an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

small domain estimation a conditional analysis abstract in estimating means totals and other parameters for small domains of a finite population the survey statistician is usually faced with a domain sample size that is random rather than controlled at the selection stage often a sensible approach is to make design based inference conditionally on the realized sample size in the domain nd in this article we suggest and analyze some small domain estimators and their design based conditional confidence intervals the conditional outlook leads us to some new small domain estimators that a are based on regression of pertinent auxiliary information and are therefore efficient to the extent that the auxiliary information is strong b are nearly design unbiased conditionally on nd as well as unconditionally and c give rise to design based confidence intervals that are valid conditionally as well as unconditionally the conditional properties of these new regression estimators are first derived theoretically then confirmed through a monte

a regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its l norm the i th singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one we show that near a local maximum however the largest singular value has a lipschitz second derivative but need not have a third derivative using this regularity result we give a quadratically convergent algorithm for computing the l norm of a transfer matrix

worst case and average h 2 performance analysis against real constant parametric uncertainty abstract in this paper we present methods for calculating both the average and worst case quadratic performances for a family of linear time invariant systems with real constant parametric uncertainty the linear systems are described by state space models with affine linear dependence on the uncertain parameters a closed form expression for the average performance is given and it is shown that the worst case calculation is similar to that of the h norm of a certain augmented system both continuous time and discrete time cases are considered

characterization of best model based predictors in survey sampling on presente des conditions necessaires et suffisantes d optimalite d un predicteur lineaire arbitraire

some asymptotic results for the systematic and stratified sampling of a finite population summary a sample mean has an asymptotically insignificant model bias under a broad set of functional relationships between the parameter of interest and an auxiliary size variable given a systematic sample from a size ordered list when based on randomly drawn samples within size strata this estimator of the population mean not only has an asymptotically insignificant model bias but is design consistent as well in addition there are more efficient estimation strategies that have insignificant model biases and may be design consistent

a new approach to weighting and inference in sample surveys the validity of design based inference is not dependent on any model assumption however it is well known that estimators derived through design based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values we propose estimators that have the potential to improve the efficiency of any estimator derived under the design based theory our main focus is limited to the improvement of the horvitz thompson estimator but we also discuss the extension to calibration estimators the new estimators are obtained by smoothing design or calibration weights using an appropriate model our approach to inference requires the modelling of only one variable the weight and it leads to a single set of smoothed weights in multipurpose surveys this is to be contrasted with other model based approaches such as the prediction approach in which it is necessary to postulate and validate a model for each variable of interest leading potentially to variable specific sets of weights our proposed approach is first justified theoretically and then evaluated through a simulation study

poststratification using regression estimators when information on strata means and sizes is missing summary poststratification is often used to increase the precision of survey estimators when applied to regression estimators it assumes that the regression relationships in the various strata are different this gives rise to the use of the separate regression estimator in this paper we consider situations where the strata affiliation of the population units is not specified in the frame so that the separate regression estimator is not available the strata means of the regressor variable and the strata sizes being unknown we propose a new regression type estimator which accounts for the different regression relationships in the various strata but no longer depends on the unknown strata means and sizes we show that this estimator is more precise than estimators that ignore the differences in the regression relationships the theoretical comparisons are illustrated by simulation results

goodness of fit tests for the cure rate in a mixture cure model summary we consider models for time to event data that allow that an event e g a relapse of a disease never occurs for a certain percentage p of the population called the cure rate we suppose that these data are subject to random right censoring and we model the data using a mixture cure model in which the survival function of the uncured subjects is left unspecified the aim is to test whether the cure rate p as a function of the covariates satisfies a certain parametric model to do so we propose a test statistic that is inspired by a goodness of fit test for a regression function due to hardle mammen 1993 we show that the statistic is asymptotically normally distributed under the null hypothesis that the model is correctly specified and under local alternatives a bootstrap procedure is proposed to implement the test the good performance of the approach is confirmed with simulations for illustration we apply the test to data on the times between first and second births

