local linear regression smoothers and their minimax efficiencies in this paper we introduce a smooth version of local linear regression estimators and address their advantages the mse and mise of the estimators are computed explicitly it turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency they are not only efficient in rates but also nearly efficient in constant factors in the nonparametric regression context the asymptotic minimax lower bound is developed via the heuristic of the hardest onedimensional subproblem of donoho and liu connections of the minimax risk with the modulus of continuity are made the lower bound is also applicable for estimating conditional mean regression and conditional quantiles for both fixed and random design regression problems

reducing variance in univariate smoothing a variance reduction technique in nonparametric smoothing is proposed at each point of estimation form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged the nearby points are chosen to maximize the variance reduction we study in detail the case of univariate local linear regression while the new estimator retains many advantages of the local linear estimator it has appealing asymptotic relative efficiencies bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation a simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes this technique is very general and has a wide range of applications

robust stochastic approximation approach to stochastic programming in this paper we consider optimization problems where the objective function is given in a form of the expectation a basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals expectations cannot be computed with high accuracy the aim of this paper is to compare two computational approaches based on monte carlo sampling techniques namely the stochastic approximation sa and the sample average approximation saa methods both approaches the sa and saa methods have a long history current opinion is that the saa method can efficiently use a specific say linear structure of the considered problem while the sa approach is a crude subgradient method which often performs poorly in practice we intend to demonstrate that a properly modified sa approach can be competitive and even significantly outperform the saa method for a certain class of convex stochastic problems we extend the analysis to the case of convex concave stochastic saddle point problems and present in our opinion highly encouraging results of numerical experiments

semiparametric density estimation by local l2 fitting this article examines density estimation by combining a parametric approach with a nonparametric factor the plug in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor the nonparametric factor is derived by a criterion called local l 2 fitting a class of estimators that have multiplicative adjustment is provided including estimators proposed by several authors as special cases and the asymptotic theories are developed theoretical comparison reveals that the estimators in this class are better than or at least competitive with the traditional kernel estimator in a broad class of densities the asymptotically best estimator in this class can be obtained from the elegant feature of the bias function

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

bootstrap for the case cohort design the case cohort design facilitates economical investigation of risk factors in a large survival study with covariate data collected only from the cases and a simple random subset of the full cohort methods that accommodate the design have been developed for various semiparametric models but most inference procedures are based on asymptotic distribution theory such inference can be cumbersome to derive and implement and does not permit confidence band construction while bootstrap is an obvious alternative how to resample is unclear because of complications from the two stage sampling design we establish an equivalent sampling scheme and propose a novel and versatile nonparametric bootstrap for robust inference with an appealingly simple single stage resampling theoretical justification and numerical assessment are provided for a number of procedures under the proportional hazards model

bias robust estimation in finite populations using nonparametric calibration a standard problem in sample survey inference is that of predicting the finite population total h of a function h y of a random variable y the model based approach to this problem first defines a working model for y and then predicts h by estimating its expectation under conditional on the sample values of y this approach leads to biased predictions if is incorrect we explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust but inefficient predictor of h and then calibrates this predictor for its bias under an application to prediction of the finite population distribution function of a population of australian beef farms is presented

quantitative concentration inequalities for empirical measures on non compact spaces we establish quantitative concentration estimates for the empirical measure of many independent variables in transportation distances as an application we provide some error bounds for particle simulations in a model mean field problem the tools include coupling arguments as well as regularity and moment estimates for solutions of certain diffusive partial differential equations

calibrated imputation in surveys under a quasi model assisted approach summary we propose to use calibrated imputation to compensate for missing values this technique consists of finding final imputed values that are as close as possible to preliminary imputed values and are calibrated to satisfy constraints preliminary imputed values potentially justified by an imputation model are obtained through deterministic single imputation using appropriate constraints the resulting imputed estimator is asymptotically unbiased for estimation of linear population parameters such as domain totals a quasi model assisted approach is considered in the sense that inferences do not depend on the validity of an imputation model and are made with respect to the sampling design and a non response model an imputation model may still be used to generate imputed values and thus to improve the efficiency of the imputed estimator this approach has the characteristic of handling naturally the situation where more than one imputation method is used owing to missing values in the variables that are used to obtain imputed values we use the taylor linearization technique to obtain a variance estimator under a general non response model for the logistic non response model we show that ignoring the effect of estimating the non response model parameters leads to overestimating the variance of the imputed estimator in practice the overestimation is expected to be moderate or even negligible as shown in a simulation study

