robust models in probability sampling in the estimation of a population mean or total from a random sample certain methods based on linear models are known to be automatically design consistent regardless of how well the underlying model describes the population a sufficient condition is identified for this type of robustness to model failure the condition which we call internal bias calibration relates to the combination of a model and the method used to fit it included among the internally bias calibrated models in addition to the aforementioned linear models are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting other models can often be made robust by using a suboptimal fitting method thus the class of model based but design consistent analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts particular applications discussed are the estimation of the size of a population subdomain as arises in tax auditing for example and the estimation of a bootstrap tail probability

estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

a predictive estimator of finite population proportion despite missing data abstract this paper considers the problem of estimating a finite population proportion when there are missing values the prediction approach is used to define a new estimator that presents desirable efficiency properties simulation studies are considered to evaluate the performance of the proposed estimator via empirical relative bias and empirical relative efficiency and favourable results are achieved

model assisted estimation for complex surveys using penalised splines summary estimation of finite population totals in the presence of auxiliary information is considered a class of estimators based on penalised spline regression is proposed these estimators are weighted linear combinations of sample observations with weights calibrated to known control totals they allow straightforward extensions to multiple auxiliary variables and to complex designs under standard design conditions the estimators are design consistent and asymptotically normal and they admit consistent variance estimation using familiar design based methods data driven penalty selection is considered in the context of unequal probability sampling designs simulation experiments show that the estimators are more efficient than parametric regression estimators when the parametric model is incorrectly specified while being approximately as efficient when the parametric specification is correct an example using forest health monitoring survey data from the u s forest service demonstrates the applicability of the methodology in the context of a two phase survey with multiple auxiliary variables

using sample survey weights in multiple regression analyses of stratified samples abstract the rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model the appropriateness of the weighted regression estimate depends on which model is chosen a proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator when applied to an analysis of the familial and environmental determinants of the educational level attained by a sample of young adults the methods lead to a revision of the initial additive model in which interaction terms between county unemployment and race as well as between sex and mother s education are included

nonparametric variance estimation under fine stratification an alternative to collapsed strata abstractfine stratification is commonly used to control the distribution of a sample from a finite population and to improve the precision of resulting estimators one per stratum designs represent the finest possible stratification and occur in practice but designs with very low numbers of elements per stratum say two or three are also common the classical variance estimator in this context is the collapsed stratum estimator which relies on creating larger pseudo strata and computing the sum of the squared differences between estimated stratum totals across the pseudo strata we propose here a nonparametric alternative that replaces the pseudo strata by kernel weighted stratum neighborhoods and uses deviations from a fitted mean function to estimate the variance we establish the asymptotic behavior of the kernel based estimator and show its superior practical performance relative to the collapsed stratum variance estimator in a simulation study an application to data from the u s consumer expe

asymptotic properties of weighted m estimators for variable probability samples i provide a systematic treatment of the asymptotic properties of weighted m estimators under variable probability stratified sampling the characterization of the sampling scheme and representation of the objective function allow for a straightforward analysis simple consistent asymptotic variance matrix estimators are proposed for a large class of problems when stratification is based on exogenous variables i show that the unweighted m estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality when population frequencies are known a more efficient weighting is possible i also show how the results carry over to multinomial sampling

optimum calibration points estimating distribution functions the calibration method has been widely discussed in the recent literature on survey sampling and calibration estimators are routinely computed by many survey organizations the calibration technique was introduced in 12 to estimate linear parameters as mean or total recently some authors have applied the calibration technique to estimate the finite distribution function and the quantiles the computationally simpler method in 14 is built by means of constraints that require the use of a fixed value t 0 the precision of the resulting calibration estimator changes with the selected point t 0 in the present paper we study the problem of determining the optimal value t 0 that gives the best estimation under simple random sampling without replacement a limited simulation study shows that the improvement of this optimal calibrated estimator over possible alternatives can be substantial

in praise of simplicity not mathematistry ten simple powerful ideas for the statistical scientist ronald fisher was by all accounts a first rate mathematician but he saw himself as a scientist not a mathematician and he railed against what george box called in his fisher lecture mathematistry mathematics is the indispensable foundation of statistics but for me the real excitement and value of our subject lies in its application to other disciplines we should not view statistics as another branch of mathematics and favor mathematical complexity over clarifying formulating and solving real world problems valuing simplicity i describe 10 simple and powerful ideas that have influenced my thinking about statistics in my areas of research interest missing data causal inference survey sampling and statistical modeling in general the overarching theme is that statistics is a missing data problem and the goal is to predict unknowns with appropriate measures of uncertainty

