on asymptotic normality and variance estimation for nondifferentiable survey estimators survey estimators of population quantities such as distribution functions and quantiles contain nondifferentiable functions of estimated quantities the theoretical properties of such estimators are substantially more complicated to derive than those of differentiable estimators in this article we provide a unified framework for obtaining the asymptotic design based properties of two common types of nondifferentiable estimators estimators of the first type have an explicit expression while those of the second are defined only as the solution to estimating equations we propose both analytical and replication based design consistent variance estimators for both cases based on kernel regression the practical behaviour of the variance estimators is demonstrated in a simulation experiment

a model calibration approach to using complete auxiliary information from survey data suppose that the finite population consists of n identifiable units associated with the ith unit are the study variable yi and a vector of auxiliary variables xi the values x1 x2 xn are known for the entire population i e complete but yi is known only if the ith unit is selected in the sample one of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage in this article a unified model assisted framework has been attempted using a proposed model calibration technique the proposed model calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of deville and sarndal and or the generalized regression estimators in the linear model case the pseudoempirical maximum likelihood estimator of chen and sitter when used in this setting gives an estimator that is asymptotically equivalent to the model calibration estimator but with positive weights some existing estimators

a standard test set for numerical approximations to the shallow water equations in spherical geometry a suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry the shallow water equations exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth these cases are designed for use in the evaluation of numerical methods proposed for climate modeling and to identify the potential trade offs which must always be made in numerical modeling before a proposed scheme is applied to a full baroclinic atmospheric model it must perform well on these problems in comparison with other currently accepted numerical methods the cases are presented in order of complexity they consist of advection across the poles steady state geostrophically balanced flow of both global and local scales forced nonlinear advection of an isolated low zonal flow impinging on an isolated mountain rossby haurwitz waves and observed atmospheric states one of the cases is also identified as a computer performance algorithm efficiency benchmark for assessing the performance of algorithms adapted to massively parallel computers

asymptotic properties of the balanced repeated replication method for sample quantiles inference including variance estimation can be made from stratified samples by selecting a balanced set of subsamples this balanced subsampling method is generically called the balanced repeated replication method in survey data analysis which includes mccarthy s balanced half samples method and its extensions for more general stratified designs we establish the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of interest is the population quantile the consistency results also hold when balanced subsampling is replaced by random subsampling as a key technical prerequisite we prove a bahadurtype representation for sample quantiles in stratified random sampling

quantile estimation from repeated measurements abstract quantile estimators for a nonparametric components of variance situation are proposed consistency and asymptotic normality are proved situations with different numbers of measurements for different subjects are considered measurements on separate subjects are assumed to be independent whereas measurements on the same subject have a fixed dependence the estimators are obtained by inverting weighted empirical distribution functions an optimal estimator and a simple estimator based on within subject averages are studied small sample properties are studied by simulation as an illustration the estimators are applied to give normal limits for differential light sensitivity of the human eye

inference from stratified samples properties of the linearization jackknife and balanced repeated replication methods the asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization jackknife and balanced repeated replication brr methods in stratified samples are established the results are obtained as l oa within the context of a sequence of finite populations jil with l strata in ji l and are valid for any stratified multistage design in which the primary sampling units psu s are selected with replacement and in which independent subsamples are taken within those psu s selected more than once in addition some exact analytical results on the bias and stability of these alternative variance estimators in the case of ratio estimation are obtained for small l under a general linear regression model

statistical inference for poverty measures with relative poverty lines relative poverty lines such as one half median income have been increasingly used in poverty studies this paper contributes to the literature by developing statistical inference for testing decomposable poverty measures with relative poverty lines the poverty lines we consider are percentages of mean income and percentages of quantiles we show that the estimates of poverty indices with relative poverty lines are asymptotically normally distributed and that the covariance structure can be consistently estimated as a consequence asymptotically distribution free statistical inference can be established in a straightforward manner

empirical likelihood confidence intervals for complex sampling designs we define an empirical likelihood approach which gives consistent design based confidence intervals which can be calculated without the need of variance estimates design effects resampling joint inclusion probabilities and linearization even when the point estimator is not linear it can be used to construct confidence intervals for a large class of sampling designs and estimators which are solutions of estimating equations it can be used for means regressions coefficients quantiles totals or counts even when the population size is unknown it can be used with large sampling fractions and naturally includes calibration constraints it can be viewed as an extension of the empirical likelihood approach to complex survey data this approach is computationally simpler than the pseudoempirical likelihood and the bootstrap approaches the simulation study shows that the confidence interval proposed may give better coverages than the confidence intervals based on linearization bootstrap and pseudoempirical likelihood our simulation study shows that under complex sampling designs standard confidence intervals based on normality may have poor coverages because point estimators may not follow a normal sampling distribution and their variance estimators may be biased

on the structure of the counting function of sparse context free languages we give an exact description of the counting function of a sparse context free language let l be a sparse context free language and let fl be its counting function then there exist polynomials p0 p1 pk 1 with rational coefficients and an integer constant k0 such that for any n k0 one has fl n pj n where j is such that j n mod k as a consequence one can easily show the decidability of some questions concerning sparse context free languages finally we show that for any sparse context free language l there exists a regular language l such that for any n 0 one has fl n fl n and therefore fl is rational

quantile estimation with a complex survey design estimation of the finite population distribution function and related statistics such as the median and interquartile range is considered large sample properties of estimators constructed from stratified cluster samples and properties of large sample confidence intervals are established the results are obtained within the context of a sequence of finite populations generated from a superpopulation