on variance estimation with imputed survey data abstract unit nonresponse and item nonresponse both occur frequently in surveys unit nonresponse is customarily handled by weighting adjustment whereas item nonresponse is usually treated by some form of imputation in particular deterministic or stochastic imputation is often used to assign values for missing item responses we provide an account of some recent work on jackknife variance estimation based on adjusted imputed values using only a single imputation and hence a single completed data set we also present linearized versions of the jackknife variance estimators we study both stratified simple random sampling and stratified multistage sampling existing computer programs for jackknife and linearization variance estimation can be modified to implement the proposed variance estimators without requiring the creation and permanent retention of supplemental data sets but for secondary analyses the completed data set must include information on response status for each item as well as on the im

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

automatic smoothing of regression functions in generalized linear models abstract we consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models nelder and wedderburn 1972 and present a generalized cross validation procedure for empirically assessing an appropriate amount of smoothing in these estimates asymptotic arguments and numerical simulations are used to show that the generalized cross validatory procedure preforms well from the point of view of a weighted mean squared error criterion the methodology adds to the battery of graphical tools for model building and checking within the generalized linear model framework included are two examples motivated by medical and horticultural applications

jackknife variance estimation with survey data under hot deck imputation summary hot deck imputation is commonly employed for item nonresponse in sample surveys it is also a common practice to treat the imputed values as if they are true values and then compute the variance estimates using standard formulae this procedure however could lead to serious underestimation of the true variance when the proportion of missing values for an item is appreciable we propose a jackknife variance estimator for stratified multistage surveys which is obtained by first adjusting the imputed values for each pseudo replicate and then applying the standard jackknife formula the proposed jackknife variance estimator is shown to be consistent as the sample size increases assuming equal response probabilities within imputation classes and using a particular hot deck imputation

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

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

a note on variance estimation for the regression estimator in double sampling abstract double sampling of a finite population occurs when a sample from the population is itself sampled with the intent of measuring varites in the subsample not already available in the sample an important example is the regression estimator for means or totals which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample this article concerns estimation of the variance of the regression estimator the estimators of variance recommended by cochran rely solely on the subsample data at least to first order this article note proposes variance estimators that make better use of the entire sample

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

local maximum likelihood estimation and inference local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique it extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment this paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local maximum likelihood estimation the approach is then applied to least squares nonparametric regression and to nonparametric logistic regression our experiences in these two settings show that the general idea outlined here is powerful and encouraging

historical developments in convergence analysis for newton s and newton like methods historical developments in convergence theory as well as error estimates for newton s method and newton like methods for nonlinear equations are described mainly for differentiable equations in banach spaces

data driven bandwidth selection in local polynomial fitting variable bandwidth and spatial adaptation when estimating a mean regression function and its derivatives locally weighted least squares regression has proven to be a very attractive technique the present paper focuses on the important issue of how to select the smoothing parameter or bandwidth in the case of estimating curves with a complicated structure a variable bandwidth is desirable furthermore the bandwidth should be indicated by the data themselves recent developments in nonparametric smoothing techniques inspired us to propose such a data driven bandwidth selection procedure which can be used to select both constant and variable bandwidths the idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator the procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives the resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves this is illustrated via a large variety of testing examples including examples with a large spatial variability the results are also compared with wavelet thresholding techniques and it seems that our results are at least comparable i e local polynomial regression using our data driven variable bandwidth has spatial adaptation properties that are similar to wavelets