bayesian approach for addressing differential covariate measurement error in propensity score methods propensity score methods are an important tool to help reduce confounding in non experimental studies and produce more accurate causal effect estimates most propensity score methods assume that covariates are measured without error however covariates are often measured with error recent work has shown that ignoring such error could lead to bias in treatment effect estimates in this paper we consider an additional complication that of differential measurement error across treatment groups such as can occur if a covariate is measured differently in the treatment and control groups we propose two flexible bayesian approaches for handling differential measurement error when estimating average causal effects using propensity score methods we consider three scenarios systematic i e a location shift heteroscedastic i e different variances and mixed both systematic and heteroscedastic measurement errors we also explore various prior choices i e weakly informative or point mass on the sensitivity parameters related to the differential measurement error we present results from simulation studies evaluating the performance of the proposed methods and apply these approaches to an example estimating the effect of neighborhood disadvantage on adolescent drug use disorders

trend and fractality assessment of mexico s stock exchange the total value of domestic market capitalization of the mexican stock exchange was calculated at 520 billion of dollars by the end of november 2013 to manage this system and make optimum capital investments its dynamics needs to be predicted however randomness within the stock indexes makes forecasting a difficult task to address this issue in this work trends and fractality were studied using gnu r over the opening and closing prices indexes over the past 24 years returns kernel density estimation autocorrelation function and r s analysis and the hurst exponent were used in this research as a result it was found that the kernel estimation density and the autocorrelation function shown the presence of long range memory effects in a first approximation the returns of closing prices seems to behave according to a markovian random walk with a length of step size given by an stable random process for extreme values returns decay asymptotically as a power law with a characteristic exponent approximately equal to 2 6

improving survey weighted least squares regression the weighted least squares wls estimator is often employed in linear regression using complex survey data to deal with the bias in ordinary least squares ols arising from informative sampling in this paper a quasi aitken wls qwls estimator is proposed qwls modifies wls in the same way that cragg s quasi aitken estimator modifies ols it weights by the usual inverse sample inclusion probability weights multiplied by a parameterized function of covariates where the parameters are chosen to minimize a variance criterion the resulting estimator is consistent for the superpopulation regression coefficient under fairly mild conditions and has a smaller asymptotic variance than wls

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

a two step semiparametric method to accommodate sampling weights in multiple imputation multiple imputation mi is a well established method to handle item nonresponse in sample surveys survey data obtained from complex sampling designs often involve features that include unequal probability of selection mi requires imputation to be congenial that is for the imputations to come from a bayesian predictive distribution and for the observed and complete data estimator to equal the posterior mean given the observed or complete data and similarly for the observed and complete variance estimator to equal the posterior variance given the observed or complete data more colloquially the analyst and imputer make similar modeling assumptions yet multiply imputed data sets from complex sample designs with unequal sampling weights are typically imputed under simple random sampling assumptions and then analyzed using methods that account for the sampling weights this is a setting in which the analyst assumes more than the imputer which can led to biased estimates and anti conservative inference less commonly used alternatives such as including case weights as predictors in the imputation model typically require interaction terms for more complex estimators such as regression coefficients and can be vulnerable to model misspecification and difficult to implement we develop a simple two step mi framework that accounts for sampling weights using a weighted finite population bayesian bootstrap method to validly impute the whole population including item nonresponse from the observed data in the second step having generated posterior predictive distributions of the entire population we use standard iid imputation to handle the item nonresponse simulation results show that the proposed method has good frequentist properties and is robust to model misspecification compared to alternative approaches we apply the proposed method to accommodate missing data in the behavioral risk factor surveillance system when estimating means and parameters of regression models

design based maps for finite populations of spatial units abstractthe estimation of the values of a survey variable in finite populations of spatial units is considered for making maps when samples of spatial units are selected by probabilistic sampling schemes the single values are estimated by means of an inverse distance weighting predictor the design based asymptotic properties of the resulting maps referred to as the design based maps are considered when the study area remains fixed and the sizes of the spatial units tend to zero conditions ensuring design based asymptotic unbiasedness and consistency are derived they essentially require the existence of a pointwise or uniformly continuous density function of the survey variable onto the study area some regularities in the size and shape of the units and the use of spatially balanced designs to select units the continuity assumption can be relaxed into a riemann integrability assumption when estimation is performed at a sufficiently small spatial grain and the estimates are subsequently aggregated

multivariate locally weighted least squares regression nonparametric regression using locally weighted least squares was first discussed by stone and by cleveland recently it was shown by fan and by fan and gijbels that the local linear kernel weighted least squares regression estimator has asymptotic properties making it superior in certain senses to the nadaraya watson and gasser muller kernel estimators in this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables we are able to derive the leading bias and variance terms for general multivariate kernel weights using weighted least squares matrix theory this approach is especially convenient when analysing the asymptotic conditional bias and variance of the estimator at points near the boundary of the support of the predictors we also investigate the asymptotic properties of the multivariate local quadratic least squares regression estimator discussed by cleveland and devlin and in the univariate case higher order polynomial fits and derivative estimation

