables when the variance components are known then under a uniform prior for the regression coefficients and normality of the error terms the frequentist and the bayesian approaches yield the same predictors and prediction mean squared errors mses defined accordingly when the variance components are unknown it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors so that the resulting empirical predictors remain the same under the two approaches the use of this paradigm requires however modifications to the expressions of the prediction mse to account for the extra variability induced by the need to estimate the variance components the main focus of this paper is to review and compare the modifications to prediction mses proposed in the literature under the two approaches with special emphasis on the orders of the bias of the resulting approximations to the true mses some new approximations based on monte carlo simulation are also proposed and compared with the existing methods the advantage of these approximations is their simplicity and generality finite sample frequentist properties of the various methods are explored by a simulation study the main conclusions of this study are that the use of second order bias corrections generally yields better results in terms of the bias of the mse approximations and the coverage properties of confidence intervals for the small area means the bayesian methods are found to have good frequentist properties but they can be inferior to the frequentist methods the second order approximations under both approaches have however larger variances than the corresponding first order approximations which in most cases result in higher mses of the mse approximations

asymptotic behavior of solutions of the compressible navier stokes equations on the half space asymptotic behavior of solutions of the compressible navier stokes equations on the half space r n n 2 is considered around a given constant equilibrium a solution formula for the linearized problem is derived and l p estimates for solutions of the linearized problem are obtained for 2 p it is shown that as in the case of the cauchy problem the leading part of the solution of the linearized problem is decomposed into two parts one that behaves like diffusion waves and the other one purely diffusively there however are some aspects different from the cauchy problem especially in considering spatial derivatives it is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary stokes problem in some l p spaces and as a result a solution formula for the nonstationary stokes problem is obtained large time behavior of solutions of the nonlinear problem is then investigated in l p spaces for 2 p by applying the results on the linearized analysis and the weighted energy method the results indicate that there may be some nonlinear interaction phenomena not appearing in the cauchy problem

small area estimation based on natural exponential family quadratic variance function models and survey weights summary we propose pseudo empirical best linear unbiased estimators of small area means based on natural exponential family quadratic variance function models when the basic data consist of survey weighted estimators of these means area specific covariates and certain summary measures involving the weights we also provide explicit approximate mean squared errors of these estimators in the spirit of prasad rao 1990 and these estimators can be readily evaluated a simulation study is undertaken to evaluate the performance of the proposed inferential procedure we estimate also the proportion of poor children in the 5 17 years age group for the different counties in one of the states in the united states

model selection by testing for the presence of small area effects and application to area level data the models used in small area inference often involve unobservable random effects while this can significantly improve the adaptivity and flexibility of a model it also increases the variability of both point and interval estimators if we could test for the existence of the random effects and if the test were to show that they were unlikely to be present then we would arguably not need to incorporate them into the model and thus could significantly improve the precision of the methodology in this article we suggest an approach of this type we develop simple bootstrap methods for testing for the presence of random effects applicable well beyond the conventional context of the natural exponential family if the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small area means such estimators can be substantially more effective for example because they enjoy much fa

time periodic solutions of compressible navier stokes equations abstract in this paper we study the navier stokes equations with a time periodic external force in r n we show that a time periodic solution exists when the space dimension n 5 under some smallness assumption the main idea is to combine the energy method and the spectral analysis for the optimal decay estimates on the linearized solution operator with the optimal decay estimates we prove the existence and uniqueness of time periodic solution in some suitable function space by the contraction mapping theorem in addition we also study the time asymptotic stability of the time periodic solution

time decay rates for the compressible viscoelastic flows abstract in this paper we investigate the time decay rates of the global smooth solutions to the compressible viscoelastic flows in r 3 the global existence and uniqueness of smooth solutions are obtained under the assumption that the h 3 norm of the initial data is small but the higher order derivatives can be arbitrarily large moreover if the initial data is bounded in h s 0 s 3 2 or b 2 s 0 s 3 2 we establish the optimal decay rates of the smooth solutions by a regularity interpolation trick and delicate energy methods

sumca simple unified monte carlo assisted approach to second order unbiased mean squared prediction error estimation we propose a simple unified monte carlo assisted approach called sumca to second order unbiased estimation of the mean squared prediction error mspe of a small area predictor the mspe estimator proposed is easy to derive has a simple expression and applies to a broad range of predictors that include the traditional empirical best linear unbiased predictor empirical best predictor and post model selection empirical best linear unbiased predictor and empirical best predictor as special cases furthermore the leading term of the mspe estimator proposed is guaranteed positive the lower order term corresponds to a bias correction which can be evaluated via a monte carlo method the computational burden for the monte carlo evaluation is much less compared with other monte carlo based methods that have been used for producing second order unbiased mspe estimators such as the double bootstrap and monte carlo jackknife the sumca estimator also has a nice stability feature theoretical and empirical results demonstrate properties and advantages of the sumca estimator

spectral properties of the linearized compressible navier stokes equation around time periodic parallel flow abstract the linearized problem around a time periodic parallel flow of the compressible navier stokes equation in an infinite layer is investigated by using the floquet theory spectral properties of the evolution operator associated with the linearized problem are studied in detail the floquet representation of a low frequency part of the evolution operator which plays an important role in the study of the nonlinear problem is obtained