model selection for extended quasi likelihood models in small samples we develop a small sample criterion aicc for the selection of extended quasi likelihood models in contrast to the akaike information criterion aic aicc provides a more nearly unbiased estimator for the expected kullback leibler information consequently it often selects better models than aic in small samples for the logistic regression model monte carlo results show that aicc outperforms aic pregibon s 1979 data analytic methods for generalized linear models ph d thesis university of toronto cp and the cp selection criteria of hosmer et al 1989 biometrics 45 1265 1270 two examples are presented

nonparametric density estimation with a parametric start the traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes the present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities for example the normal while not losing much in precision when the true density is far from the parametric class the idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor this works well in cases where the correction factor function is less rough than the original density itself extensive comparisons with the kernel estimator are carried out including exact analysis for the class of all normal mixtures the new method with a normal start wins quite often even in many cases where the true density is far from normal procedures for choosing the smoothing parameter of the estimator are also discussed the new estimator should be particularly useful in higher dimensions where the usual nonparametric methods have problems the idea is also spelled out for nonparametric regression

the kernel estimate of a regression function in likelihood based models abstract smoothing splines have a penalized likelihood motivation good and gaskins 1971 allowing direct application to nonparametric regression in likelihood based models the notion of a weighted likelihood for the nonparametric kernel estimation of a regression function is proposed generalizing the local likelihood theory of tibshirani and hastie 1987 let the data be of the form xi yi i 1 n where xi 0 1 d are lattice points and the yi are independent random variables from a family of distributions with parameter i g xi with g having continuous partial derivatives of order k 2 the goal is to arrive at a nonparametric estimate o of o g xo for a fixed point xo 0 1 d we consider the estimator o that maximizes the weighted likelihood function w n i 1 w xo xi b log f yi with f the density of yi w a symmetric kernel with compact support and b the bandwidth that controls the degree of smoothing sufficient conditions for consistency and asympt

inference from stratified samples second order analysis of three methods for nonlinear statistics abstract for stratified samples and nonlinear statistics that can be expressed as functions of estimated totals second order asymptotic expansions of the linearization jackknife and balanced repeated replication variance estimators are obtained based on these comparisons are made in terms of their biases some higher order asymptotic equivalence results are also established the special case of a combined ratio estimator is investigated in detail some results on bias reduction achieved by the jack knife and balanced repeated replication estimators of a nonlinear function of totals are also given

a resampling procedure for complex survey data abstract in complex survey data often the sampling design induces a non iid structure to the data e g without replacement sampling stratification multistage or unequal probability of selection though techniques for variance estimation and confidence intervals do exist they often are cumbersome to implement or do not extend to complex designs it would be desirable to have resampling methods that reuse the existing estimation system repeatedly using computing power to avoid theoretical work and that can be applied to such data in recognition of this need various resampling procedures for variance estimation and confidence intervals in sample survey data where the sampling is without replacement have been proposed in the literature these include the jackknife the with replacement bootstrap bwr the without replacement bootstrap bwo and the rescaling bootstrap the bwr and bwo are applicable only to simple sampling designs others have shown the asymptotic consistency of jackknife vari

bootstrap for imputed survey data abstract most surveys use imputation to compensate for missing data however treating the imputed data set as the complete data set and directly applying existing methods e g the linearization the jackknife and the bootstrap for variance estimation and or statistical inference does not produce valid results because these methods do not account for the effect of missing data and or imputation in this article we show that correct bootstrap estimates can be obtained by imitating the process of imputing the original data set in the bootstrap resampling that is by imputing the bootstrap data sets in exactly the same way that the original data set is imputed the proposed bootstrap is asymptotically valid irrespective of the sampling design the imputation method or the type of statistic used in inference this enables us to use a unified method in a variety of problems and in fact this is the only method that works without any restriction on the sampling design the imputation method or the type

variance estimation under two phase sampling with application to imputation for missing data summary ratio estimation under two phase simple random sampling is studied a new linearisation variance estimator that makes more complete use of the sample data than a standard one is proposed a jackknife variance estimator and its linearised version are also obtained unconditional and conditional repeated sampling properties of these variance estimators are studied through simulation applications to mass imputation under two phase sampling and deterministic imputation for missing data are also given