relative efficiencies of two stage sampling schemes for mean estimation in multilevel populations when cluster size is informative in multilevel populations there are two types of population means of an outcome variable ie the average of all individual outcomes ignoring cluster membership and the average of cluster specific means to estimate the first mean individuals can be sampled directly with simple random sampling or with two stage sampling tss that is sampling clusters first and then individuals within the sampled clusters when cluster size varies in the population three tss schemes can be considered ie sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster sampling clusters with equal probability and then sampling the same percentage of individuals per cluster and sampling clusters with equal probability and then sampling the same number of individuals per cluster unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative furthermore the three tss schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size the relative efficiency of the sampling schemes is shown to vary across different cluster size distributions however sampling clusters with probability proportional to size is the most efficient tss scheme for many cluster size distributions model based and design based inference are compared and are shown to give similar results the results are applied to the distribution of high school size in italy and the distribution of patient list size for general practices in england

moduli spaces of higgs bundles on degenerating riemann surfaces abstract we prove a gluing theorem for solutions a 0 0 of hitchin s self duality equations with logarithmic singularities on a rank 2 vector bundle over a noded riemann surface 0 representing a boundary point of teichmuller moduli space we show that every nearby smooth riemann surface 1 carries a smooth solution a 1 1 of the self duality equations which may be viewed as a desingularization of a 0 0

estimation of finite population domain means a model assisted empirical best prediction approach in this article we introduce a general methodology for producing a model assisted empirical best predictor ebp of a finite population domain mean using data from a complex survey our method improves on the commonly used design consistent survey estimator by using a suitable mixed model such a model combines information from related sources such as census and administrative data unlike a purely model based ebp the proposed model assisted ebp converges in probability to the customary design consistent estimator as the domain and sample sizes increase the convergence in probability is shown to hold with respect to the sampling design irrespective of the assumed mixed model a property commonly known as design consistency this property ensures robustness of the proposed predictor against possible model failures in addition the convergence in probability is shown to be valid with respect to the assumed mixed model model consistency a new mean squared prediction error mspe estimator is proposed

survey design under the regression superpopulation model abstract the construction of sample designs and estimators under a linear regression superpopulation model is considered the anticipated variance the variance of the predictor computed with respect to the sampling design and the superpopulation model is used as a criterion for evaluating probability designs and model unbiased predictors regression predictors that are model unbiased and design consistent are constructed

estimating marginal causal effects in a secondary analysis of case control data when an initial case control study is performed data can be used in a secondary analysis to evaluate the effect of the case defining event on later outcomes in this paper we study the example in

fitting a bivariate additive model by local polynomial regression while the additive model is a popular nonparametric regression method many of its theoretical properties are not well understood especially when the backfitting algorithm is used for computation of the estimators this article explores those properties when the additive model is fitted by local polynomial regression sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed this model is shown to have the same rate of convergence as that of univariate local polynomial regression

penalized balanced sampling summary linear mixed models are flexible and extensible models that c over a wide range of statistical methods they have found many uses in estimation for complex surveys particularly in small area estimation and in extensions of generalized regression estimation they have also been used as a means of relaxing constraints in calibration estimatio n the purpose of this work is to consider methods by which linear mixed models may be used at the design stage of a survey this paper reviews the ideas of balanced sampling and the cube algorithm and proposes an implementation of the cube algorithm by which penalized balanced samples can be selected such samples have the property that horvitz thompson estimators from penalized balanced samples behave like linear mixed model assisted survey regression estimators from unbalanced samples the methodology is evaluated by using nonparametric and temporal linear mixed models in simulation experiments and by using a spatial linear mixed model in an artificial but realistic sampling application motivated by a 1991 1996 environmental protection agency survey of lakes in the northeastern states of the united states

aligning estimates for common variables in two or more sample surveys abstract in practice for many sample surveys the estimates of several population totals are based on one set of weights which reproduces the known population totals of auxiliary variables such a set can always be obtained by using the general regression estimator if some variables not necessarily with known population totals are jointly collected in two sample surveys then it may be desirable that the weights of both surveys produce the same estimates for the unknown population totals of the common variables in this article we propose adjusting the general regression estimator to meet this consistency requirement by considering the common variables as additional auxiliary variables it turns out that the adjusted general regression estimator generalizes zieschang s method

