Improving the estimation of the odds ratio in sampling surveys using auxiliary information

The odds-ratio measure is widely used in Health and Social surveys where the aim is to compare the odds of a certain event between a population at risk and a population not at risk. It can be defined using logistic regression through an estimating equation that allows a generalization to continuous risk variable. Data from surveys need to be analyzed in a proper way by taking into account the survey weights. Because the odds-ratio is a complex parameter, the analyst has to circumvent some difficulties when estimating confidence intervals. The present paper suggests a nonparametric approach that can take advantage of some auxiliary information in order to improve on the precision of the odds-ratio estimator. The approach consists in B-spline modelling which can handle the nonlinear structure of the parameter in a exible way and is easy to implement. The variance estimation issue is solved through a linearization approach and confidence intervals are derived. Two small applications are discussed

Improving the estimation of the odds ratio in sampling surveys using auxiliary information

The odds-ratio measure is widely used in Health and Social surveys where the aim is to compare the odds of a certain event between a population at risk and a population not at risk. It can be defined using logistic regression through an estimating equation that allows a generalization to continuous risk variable. Data from surveys need to be analyzed in a proper way by taking into account the survey weights. Because the odds-ratio is a complex parameter, the analyst has to circumvent some difficulties when estimating confidence intervals. The present paper suggests a nonparametric approach that can take advantage of some auxiliary information in order to improve on the precision of the odds-ratio estimator. The approach consists in B-spline modelling which can handle the nonlinear structure of the parameter in a exible way and is easy to implement. The variance estimation issue is solved through a linearization approach and confidence intervals are derived. Two small applications are discussed

Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data

Revised version for the Electronic Journal of StatisticsInternational audienceWhen the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator are uniformly consistent. Then, under additional assumptions, we prove a functional central limit theorem and we assess rigorously a fast technique based on simulations of Gaussian processes which is employed to build asymptotic confidence bands. The accuracy of the variance function estimator is evaluated on a real dataset of sampled electricity consumption curves measured every half an hour over a period of one week

Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories

In the near future, millions of load curves measuring the electricity consumption of French households in small time grids (probably half hours) will be available. All these collected load curves represent a huge amount of information which could be exploited using survey sampling techniques. In particular, the total consumption of a specific cus- tomer group (for example all the customers of an electricity supplier) could be estimated using unequal probability random sampling methods. Unfortunately, data collection may undergo technical problems resulting in missing values. In this paper we study a new estimation method for the mean curve in the presence of missing values which consists in extending kernel estimation techniques developed for longitudinal data analysis to sampled curves. Three nonparametric estimators that take account of the missing pieces of trajectories are suggested. We also study pointwise variance estimators which are based on linearization techniques. The particular but very important case of stratified sampling is then specifically studied. Finally, we discuss some more practical aspects such as choosing the bandwidth values for the kernel and estimating the probabilities of observation of the trajectories.Comment: Version revised for Statistics and Probability Letter