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

variance estimation for the regression estimator in two phase sampling abstract many techniques in survey sampling depend on the possession of information about an auxiliary variable x or a vector of auxiliary variables available for the entire population regression estimates require the population mean if such information is unavailable then one can sometimes obtain a large preliminary sample of xi relatively cheaply and use this to obtain a good estimate say of a smaller subsample can then be taken and the characteristic of interest yi measured a regression estimator can then be used treating as if it were this is termed double sampling or two phase sampling this article focuses on variance estimators for the regression estimator in the aforementioned context and their use in constructing confidence intervals a design based linearization variance estimator that makes more complete use of the sample data than the standard one is considered for two phase sampling a jackknife variance estimator and its linearized version are obtained and shown to be design c

local quasi likelihood with a parametric guide generalized linear models and the quasi likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response nonparametric methods need no explicit parametric specification and the resulting model is completely determined by the data themselves however nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models studied in fan heckman and wand j amer statist assoc 90 1995 141 150 in this work we propose a unified family of parametrically guided nonparametric estimation schemes this combines the merits of both parametric and nonparametric approaches and enables us to incorporate prior knowledge asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

asymptotic analysis of penalized likelihood and related estimators a general approach to the first order asymptotic analysis ofpenalized likelihood and related estimators is described the method gives expansions for the systematic and random error asymptotic convergence rates in a family of spectral norms are obtained the theory applies to a broad range of function estimation prob erns including non paxametric dellsity hazard and generalized regression curve estimation some examples are provided ams 1980 subject classifications primary 62 g05 secondary 62j05 41 a35 41 a25 47 a53 45 llo 45 m05

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

parametrically assisted nonparametric estimation of a density in the deconvolution problem nonparametric estimation of a density from contaminated data is a difficult problem for which convergence rates are notoriously slow we introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density without degrading much the quality of purely nonparametric estimators in other cases we establish optimal convergence rates for our problem and discuss estimators that attain these rates the very good numerical properties of the methods are illustrated via a simulation study supplementary materials for this article are available online

the finite population linear regression estimator and estimators of its variance an empirical study abstract the usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction superpopulation models its bias is compared with that of the least squares variance estimator also described are three bias robust alternatives one of which is the jackknife variance estimator the theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive nonrandom samples are drawn from six real populations the results illustrate the need for prediction models and the inadequacy of randomization per se in providing a theoretical framework for robust inferences

poststratification and conditional variance estimation poststratification estimation is a technique used in sample surveys to improve efficiency of estimators survey weights are adjusted to force the estimated numbers of units in each of a set of estimation cells to be equal to known population totals the resulting weights are then used in forming estimates of means or totals of variables collected in the survey for example in a household survey the estimation cells may be based on age race sex categories of individuals and the known totals may come from the most recent population census although the variance of a poststratified estimator can be computed over all possible sample configurations inferences made conditionally on the achieved sample configuration are desirable theory and a simulation study using data from the u s current population survey are presented to study both the conditional bias and variance of the poststratified estimator of a total the linearization balanced repeated replication and jackknife variance estimators are also exa

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

pseudo population bootstrap methods for imputed survey data the most common way to treat item nonresponse in surveys is to replace a missing value by a plausible value constructed on the basis of fully observed variables treating the imputed values as if they were observed may lead to invalid inferences bootstrap variance estimators for various finite population parameters are obtained using two pseudo population bootstrap schemes we establish the asymptotic properties of the resulting bootstrap variance estimators for population totals and population quantiles a simulation study suggests that the methods perform well in terms of relative bias and coverage probability

bootstrapping clustered data summary various bootstraps have been proposed for bootstrapping clustered data from one way arrays the simulation results in the literature suggest that some of these methods work quite well in practice the theoretical results are limited and more mixed in their conclusions for example mccullagh reached negative conclusions about the use of non parametric bootstraps for one way arrays the purpose of this paper is to extend our understanding of the issues by discussing the effect of different ways of modelling clustered data the criteria for successful bootstraps used in the literature and extending the theory from functions of the sample mean to include functions of the between and within sums of squares and non parametric bootstraps to include model based bootstraps we determine that the consistency of variance estimates for a bootstrap method depends on the choice of model with the residual bootstrap giving consistency under the transformation model whereas the cluster bootstrap gives consistent estimates under both the transformation and the random effect model in addition we note that the criteria based on the distribution of the bootstrap observations are not really useful in assessing consistency