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

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

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

lqg optimal scalar static output feedback an eigenproblem based technique is given for computing the stabilizing scalar static output feedback gain that minimizes the standard linear quadratic performance index in the presence of a gaussian white noise disturbance the method adapts recent work on eigenproblem based computation of h norms

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

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

the single index cox mixture cure model in survival analysis it often happens that a certain fraction of the subjects under study never experience the event of interest that is they are considered cured in the presence of covariates a common model for this type of data is the mixture cure model which assumes that the population consists of two subpopulations namely the cured and the non cured ones and it writes the survival function of the whole population given a set of covariates as a mixture of the survival function of the cured subjects which equals one and the survival function of the non cured ones in the literature one usually assumes that the mixing probabilities follow a logistic model this is however a strong modeling assumption which might not be met in practice therefore in order to have a flexible model which at the same time does not suffer from curse of dimensionality problems we propose in this paper a single index model for the mixing probabilities for the survival function of the non cured subjects we assume a cox proportional hazards model we estimate this model using a maximum likelihood approach we also carry out a simulation study in which we compare the estimators under the single index model and under the logistic model for various model settings and we apply the new model and estimation method on a breast cancer data set

variance estimation of nominal scale inter rater reliability with random selection of raters most inter rater reliability studies using nominal scales suggest the existence of two populations of inference the population of subjects collection of objects or persons to be rated and that of raters consequently the sampling variance of the inter rater reliability coefficient can be seen as a result of the combined effect of the sampling of subjects and raters however all inter rater reliability variance estimators proposed in the literature only account for the subject sampling variability ignoring the extra sampling variance due to the sampling of raters even though the latter may be the biggest of the variance components such variance estimators make statistical inference possible only to the subject universe this paper proposes variance estimators that will make it possible to infer to both universes of subjects and raters the consistency of these variance estimators is proved as well as their validity for confidence interval construction these results are applicable only to fully crossed designs where each rater must rate each subject a small monte carlo simulation study is presented to demonstrate the accuracy of large sample approximations on reasonably small samples

kernel and probit estimates in quantal bioassay abstract a kernel method for the estimation of quantal dose response curves is considered in contrast to parametric modeling this local smoothing method does not require any assumptions beyond smoothness of the dose response curve and in this sense is nonparametric in finite sample situations the kernel estimate of the dose response curve is not necessarily monotone and therefore if the additional assumption of monotonicity of the dose response curve is made a monotonized version is discussed bias variance asymptotic normality and uniform consistency including rates of convergence of kernel estimates are derived and applied to establish consistency and limiting distribution of kernel estimates of the ed here ed is the effective dose at level that is the dose where 100 of the subjects show a response the properties of the kernel estimated ed are compared with the corresponding properties of the maximum likelihood estimator assuming the probit model practical application of the k

weighting in survey analysis under informative sampling sampling related to the outcome variable of a regression analysis conditional on covariates is called informative sampling and may lead to bias in ordinary least squares estimation weighting by the reciprocal of the inclusion probability approximately removes such bias but may inflate variance this paper investigates two ways of modifying such weights to improve efficiency while retaining consistency one approach is to multiply the inverse probability weights by functions of the covariates the second is to smooth the weights given values of the outcome variable and covariates optimal ways of constructing weights by these two approaches are explored both approaches require the fitting of auxiliary weight models the asymptotic properties of the resulting estimators are investigated and linearization variance estimators are obtained the approach is extended to pseudo maximum likelihood estimation for generalized linear models the properties of the different weighted estimators are compared in a limited simulation study the robustness of the estimators to misspecification of the auxiliary weight model or of the regression model of interest is discussed

optimal probability weights for inference with constrained precision abstractprobability weights are used in many areas of research including complex survey designs missing data analysis and adjustment for confounding factors they are useful analytic tools but can lead to statistical inefficiencies when they contain outlying values this issue is frequently tackled by replacing large weights with smaller ones or by normalizing them through smoothing functions while these approaches are practical they are also prone to yield biased inferences this article introduces a method for obtaining optimal weights defined as those with smallest euclidean distance from target weights among all sets of weights that satisfy a constraint on the variance of the resulting weighted estimator the optimal weights yield minimum bias estimators among all estimators with specified precision the method is based on solving a constrained nonlinear optimization problem whose lagrange multipliers and objective function can help assess the trade off between bias and precision of the resulting