the weighted residual technique for estimating the variance of the general regression estimator of the finite population total summary the paper deals with design based estimation of the variance of the general regression estimator of the finite population total the usual taylor linearization variance estimator is an expression in the design weighted regression residuals in many applications the resulting expression is counterintuitive from a model based standpoint the improved variance estimator in this paper attaches another simple weight called g weight to each individual residual this new variance estimator i gives valid design based confidence intervals ii is nearly unbiased uiider a suitably chosen regression model and iii works well for conditional inference examples are given

regression analysis of data from a cluster sample abstract for the case of different regression relationships in different subgroups of a finite population only part of which are sampled the extended least squares estimator of any weighted average of the distinct coefficients is derived under assumptions relating only to the first two moments of the distribution of the coefficients under these assumptions the estimator is shown to be the best linear unbiased estimator while under further distributional assumptions it is also the bayesian estimator for a quadratic loss function for the case of unknown variances a method for estimating them from the sample is proposed the empirical estimator thus obtained is shown to perform well by a simulation comparison with the optimal estimator and with other proposed empirical estimators

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

horvitz thompson estimators for functional data asymptotic confidence bands and optimal allocation for stratified sampling when dealing with very large datasets of functional data survey sampling approaches are useful in order to obtain estimators of simple functional quantities without being obliged to store all the data we propose a horvitz thompson estimator of the mean trajectory in the context of a superpopulation framework we prove under mild regularity conditions that we obtain uniformly consistent estimators of the mean function and of its variance function with additional assumptions on the sampling design we state a functional central limit theorem and obtain asymptotic confidence bands stratified sampling is studied in detail and we also obtain a functional version of the usual optimal allocation rule considering a mean variance criterion these techniques are illustrated by a test population of n 18 902 electricity meters for which we have individual electricity consumption measures every 30 minutes over one week we show that stratification can substantially improve both the accuracy of the estimators and reduce the width of the global confidence bands compared with simple random sampling without replacement

to model or not to model competing modes of inference for finite population sampling finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution rather than on statistical models for the measured variables this article reviews the debate between design based and model based inference the basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples strengths and weakness of design based and model based inference for surveys are discussed it is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings these ideas are illustrated using the problem of inference from unequal probability samples a model based regression analysis that leads to a combination of design based and model based weighting is described

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

precision estimation in sample survey inference a criterion for choice between variance estimators summary we advocate the mean squared error of predicted squared error as a universal criterion for the choice between variance estimators in sample survey inference the predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample this makes the new measure more satisfactory than the simpler mean squared error of the variance estimator the criterion turns out to be the same for design based as for model based inference and may also be used for comparison between the design and model based theoretical variances the theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature these calculations are primarily made under a proportional regression model but consideration is also paid to model robustness three of the six estimators are shown to be inferior to the three others which are approximately equivalent

optimal auxiliary covariate based two phase sampling design for semiparametric efficient estimation of a mean or mean difference with application to clinical trials to address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint y one approach employs a two phase sampling design wherein inexpensive auxiliary variables w predictive of y are measured in everyone y is measured in a random sample and the semiparametric efficient estimator is applied this approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs while this approach is familiar to survey samplers it apparently has seldom been used in clinical trials and several novel results practicable for clinical trials are developed we perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice we provide proofs and r code the optimality results are developed to design an hiv vaccine trial with objective to compare the mean importance weighted breadth y of the t cell response between randomized vaccine groups the trial collects an auxiliary response w highly predictive of y and measures y in the optimal subset we show that the optimal design estimation approach can confer anywhere between absent and large efficiency gain up to 24 in the examples compared to the approach with the same efficient estimator but simple random sampling where greater variability in the cost standardized conditional variance of y given w yields greater efficiency gains accurate estimation of e y w is important for realizing the efficiency gain which is aided by an ample phase two sample and by using a robust fitting method copyright 2013 john wiley sons ltd

on the use of sampling weights when estimating regression models with survey data abstract in this paper it is argued that when the population regression coefficient is of interest the use of sampling weights can be desirable in regression models with complex survey data a two step ml estimator is proposed as an alternative to ols and weighted least squares specification tests are given the ml estimator does well in simulations including several cases where it is based on a misspecified model the specification tests are effective in selecting the best estimator as an example the methods are used to estimate the returns to education using data from the canadian survey of consumer finances

non parametric bayesian models for samples from finite populations summary using ferguson s 1973 non parametric priors in a bayesian analysis of finite popula tions we show that asymptotically at least the usual estimates and confidence intervals for the population mean in simple and stratified random samples can be justified in bayesian terms we then apply these models for estimating population percentiles and a new procedure for interval estimates in stratified sampling is developed at present there are a number of general approaches in the statistical literature for making inferences based on data selected from a finite population many of these are summarized in smith 1976 probably the most widely used methodology in practice is the design based inference from random samples where criteria such as bias and mean squared error derived from the sampling distribution of the data are used this methodology does not preclude the possibility that the estimator may be based on an inherent superpopulation model however confidence intervals and mean squared errors are based only on the probability distribution of the design and ignore the model one of the reasons for the popularity of this approach may be that it is non parametric in nature and sample sizes tend to be large for many applications so that the loss of efficiency compared with parametric superpopulation approaches is considered less important than the robustness of the design based approach with respect to a wide class of models

local polynomial regresssion estimators in survey sampling estimation of finite population totals in the presence of auxiliary information is considered a class of estimators based on local polynomial regression is proposed like generalized regression estimators these estimators are weighted linear combinations of study variables in which the weights are calibrated to known control totals but the assumptions on the superpopulation model are considerably weaker the estimators are shown to be asymptotically design unbiased and consistent under mild assumptions a variance approximation based on taylor linearization is suggested and shown to be consistent for the design mean squared error of the estimators the estimators are robust in the sense of asymptotically attaining the godambe joshi lower bound to the anticipated variance simulation experiments indicate that the estimators are more efficient than regression estimators when the model regression function is incorrectly specified while being approximately as efficient when the parametric specification is correct

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

hypothesis testing with complex survey data the use of classical quadratic test statistics with particular reference to regression problems abstract sample surveys often have complex sample designs with multistage cluster sampling stratification and differential selection probabilities this article is concerned with testing the null hypothesis h 0 where the p dimensional parameter g and is a q dimensional vector of means the asymptotic framework that consists of a sequence of increasing finite populations is used to define as the limit of finite population means as part of the inference we use replicated estimates of variances that take into account the complex sample design the wald statistic can be used to test h 0 but inference for based on the wald statistic can have low power thus an alternative to using a wald test is pursued in this article first define a classical quadratic test statistic that would be used if one had a simple random sample of the population second treating this quadratic form as a population parameter use design based methods to estimate it from the observed survey data last use

models for nonresponse in sample surveys abstract the literature on the analysis of incomplete data using models is reviewed in the context of nonresponse in sample surveys the modeling approach provides a large body of methods for handling unit and item nonresponse some of which cannot be derived from the randomization theory of inference for surveys key concepts from the literature on incomplete data such as factorizations of the likelihood for special data patterns the em algorithm for general data patterns and ignorability of the response mechanism are discussed within the survey context model based procedures are related to common methods for handling nonresponse in surveys such as weighting or imputation of means within subclasses of the population

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

computing kernel smoothed conditional quantiles from many observations abstract quantiles of a variable y conditional on another variable x when plotted against x can be a useful descriptive tool these plots give a quick impression of the functional form of the relation between x and the location spread and shape of the conditional distribution of y if several y are observed for each x then sample quantiles could be calculated for each x the resulting quantile plot may be quite noisy however and smoothing across x may be desired this article presents an algorithm that calculates kernel smoothed conditional quantiles with a cross validation choice of bandwidth for x it is computationally feasible for large data sets when x assumes a small number of values since it requires only one pass through the full data set the cross validation does not require a pass through the data because of simplifications arising from the l 1 loss function being based on absolute values the technique is illustrated by plotting the conditional quantiles of the net wealth of a sample of

design adaptive nonparametric regression abstract in this article we study the method of nonparametric regression based on a weighted local linear regression this method has advantages over other popular kernel methods moreover such a regression procedure has the ability of design adaptation it adapts to both random and fixed designs to both highly clustered and nearly uniform designs and even to both interior and boundary points it is shown that the local linear regression smoothers have high asymptotic efficiency i e can be 100 with a suitable choice of kernel and bandwidth among all possible linear smoothers including those produced by kernel orthogonal series and spline methods the finite sample property of the local linear regression smoother is illustrated via simulation studies nonparametric regression is frequently used to explore the association between covariates and responses there are many versions of kernel regression smoothers some estimators are not good for random designs such as in observational studies and

nonparametric model calibration estimation in survey sampling calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter calibrating the observation weights on population means totals of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean total implicitly calibration techniques rely on a linear relation between the survey variable and the auxiliary variables however when auxiliary information is available for all units in the population more complex modeling can be handled by means of model calibration auxiliary variables are used to obtain fitted values of the survey variable for all units in the population and estimation weights are sought to satisfy calibration constraints on the fitted values population mean rather than on the auxiliary variables one in this work we extend model calibration considering more general superpopulation models and use nonparametric methods to obtain the fitted values on which t