bootstrap methods for finite populations abstract we show that the familiar bootstrap plug in rule of efron has a natural analog in finite population settings in our method a characteristic of the population is estimated by the average value of the characteristic over a class of empirical populations constructed from the sample our method extends that of gross to situations in which the stratum sizes are not integer multiples of their respective sample sizes moreover we show that our method can be used to generate second order correct confidence intervals for smooth functions of population means a property that has not been established for other resampling methods suggested in the literature a second resampling method is proposed that also leads to second order correct confidence intervals and is less computationally intensive than our bootstrap but a simulation study reveals that the second method can be quite unstable in some situations whereas our bootstrap performs very well

bootstrap confidence intervals for adaptive cluster sampling consider a collection of spatially clustered objects where the clusters are geographically rare of interest is estimation of the total number of objects on the site from a sample of plots of equal size under these spatial conditions adaptive cluster sampling of plots is generally useful in improving efficiency in estimation over simple random sampling without replacement srswor in adaptive cluster sampling when a sampled plot meets some predefined condition neighboring plots are added to the sample when populations are rare and clustered the usual unbiased estimators based on small samples are often highly skewed and discrete in distribution thus confidence intervals based on asymptotic normal theory may not be appropriate we investigated several nonparametric bootstrap methods for constructing confidence intervals under adaptive cluster sampling to perform bootstrapping we transformed the initial sample in order to include the information from the adaptive portion of the sample yet maintain a fixed sample size in general coverages of bootstrap percentile methods were closer to nominal coverage than the normal approximation

nonlinear stochastic programming with a case study in continuous switching the optimal solution as well as the objective of stochastic programming problems vary with the underlying probability measure this paper addresses stability with respect to the underlying probability measure and stability of the objective the techniques presented are employed to make problems numerically tractable which are formulated by involving numerous scenarios or even by involving a continuous probability measure the results justify clustering techniques which significantly reduce computation times while guaranteeing a desired approximation quality the second part of the paper highlights newton s method to solve the reduced stochastic recourse problems the techniques presented exploit the particular structure of the recourse function of the stochastic optimization problem the tools are finally demonstrated on a benchmark problem which is taken from electrical power flows

variance estimation for survey data with composite imputation and nonnegligible sampling fractions abstract this article considers variance estimation for horvitz thompson type estimated totals based on survey data with imputed non respondents and with nonnegligible sampling fractions a method based on a variance decomposition is proposed our method can be applied to complicated situations where a composite of some deterministic and or random imputation methods is used including using imputed data in subsequent imputations although here linearization or taylor expansion type techniques are adopted replication methods such as the jackknife balanced repeated replication and random groups can also be used in applying our method to derive variance estimators using our method variance estimators can be derived under either the customary design based approach or the model assisted approach and are asymptotically unbiased and consistent the transportation annual survey conducted at the u s census bureau in which nonrespondents are imputed using a composite of cold deck and ratio type imputation m

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

bootstrap variance estimation for rejective sampling abstractreplication procedures have proven useful for variance estimation for large scale complex surveys as an extension of bootstrap procedures to rejective samples we define a bootstrap sample that is a rejective unequal probability replacement sample selected from the original sample a modification of the bootstrap with improved performance is suggested for stratified samples with small stratum sizes simulations for poisson and stratified rejective samples support the use of replicates in estimating the variance of the regression estimator for rejective samples

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

median estimation in the presence of auxiliary information summary this paper deals with the estimation under simple random sampling of a finite population median in the presence of an auxiliary variable an estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach these estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known on the basis of the asymptotic properties derived and some simulation results the efficiencies of these estimators are compared it is shown that the two estimators proposed unlike that obtained from modifying the ratio estimator always dominate the sample median in mean squared error and that their efficiencies depend directly on the probability of concordance rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable when the linearity assumption is approximately satisfied the three estimators are seen to have comparable efficiencies while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumnption