Analysis

All (3) ((3 results))

• 1. Sample-based estimation of mean electricity consumption curves for small domains

  Articles and reports: 12-001-X201800254955

  Description:

  Many studies conducted by various electric utilities around the world are based on the analysis of mean electricity consumption curves for various subpopulations, particularly geographic in nature. Those mean curves are estimated from samples of thousands of curves measured at very short intervals over long periods. Estimation for small subpopulations, also called small domains, is a very timely topic in sampling theory.

  In this article, we will examine this problem based on functional data and we will try to estimate the mean curves for small domains. For this, we propose four methods: functional linear regression; modelling the scores of a principal component analysis by unit-level linear mixed models; and two non-parametric estimators, with one based on regression trees and the other on random forests, adapted to the curves. All these methods have been tested and compared using real electricity consumption data for households in France.

  Release date: 2018-12-20

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• 2. Linearization versus bootstrap for variance estimation of the change between Gini indexes Archived

  Articles and reports: 12-001-X201800154926

  Description:

  This paper investigates the linearization and bootstrap variance estimation for the Gini coefficient and the change between Gini indexes at two periods of time. For the one-sample case, we use the influence function linearization approach suggested by Deville (1999), the without-replacement bootstrap suggested by Gross (1980) for simple random sampling without replacement and the with-replacement of primary sampling units described in Rao and Wu (1988) for multistage sampling. To obtain a two-sample variance estimator, we use the linearization technique by means of partial influence functions (Goga, Deville and Ruiz-Gazen, 2009). We also develop an extension of the studied bootstrap procedures for two-dimensional sampling. The two approaches are compared on simulated data.

  Release date: 2018-06-21

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• 3. Comparison of different sample designs and construction of confidence bands to estimate the mean of functional data: An illustration on electricity consumption Archived

  Articles and reports: 12-001-X201300211888

  Description:

  When the study variables are functional and storage capacities are limited or transmission costs are high, using survey techniques to select a portion of the observations of the population is an interesting alternative to using signal compression techniques. In this context of functional data, our focus in this study is on estimating the mean electricity consumption curve over a one-week period. We compare different estimation strategies that take account of a piece of auxiliary information such as the mean consumption for the previous period. The first strategy consists in using a simple random sampling design without replacement, then incorporating the auxiliary information into the estimator by introducing a functional linear model. The second approach consists in incorporating the auxiliary information into the sampling designs by considering unequal probability designs, such as stratified and pi designs. We then address the issue of constructing confidence bands for these estimators of the mean. When effective estimators of the covariance function are available and the mean estimator satisfies a functional central limit theorem, it is possible to use a fast technique for constructing confidence bands, based on the simulation of Gaussian processes. This approach is compared with bootstrap techniques that have been adapted to take account of the functional nature of the data.

  Release date: 2014-01-15

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Articles and reports (3) ((3 results))

• 1. Sample-based estimation of mean electricity consumption curves for small domains

  Articles and reports: 12-001-X201800254955

  Description:

  Many studies conducted by various electric utilities around the world are based on the analysis of mean electricity consumption curves for various subpopulations, particularly geographic in nature. Those mean curves are estimated from samples of thousands of curves measured at very short intervals over long periods. Estimation for small subpopulations, also called small domains, is a very timely topic in sampling theory.

  In this article, we will examine this problem based on functional data and we will try to estimate the mean curves for small domains. For this, we propose four methods: functional linear regression; modelling the scores of a principal component analysis by unit-level linear mixed models; and two non-parametric estimators, with one based on regression trees and the other on random forests, adapted to the curves. All these methods have been tested and compared using real electricity consumption data for households in France.

  Release date: 2018-12-20

  ---

• 2. Linearization versus bootstrap for variance estimation of the change between Gini indexes Archived

  Articles and reports: 12-001-X201800154926

  Description:

  This paper investigates the linearization and bootstrap variance estimation for the Gini coefficient and the change between Gini indexes at two periods of time. For the one-sample case, we use the influence function linearization approach suggested by Deville (1999), the without-replacement bootstrap suggested by Gross (1980) for simple random sampling without replacement and the with-replacement of primary sampling units described in Rao and Wu (1988) for multistage sampling. To obtain a two-sample variance estimator, we use the linearization technique by means of partial influence functions (Goga, Deville and Ruiz-Gazen, 2009). We also develop an extension of the studied bootstrap procedures for two-dimensional sampling. The two approaches are compared on simulated data.

  Release date: 2018-06-21

  ---

• 3. Comparison of different sample designs and construction of confidence bands to estimate the mean of functional data: An illustration on electricity consumption Archived

  Articles and reports: 12-001-X201300211888

  Description:

  When the study variables are functional and storage capacities are limited or transmission costs are high, using survey techniques to select a portion of the observations of the population is an interesting alternative to using signal compression techniques. In this context of functional data, our focus in this study is on estimating the mean electricity consumption curve over a one-week period. We compare different estimation strategies that take account of a piece of auxiliary information such as the mean consumption for the previous period. The first strategy consists in using a simple random sampling design without replacement, then incorporating the auxiliary information into the estimator by introducing a functional linear model. The second approach consists in incorporating the auxiliary information into the sampling designs by considering unequal probability designs, such as stratified and pi designs. We then address the issue of constructing confidence bands for these estimators of the mean. When effective estimators of the covariance function are available and the mean estimator satisfies a functional central limit theorem, it is possible to use a fast technique for constructing confidence bands, based on the simulation of Gaussian processes. This approach is compared with bootstrap techniques that have been adapted to take account of the functional nature of the data.

  Release date: 2014-01-15

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