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

interpolation methods for adapting to sparse design in nonparametric regression abstract we suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing these methods are based on simple rules determined by the kernel and bandwidth for deciding when and where pseudo design points should be added to augment the original design sequence new ordinates for the added design points are computed by simple interpolation then local linear smoothing is applied directly to the expanded dataset the method is competitive with alternatives e g those involving ridge regression in terms of both simplicity and performance

approximate bayesian inference under informative sampling summary statistical inference with complex survey data is challenging because the sampling design can be informative and ignoring it can produce misleading results current methods of bayesian inference under complex sampling assume that the sampling design is noninformative for the specified model in this paper we propose a bayesian approach which uses the sampling distribution of a summary statistic to derive the posterior distribution of the parameters of interest asymptotic properties of the method are investigated it is directly applicable to combining information from two independent surveys and to calibration estimation in survey sampling a simulation study confirms that it can provide valid estimation under informative sampling we apply it to a measurement error problem using data from the korean longitudinal study of aging

multi level modelling under informative sampling we consider a model dependent approach for multi level modelling that accounts for informative probability sampling of first and lower level population units the proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample as a function of the corresponding population model and the first and lower level sample selection probabilities and then fitting the resulting sample model using bayesian methods an important implication of the use of the model holding for the sample is that the sample selection probabilities feature in the analysis as additional data that possibly strengthen the estimators a simulation experiment is carried out in order to study the performance of this approach and compare it to the use of design based methods the simulation study indicates that both approaches perform in general equally well in terms of point estimation but the model dependent approach yields confidence credibility intervals with better coverage properties another simulation study assesses the impact of misspecification of the models assumed for the sample selection probabilities the use of maximum likelihood estimation is also considered

use of functionals in linearization and composite estimation with application to two sample survey data summary an important problem associated with two sample surveys is the estimation of nonlinear functions of finite population totals such as ratios correlation coefficients or measures of income inequality computation and estimation of the variance of such complex statistics are made more difficult by the existence of overlapping units in one sample surveys the linearization method based on the influence function approach is a powerful tool for variance estimation we introduce a two sample linearization technique that can be viewed as a generalization of the one sample influence function approach our technique is based on expressing the parameters of interest as multivariate functionals of finite and discrete measures and then using partial influence functions to compute the linearized variables under broad assumptions the asymptotic variance of the substitution estimator derived from deville 1999 is shown to be the variance of a weighted sum of the linearized variables the paper then focuses on a general class of composite substitution estimators and from this class the optimal estimator for minimizing the asymptotic variance is obtained the efficiency of the optimal composite estimator is demonstrated through an empirical study

estimating a finite population mean from unequal probability samples abstract two approaches to estimating a finite population mean from unequal probability samples are contrasted in the prediction approach a model is specified for the population values and is used to predict the nonsampled values in the generalized regression approach the horvitz thompson estimator of the population mean is modified to allow the introduction of covariate information sarndal 1980 generalized regression estimates have the desirable property of asymptotic design consistency which is not always enjoyed by estimates in the prediction class however it is suggested that the prediction approach is the more principled method of estimation if asymptotic design consistency is a desirable property in a given application then only models that yield asymptotically design consistent prediction estimates should be used two classes of models with this property are suggested namely fixed and random effects models that allow a separate intercept for subclasses of the population indexed by the pr

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

from brownian motion to operational risk statistical physics and financial markets abstract high frequency returns of the dax german blue chip stock index are used to test geometric brownian motion the standard model for financial time series even on a 15 s time scale the linear correlations of dax returns have a zero time delta function which carries 90 of the weight while the remaining 10 are positively correlated with a decay time of 53 s and negatively correlated on a 9 4 min scale the probability density of the returns possesses fat tails with power laws whose exponents continuously increase with time scales it is suggested that hydrodynamic turbulence may provide a phenomenological framework for the description of these data and at the same time open a way to use them for risk management purposes e g option pricing and hedging option pricing also is the cornerstone of credit valuation an area of much practical importance not considered explicitly in most other physics inspired papers on finance finally operational risk is introduced as a new risk category currently emphasized by regulators which will become important in many banks in the near future

finite population sampling with multivariate auxiliary information abstract this article examines strategies that are approximately design unbiased and nearly optimal assuming a large sample survey and a regression superpopulation model a new class of predictors is proposed to link certain features of optimal design unbiased and model unbiased predictors generalized regression predictors are shown to pervade the subclass of asymptotically design unbiased adu predictors generalized regression predictors are combined with model based stratification to construct highly efficient adu strategies

calibration estimators in survey sampling abstract this article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information estimation is equivalent to attaching weights to the survey data we focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations we briefly mention an application to the case in which the information consists of known marginal counts in a two or multi way table known as generalized raking the general regression estimator greg was conceived with multivariate auxiliary information in mind ordinarily this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x but we note that the greg can be derived by a different route by focusing instead on the weights the ordinary sampling weights of the kth observation is 1 k where k is the inclusion probabilit