a mixture model combining logistic regression with proportional hazards regression summary a model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event the proposed model is a semiparametric generalization of a parametric model due to farewell 1982 estimates of the regression parameters are obtained by maximizing a monte carlo approximation of a marginal likelihood and the em algorithm is used to estimate the baseline survivor function we present some simulation results to verify the validity of the suggested estimation procedure it appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions

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

asymptotics for a censored generalized linear model with unknown link function for censored response variable against projected co variable a generalized linear model with an unknown link function can cover almost all existing models under censorship its special cases include the accelerated failure time model with censored data such a model in the uncensored case is called the single index model in econometrics in this paper we systematically study the asymptotic properties we derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter we also obtain the optimal convergence rate of an estimator of the unknown link function in the model

robust schur stability of a polytope of polynomials the main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle the criterion obtained serves as a discrete time counterpart for results in s bialas 1985 and f fu and b r barmish 1987 for the continuous case also the results are reduced to operations on n 1 n 1 matrices it is concluded that by the edge result of a c bartlett et al 1987 it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region d

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

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

weighted likelihood estimation under two phase sampling we develop asymptotic theory for weighted likelihood esti mators wle under two phase stratied sampling without replacement we also consider several variants of wle s involving estimated weights and calibration a set of empirical process tools are developed including a glivenko cantelli theorem a theorem for rates of convergence of z estimators and a donsker theorem for the inverse probability weighted em pirical processes under two phase sampling and sampling without replace ment at the second phase using these general results we derive asymptotic distributions of the wle of a nite dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is es timable either at regular or non regular rates we illustrate these results and methods in the cox model with right censoring and interval censor ing we compare the methods via their asymptotic variances under both sampling without replacement and the more usual and easier to analyze assumption of bernoulli sampling at the second phase ams 2000 subject classications primary 62e20 secondary 62g20 62d99 62n01

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

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

a jackknife variance estimator for unistage stratified samples with unequal probabilities summary existing jackknife variance estimators used with sample surveys can seriously overestimate the true variance under unistage stratified sampling without replacement with unequal probabilities a novel jackknife variance estimator is proposed which is as numerically simple as existing jackknife variance estimators under certain regularity conditions the proposed variance estimator is consistent under stratified sampling without replacement with unequal probabilities the high entropy regularity condition necessary for consistency is shown to hold for the rao sampford design an empirical study of three unequal probability sampling designs supports our findings

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

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

an implicit small gain condition and an upper bound for the real structured singular value in this paper we develop an upper bound for the real structured singular value that has the form of an implicit small gain theorem the implicit small gain condition involves a shifted plant whose dynamics depend upon the uncertainty set bound and unlike prior bounds does not require frequency dependent scales or multipliers numerical results show that the implicit small gain bound compares favorably with real bounds that involve frequency dependent scales and multipliers

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

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

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

design consistent versus model dependent estimation for small domains abstract for small domains we have a choice between design consistent estimators that make the strongest possible use of auxiliary information and model dependent design biased alternatives such as the synthetic estimator in this article a design consistent method is developed that borrows strength in the same way that the design biased synthetic estimator does the latter has a design based mean squared error mse advantage in small samples under the supposition that domains resemble each other under deviations from that model however and with moderate to large samples the design consistent method gives a smaller mse it also has the advantage that design based variance estimators and design based confidence intervals can be easily obtained this article emphasizes that the choice of estimation method depends on a complex interaction of factors that include sample size sampling fraction domain size and departures from the model

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

a jackknife variance estimator for unequal probability sampling the jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs we propose a jackknife variance estimator which is defined for any without replacement unequal probability sampling design we demonstrate design consistency of this estimator for a broad class of point estimators a monte carlo study shows how the proposed estimator may improve on existing estimators

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