a noninformative bayesian approach to interval estimation in finite population sampling abstract a noninformative bayesian approach to interval estimation in finite population sampling is discussed given the sample this method introduces the polya distribution as a pseudo posterior distribution over the unobserved members of the population in many cases this distribution yields interval estimates similar to those of standard frequentist theory in addition it can be used in situations where the standard methods are difficult to apply for example in producing an interval estimate for the ratio of two medians we also consider related point estimation problems and observe that estimators derived from the pseudo posterior often perform better than classical alternatives

functional central limit theorems for single stage sampling designs for a joint model based and design based inference we establish functional central limit theorems for the horvitz thompson empirical process and the h ajek empirical process centered by their finite population mean as well as by their super population mean in a survey sampling framework the results apply to single stage unequal probability sampling designs and essentially only require conditions on higher order correlations we apply our main results to a hadamard differentiable statistical functional and illustrate its limit behavior by means of a computer simulation

generic inference on quantile and quantile effect functions for discrete outcomes quantile and quantile effect qe functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation existing inference methods for these functions

spectral transform solutions to the shallow water test set abstract solutions to the test case suite proposed by williamson et al j comput phys 102 211 1992 for the shallow water equations in spherical geometry are presented the solutions have been generated using a conventional spectral transform technique combined with a semi implicit time differencing scheme for several of the test cases closed form solutions do not exist for these cases high resolution numerical integrations of the spectral transform model are used to provide reference solutions against which alternative numerical schemes and lower resolution spectral transform solutions can be evaluated the sensitivity of the high resolution numerical solutions associated with temporal truncation spatial truncation and internal dissipation are quantified in order to help bound their uncertainty in almost all of the test cases the spectral transform method proves to be a highly accurate solution technique this is particularly the case at resolutions typically associated with atmospheric general circulation models used to simulate the atmosphere s climate the most serious deficiency of the spectral transform method in the context of the test cases is the introduction of spurious minima and maxima into the solution caused by gibbs phenomenon when sharp gradients exist although this behavior is not necessarily a problem for accurately simulating fluid flow it can become a serious problem for atmospheric general circulation models if the spurious wave structures result in nonphysical states such as negative water vapor mixing ratio

asymptotic inference from multi stage samples i develop a gmm based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering i set up the estimation problem derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample design effects the analysis is then extended to nonparametric regression and to semiparametric estimation based on u processes empirical illustrations are provided using consumption expenditure data from the complexly designed indian national household survey

l statistics in complex survey problems we study linear combinations of order statistics l statistics in survey problems with a stratified multistage sampling design two general types of l statistics are considered smooth l statistics with weights generated by a smooth function and nonsmooth l statistics sample quantiles the trimmed sample mean the decile mean and variance the sample lorenz curve and the sample gini s family parameters are examples of smooth lstatistics or functions of smooth l statistics used in survey problems it is shown that under weak conditions the smooth l statistics are asymptotically normal and their asymptotic variances can be consistently estimated by jackknifing for the sample quantiles their asymptotic normality requires more conditions on the finite population distribution functions consistent estimators for the asymptotic variances of the sample quantiles are derived asymptotic validity of the woodruff s confidence intervals for population quantiles is also proved

bayesian empirical likelihood inference with complex survey data we propose a bayesian empirical likelihood approach to survey data analysis on a vector of finite population parameters defined through estimating equations our method allows overidentified estimating equation systems and is applicable to both smooth and non differentiable estimating functions our proposed bayesian estimator is design consistent for general sampling designs and the bayesian credible intervals are calibrated in the sense of having asymptotically valid design based frequentist properties under single stage unequal probability sampling designs with small sampling fractions large sample properties of the bayesian inference proposed are established for both non informative and informative priors under the design based framework we also propose a bayesian model selection procedure with complex survey data and show that it works for general sampling designs an efficient markov chain monte carlo procedure is described for the required computation of the posterior distribution for general vector parameters simulation studies and an application to a real survey data set are included to examine the finite sample performances of the methods proposed as well as the effect of different types of prior and different types of sampling design

a semiparametric transformation approach to estimating usual daily intake distributions abstract the distribution of usual intakes of dietary components is important to individuals formulating food policy and to persons designing nutrition education programs the usual intake of a dietary component for a person is the long run average of daily intakes of that component for that person because it is impossible to directly observe usual intake for an individual it is necessary to develop an estimator of the distribution of usual intakes based on a sample of individuals with a small number of daily observations on a subsample of the individuals daily intake data for individuals are nonnegative and often very skewed also there is large day to day variation relative to the individual to individual variation and the within individual variance is correlated with the individual means we suggest a methodology for estimating usual intake distributions that allows for varying degrees of departure from normality and recognizes the measurement error associated with one day dietary intakes the est

use of estimating functions for estimation from complex surveys abstract we describe a method for point and interval estimation of population parameters from complex surveys using estimating functions the theory was originally developed for infinite populations and has recently been applied to finite populations with estimating functions a unifying framework can be given for point and interval estimation of both finite and infinite population parameters we discuss test inversion methods to derive confidence intervals for one dimensional parameters and propose a method for eliminating nuisance parameters in the multidimensional setting we show that special cases of our proposal result in conditional and orthogonal methods proposed in the literature we describe a simulation study using real data to compare the coverage probabilities of confidence intervals obtained under various approaches

a global semi lagrangian spectral model of the shallow water equations with variable resolution a new formulation of a semi implicit semi lagrangian spectral method is given together with a conformal mapping of the underlying gaussian grid the mapping based on the schmidt transformation focuses grid resolution on a particular region the advective form of the vorticity divergence equations allows the conformal map to be incorporated in a semi lagrangian transport step while maintaining an efficient spectral transform algorithm the shallow water equations on the sphere are solved to test the variable resolution spectral model by focusing on a specified location local details of the flow are more accurately resolved accuracy and stability of the method are compared with uniform spectral solutions