Search results for "Survey sampling"
showing 10 items of 24 documents
Properties of Design-Based Functional Principal Components Analysis.
2010
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and con…
Horvitz-Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling
2009
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 here 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 deduce asymptotic confidence bands. Stratified sampling is studied in detail, and we also obtain a functional version of the usual optimal …
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
2013
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajectories, sampling scheme, and smoothing bandwidth, we prove a Central Limit theorem in the space of …
Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
2013
When 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 …
Estimation of total electricity consumption curves by sampling in a finite population when some trajectories are partially unobserved
2019
International audience; Millions of smart meters that are able to collect individual load curves, that is, electricity consumption time series, of residential and business customers at fine scale time grids are now deployed by electricity companies all around the world. It may be complex and costly to transmit and exploit such a large quantity of information, therefore it can be relevant to use survey sampling techniques to estimate mean load curves of specific groups of customers. Data collection, like every mass process, may undergo technical problems at every point of the metering and collection chain resulting in missing values. We consider imputation approaches (linear interpolation, k…
Using Complex Surveys to Estimate theL1-Median of a Functional Variable: Application to Electricity Load Curves
2012
Mean proles are widely used as indicators of the electricity consumption habits of customers. Currently, Electricit e De France (EDF), estimates class load proles by using point-wise mean function. Unfortunately, it is well known that the mean is highly sensitive to the presence of outliers, such as one or more consumers with unusually high-levels of consumption. In this paper, we propose an alternative to the mean prole: the L1-median prole which is more robust. When dealing with large datasets of functional data (load curves for example), survey sampling approaches are useful for estimating the median prole and avoid storing all of the data. We propose here estimators of the median trajec…
Analysis of Educational Frequency Data from a Complex Sample Survey
1991
Abstract Some recent methods are presented for analyzing categorial data from complex surveys involving clustering familiar in educational research where e.g. teaching groups are used as sample clusters. The methods are introduced through a discussion of the test of independence on a two‐way table and the analysis of a two‐way table using logistic regression models. The analyses are illustrated using data from the First National Assessment of the Finnish Comprehensive School 1979. The primary focus of the paper is on the methods that provide first‐order corrections to standard multinomial‐based chi‐square tests by taking account of survey design effects. Both first‐ and second‐order correct…
Bayesian Estimation of Political Transition Matrices
1994
A decision framework is used to propose a procedure designed to estimate the reallocation of the vote of each individual party between two consecutive political elections, given the results of the elections, the information provided by a sample survey, and some assumptions on the hierarchical structure of the population.
Improving predictive accuracy of exit polls
2010
Abstract Exit polls are best known for their use in election forecasting. In recent years, however, some prominent mistaken predictions have been made, undermining public confidence in the accuracy of both exit polls and survey methods. Nonresponse bias has been claimed as being one of the main reasons for inaccurate projections. Traditionally, the issue has been handled through an age–race–sex adjustment at the national and state levels. An alternative solution is suggested and detailed in this paper. A two-step strategy is proposed to reduce nonresponse bias and improve predictions. First, “vote-remembering” (vote recall) is used to correct party proportion estimates at polling locations;…
Semiparametric Models with Functional Responses in a Model Assisted Survey Sampling Setting : Model Assisted Estimation of Electricity Consumption Cu…
2010
This work adopts a survey sampling point of view to estimate the mean curve of large databases of functional data. When storage capacities are limited, selecting, with survey techniques a small fraction of the observations is an interesting alternative to signal compression techniques. We propose here to take account of real or multivariate auxiliary information available at a low cost for the whole population, with semiparametric model assisted approaches, in order to improve the accuracy of Horvitz-Thompson estimators of the mean curve. We first estimate the functional principal components with a design based point of view in order to reduce the dimension of the signals and then propose s…