adjusted jackknife for imputation under unequal probability sampling without replacement imputation is commonly used to compensate for item non response in sample surveys if we treat the imputed values as if they are true values and then compute the variance estimates by using standard methods such as the jackknife we can seriously underestimate the true variances we propose a modified jackknife variance estimator which is defined for any without replacement unequal probability sampling design in the presence of imputation and non negligible sampling fraction mean ratio and random imputation methods will be considered the practical advantage of the method proposed is its breadth of applicability

post stratification a modeler s perspective abstract post stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates the basic technique divides the sample into post strata and computes a post stratification weight w ih rp h r h for each sample case in post stratum h where r h is the number of survey respondents in post stratum h p h is the population proportion from a census and r is the respondent sample size survey estimates such as functions of means and totals then weight cases by w h variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions literature on post stratification is limited and has mainly taken the randomization or design based perspective where inference is based on the sampling distribution with population values held fixed this article develops bayesian model based theory for the method a basic normal post stratification mod

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

conditionally consistent estimators using only probabilities of selection in complex sample surveys abstract predictive regression estimators using functions of the probability of selection i as covariates are studied as an alternative to classical p weighting estimators for the finite population mean in complex sample surveys variance estimators are developed based on the relationship var y i i where y is the response and i is the probability of selection extensions to cluster sample designs are outlined and an example is given from the national educational longitudinal survey of 1988

compensating asynchrony effects in the calculation of financial correlations abstract we present a method to compensate statistical errors in the calculation of correlations on asynchronous time series the method is based on the assumption of an underlying time series we set up a model and apply it to financial data to examine the decrease of calculated correlations towards smaller return intervals epps effect we show that the discovered statistical effect is a major cause of the epps effect hence we are able to quantify and to compensate it using only trading prices and trading times

optimal calibration estimators in survey sampling we show that the model calibration estimator for the finite population mean which was proposed by wu sitter 2001 through an intuitive argument is optimal among a class of calibration estimators we also present optimal calibration estimators for the finite population distribution function the population variance the variance of a linear estimator and other quadratic finite population functions under a unified framework the proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified a limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial the question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation

model based multiplicity estimation of population size a survey is conducted at w of k selection units or lists e g health care institutions or weeks in a year to estimate n the total number of individuals with particular characteristics our estimator utilizes two items determined for each survey participant the number u among the w lists in s and the number j among all k lists on which each survey participant appears in its traditional form selection units are chosen using probability sampling and the statistical properties of the estimator derive from the sampling mechanism here selection units are purposively chosen to maximize the chance that they are typical and a model based analysis is used for inference if the sample is typical the ml estimators of n and e j are unbiased if a condition on the second moment of u j is satisfied the model based variance of the estimator of n based on a purposively chosen typical sample is smaller than one based on a randomly chosen sample methods to test whether the typical assumption is valid using data from the survey are not yet available the importance of proper selection of the sample to maximize the chance that it is typical and model breakdown does not occur must be emphasized

correlations in commodity markets abstract in this paper we analyzed dependencies in commodity markets investigating correlations of future contracts for commodities over the period 1998 09 01 2007 12 14 we constructed a minimal spanning tree based on the correlation matrix the tree provides evidence for sector clusterization of investigated contracts we also studied dynamical properties of commodity dependencies it turned out that the market was constantly getting more correlated within the investigated period although the increase of correlation was distributed non uniformly among all contracts and depended on contracts branches

evidence of markov properties of high frequency exchange rate data we present a stochastic analysis of a data set consisting of 106 quotes of the us dollar german mark exchange rate evidence is given that the price changes x upon different delay times can be described as a markov process evolving in thus the dependence of the probability density function pdf p x on the delay time can be described by a fokker planck equation a generalized diffusion equation for p x this equation is completely determined by two coefficients d1 x and d2 x drift and diffusion coefficient respectively we demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process furthermore it is shown that the solutions of the resulting fokker planck equation describe the empirical pdfs correctly including the pronounced tails

efficient estimation of non linear finite population parameters by using non parametrics summary currently high precision estimation of non linear parameters such as gini indices low income proportions or other measures of inequality is particularly crucial we propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population through a non parametric model assisted approach we construct a unique system of survey weights that can be used to estimate any non linear parameter that is associated with any study variable of the survey using a plug in principle based on a rigorous functional approach and a linearization principle the asymptotic variance of the estimators proposed is derived and variance estimators are shown to be consistent under mild assumptions the theory is fully detailed for penalized b spline estimators together with suggestions for practical implementation and guidelines for choosing the smoothing parameters the validity of the method is demonstrated on data extracted from the french labour force survey point and confidence interval estimation for the gini index and the low income proportion are derived theoretical and empirical results highlight our interest in using a non parametric versus a parametric approach when estimating non linear parameters in the presence of auxiliary information