rectangular regions of maximum probability content the problem of characterizing the rectangular region of maximum probability content among the rectangles of fixed area is considered the rectangles are assumed to have their sides parallel to the axes and the bivariate distribution is assumed to have density elliptically contoured and unimodal

l q l r estimates for solutions of the nonstationary stokes equations in an exterior domain and the navier stokes initial value problems inl q spaces

global existence of small solutions to a class of nonlinear evolution equations on etudie le comportement global des solutions d une classe d equations d evolution non lineaires on considere le probleme aux valeurs initiales pour des equations quasilineaires qui sont des perturbations d equations lineaires dissipatives

stability of planar stationary solutions to the compressible navier stokes equation on the half space stability of planar stationary solutions to the compressible navier stokes equation on the half space bf r n n geq 2 under outflow boundary condition is investigated it is shown that the planar stationary solution is stable with respect to small perturbations in h s left bf r n right with s n 2 1 and the perturbations decay in l norm as t provided that the magnitude of the stationary solution is sufficiently small the stability result is proved by the energy method in the proof an energy functional based on the total energy of the system plays an important role

some estimates of solutions for the equations of motion of compressible viscous fluid in the three dimensional exterior domain abstract we consider the equations of motion of compressible viscous fluid in an exterior domain in r 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem in particular we shall give l 1 estimates which implies the diffusion wave of compressible navier stokes flow

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

large time behavior of solutions to the compressible navier stokes equations around periodic steady states abstract this paper shows that the strong solution to the compressible navier stokes equation around spatially periodic stationary solution in a periodic layer of r n n 2 3 exists globally in time if reynolds and mach numbers are sufficiently small it is proved that the asymptotic leading part of the perturbation is given by a solution to the one dimensional viscous burgers equation multiplied by a spatially periodic function when n 2 and by a solution to the two dimensional heat equation multiplied by a spatially periodic function when n 3

parametric bootstrap approximation to the distribution of eblup and related prediction intervals in linear mixed models empirical best linear unbiased prediction eblup method uses a linear mixed model in combining information from different sources of information this method is particularly useful in small area problems the variability of an eblup is traditionally measured by the mean squared prediction error mspe and interval estimates are generally constructed using estimates of the mspe such methods have shortcomings like under coverage or over coverage excessive length and lack of interpretability we propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled eblup the bootstrap histogram is highly accurate and differs from the true eblup distribution by only o d 3 n 3 2 where d is the number of parameters and n the number of observations this result is used to obtain highly accurate prediction intervals simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models

uc hierarchy and monodromy preserving deformation the uc hierarchy is an extension of the kp hierarchy which possesses not only an infinite set of positive time evolutions but also that of negative ones through a similarity reduction we derive from the uc hierarchy a class of the schlesinger systems including the garnier sys

fence methods for mixed model selection many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure asymptotic properties for these types of procedures in settings like linear regression and arma time series have been studied but these do not naturally extend to nonstandard situations such as mixed effects models where simple definition of the sample size is not meaningful this paper introduces a new class of strategies known as fence methods for mixed model selection which includes linear and generalized linear mixed models the idea involves a procedure to isolate a subgroup of what are known as correct models of which the optimal model is a member this is accomplished by constructing a statistical fence or barrier to carefully eliminate incorrect models once the fence is constructed the optimal model is selected from among those within the fence according to a criterion which can be made flexible in addition we propose two variations of the fence the first is a stepwise procedure to handle situations of many predictors the second is an adaptive approach for choosing a tuning constant we give sufficient conditions for consistency of fence and its variations a desirable property for a good model selection procedure the methods are illustrated through simulation studies and real data analysis

bayesian prediction in linear models applications to small area estimation this paper introduces a hierarchical bayes hb approach for prediction in general mixed linear models the results find application in small area estimation our model unifies and extends a number of models previously considered in this area computational formulas for obtaining the bayes predictors and their standard errors are given in the general case the methods are applied to two actual data sets also in a special case the hb predictors are shown to possess some interesting frequentist properties

weighting for unequal selection probabilities in multilevel models when multilevel models are estimated from survey data derived using multistage sampling unequal selection probabilities at any stage of sampling may induce bias in standard estimators unless the sources of the unequal probabilities are fully controlled for in the covariates this paper proposes alternative ways of weighting the estimation of a two level model by using the reciprocals of the selection probabilities at each stage of sampling consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase scaling of the weights is proposed to improve the properties of the estimators and to simplify computation variance estimators are also proposed in a limited simulation study the scaled weighted estimators are found to perform well although non negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small the variance estimators perform extremely well the procedures are illustrated using data from the survey of psychiatric morbidity

large time behavior of the semigroup on lp spaces associated with the linearized compressible navier stokes equation in a cylindrical domain abstract large time behavior of solutions to the linearized compressible navier stokes equation around the motionless state in a cylindrical domain is investigated the l p decay estimates of the associated semigroup are established for all 1 p it is also shown that the time asymptotic leading part of the semigroup is given by a one dimensional heat semigroup