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 dynamic programming algorithm for input estimation on linear time variant systems a time domain input estimation algorithm for linear systems with general time varying parameters is developed the algorithm is an extension of an existing approach for time invariant state space models and several new features such as higher order input approximations and an extended time variant output relation including direct input influence are introduced numerical examples are given to illustrate the new features and show that the algorithm is valid in a general time variant setting in particular excellent results are obtained for an ill posed moving force identification problem with noise contaminated data treated with tikhonov regularization

an inverse non linear force vibration problem of estimating the external forces in a damped system with time dependent system parameters abstract an inverse non linear force vibration problem based on the iterative regularization method i e the conjugate gradient method cgm is used to estimate the unknown time dependent external forces in a damped system having time dependent system parameters by using the measured system displacement it is assumed that no prior information is available on the functional form of the unknown external forces in the present study thus it is classified as the function estimation in inverse calculation the accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements the numerical simulations are performed to test the validity of present algorithm by using different types of external forces and measurements results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses within a couple of seconds of cpu time at pentium ii 300 mhz pc

on conjugacies between piecewise smooth circle maps abstract let f i i 1 2 be piecewise c 1 circle homeomorphisms with two break points log d f i i 1 2 are absolutely continuous on each continuity interval of d f i and d log d f i l p for some p 1 suppose the jump ratios of f 1 and f 2 at their break points do not coincide but f 1 f 2 have the same total jumps i e the product of jump ratios and identical irrational rotation number of bounded type then the map h conjugating f 1 and f 2 is a singular function that is it is continuous on s 1 but d h x 0 almost everywhere with respect to lebesgue measure

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

on c2 diffeomorphisms of the circle which are of type iii1 for every irrational number 0 1 which is not of constant type we construct ac 2 diffeomorphism of the circle with rotation number which is of type iii1 this diffeomorphism can be chosen arbitrarily close to the rotationr our methods also allow us to construct for every liouville number 0 1 ac diffeomorphism of the circle with rotation number which is of type iii1

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

conjugations between circle maps with a single break point abstract consider two circle homeomorphisms f i c 2 s b i 0 i 1 2 with a single break point b i i e a discontinuity in the derivative df i and identical irrational rotation number suppose the jump ratios 1 df 1 b 1 0 df 1 b 1 0 and 2 df 2 b 2 0 df 2 b 2 0 do not coincide then the map conjugating f 1 and f 2 is a singular function i e it is continuous on s 1 and d x 0 a e with respect to lebesgue measure

a non linear inverse vibration problem of estimating the external forces for a system with displacement dependent parameters the conjugate gradient method i e the iterative regularization method is used in an inverse non linear force vibration problem of estimating the unknown time dependent external forces in a damped system with the displacement dependent spring constant and damping coefficients the accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements since the system parameters are functions of displacement the present study from a purely mathematical viewpoint is thus a genuine non linear inverse vibration problem the numerical simulations are performed to test the validity of the present algorithm by using different types of system parameters external forces and measurement errors results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses with a couple of second s cpu time at pentium iii 500 mhz pc

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

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

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

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

renormalization and conjugacy of piecewise linear lorenz maps abstract we investigate the uniform piecewise linearizing question for a family of lorenz maps let f be a piecewise linear lorenz map with different slopes and positive topological entropy we show that f is conjugate to a linear mod one transformation and the conjugacy admits a dichotomy it is either bi lipschitz or singular depending on whether f is renormalizable or not f is renormalizable if and only if its rotation interval degenerates to be a rational point furthermore if the endpoints are periodic points with the same rotation number then the conjugacy is quasisymmetric

singular measures in circle dynamics critical circle homeomorphisms have an invariant measure totally singular with respect to the lebesgue measure we prove that singularities of the invariant measure are of holder type the hausdorff dimension of the invariant measure is less than 1 but greater than 0

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