outlier resistant alternatives to the ratio estimator abstract many techniques have been suggested to lower the impact of outliers on sample survey estimates outliers can be downweighted by winsorization that is by replacing extreme data points by a data dependent or a predetermined value before calculating estimates another approach is to reduce the weight of outliers from the inverse sampling fraction to 1 in the estimation of population characteristics in this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered a resistant version of the ratio estimator is introduced it is constructed with a m or a gm estimator of the slope of the regression model through the origin which is implicitly called on when considering the ratio estimator the asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan the selection of a resistant estimator is seen to involve a trade off betwee

on asymptotically design unbiased estimators of a finite population mean summary certain regression type estimators of a finite population mean are examined for their asymptotic design properties a sufficient condition that implies the design consistency or asymptotic design unbiasedness is discussed for a general regression estimator the leading term of its asymptotic bias is explicitly derived when this condition holds as well as when it does not hold

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

resampling hierarchical processes in the wavelet domain a case study using atmospheric turbulence abstract there is a growing need for statistical methods that generate an ensemble of plausible realizations of a hierarchical process from a single run or experiment the main challenge is how to construct such an ensemble in a manner that preserves the internal dynamics e g intermittency and temporal persistency a popular hierarchical process often used as a case study in such problems is atmospheric turbulent flow analogies to turbulence are often called upon when information flow from large to small scales non gaussian statistics and intermittency are inherent attributes of the hierarchical process under consideration these attributes are key defining syndromes of the turbulent cascade thereby making turbulence time series ideal for testing such ensemble generation schemes in this study we propose a wavelet based resampling scheme wb and compare it to the traditional fourier based phase randomization bootstrap fb approach within the context of the turbulence energy cascade the comparison between the two resampling methods and observed ensemble statistics constructed by clustering similar meteorological conditions demonstrate that the wb reproduces several features related to intermittency of the ensemble series when compared to fb in particular the wb exhibited an increase in wavelet energy activity and an increase in the wavelet flatness factor with increasing frequency consistent with the cluster of ensemble statistics on the other hand the fb yielded no increase in such energy activity with scale and resulted in near gaussian wavelet coefficients at all frequencies within the inertial subrange the scaling behavior of the longitudinal u and vertical w velocity structure functions of various order p 0 confirms that wb preserves the small scale intermittency whereas fb completely destroys it the extension of wb to the multivariate case is also demonstrated via the conservation of co spectra between u and w time series because the resampling strategy proposed here is conducted in the wavelet domain gap infected and uneven sampled time series can be readily accommodated within the wb finally recommendations about the filter and block sizes are discussed

inference on inequality from household survey data abstract i develop a theory of asymptotic inference for the lorenz curve and the gini coefficient for testing economic inequality when the data come from stratified and clustered household surveys with large number of clusters per stratum using the asymptotic framework of bhattacharya asymptotic inference from multi stage surveys journal of econometrics 126 1 145 171 i derive a weak convergence result for the continuously indexed lorenz process even when the underlying density is not uniformly bounded away from zero i provide analytical formulae for the asymptotic covariance functions that are corrected for both stratification and clustering and develop consistent tests for lorenz dominance inference on the gini coefficient follows as a corollary the methods are applied to per capita household expenditure data from the complexly designed indian national sample survey to test for changes in inequality before and after the reforms of the early 1990s ignoring the survey design is seen to produce qualitatively different results especially in the urban sector where the population sorts more completely into rich and poor neighborhoods

universal features in the growth dynamics of complex organizations we analyze the fluctuations in the gross domestic product gdp of 152 countries for the period 1950 1992 we find that i the distribution of annual growth rates for countries of a given gdp decays with fatter tails than for a gaussian and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with results on firm growth these results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms s0031 9007 98 07339 6 pacs numbers 02 50 ey 01 75 m 05 40 j 05 45 b in the study of physical systems the analysis of the scaling properties of the fluctuations has been shown to give important information regarding the underlying processes responsible for the observed macroscopic behavior in contrast most studies on the time evolution of economic time series have concentrated on average growth rates 1 18 here we investigate the possibility that the study of fluctuations in economics may also lead to a better understanding of the mechanisms responsible for the observed dynamics 19 23 we therefore analyze the fluctuations in the growth rate of the gross domestic product gdp of 152 countries during the period 1950 1992 24 we will show that i the distribution of annual growth rates for countries of a given gdp is consistent for a certain range with an exponential decay and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with