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- Articles and reports: 12-001-X201000211377Description:
We consider the problem of parameter estimation with auxiliary information, where the auxiliary information takes the form of known moments. Calibration estimation is a typical example of using the moment conditions in sample surveys. Given the parametric form of the original distribution of the sample observations, we use the estimated importance sampling of Henmi, Yoshida and Eguchi (2007) to obtain an improved estimator. If we use the normal density to compute the importance weights, the resulting estimator takes the form of the one-step exponential tilting estimator. The proposed exponential tilting estimator is shown to be asymptotically equivalent to the regression estimator, but it avoids extreme weights and has some computational advantages over the empirical likelihood estimator. Variance estimation is also discussed and results from a limited simulation study are presented.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000211381Description:
Taylor linearization methods are often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, and (ii) validity under a conditional repeated sampling framework. Demnati and Rao (2004) proposed a unified approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs. When analyzing survey data, finite populations are often assumed to be generated from super-population models, and analytical inferences on model parameters are of interest. If the sampling fractions are small, then the sampling variance captures almost the entire variation generated by the design and model random processes. However, when the sampling fractions are not negligible, the model variance should be taken into account in order to construct valid inferences on model parameters under the combined process of generating the finite population from the assumed super-population model and the selection of the sample according to the specified sampling design. In this paper, we obtain an estimator of the total variance, using the Demnati-Rao approach, when the characteristics of interest are assumed to be random variables generated from a super-population model. We illustrate the method using ratio estimators and estimators defined as solutions to calibration weighted estimating equations. Simulation results on the performance of the proposed variance estimator for model parameters are also presented.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000111246Description:
Many surveys employ weight adjustment procedures to reduce nonresponse bias. These adjustments make use of available auxiliary data. This paper addresses the issue of jackknife variance estimation for estimators that have been adjusted for nonresponse. Using the reverse approach for variance estimation proposed by Fay (1991) and Shao and Steel (1999), we study the effect of not re-calculating the nonresponse weight adjustment within each jackknife replicate. We show that the resulting 'shortcut' jackknife variance estimator tends to overestimate the true variance of point estimators in the case of several weight adjustment procedures used in practice. These theoretical results are confirmed through a simulation study where we compare the shortcut jackknife variance estimator with the full jackknife variance estimator obtained by re-calculating the nonresponse weight adjustment within each jackknife replicate.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111247Description:
In this paper, the problem of estimating the variance of various estimators of the population mean in two-phase sampling has been considered by jackknifing the two-phase calibrated weights of Hidiroglou and Särndal (1995, 1998). Several estimators of population mean available in the literature are shown to be the special cases of the technique developed here, including those suggested by Rao and Sitter (1995) and Sitter (1997). By following Raj (1965) and Srivenkataramana and Tracy (1989), some new estimators of the population mean are introduced and their variances are estimated through the proposed jackknife procedure. The variance of the chain ratio and regression type estimators due to Chand (1975) are also estimated using the jackknife. A simulation study is conducted to assess the efficiency of the proposed jackknife estimators relative to the usual estimators of variance.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111251Description:
Calibration techniques, such as poststratification, use auxiliary information to improve the efficiency of survey estimates. The control totals, to which sample weights are poststratified (or calibrated), are assumed to be population values. Often, however, the controls are estimated from other surveys. Many researchers apply traditional poststratification variance estimators to situations where the control totals are estimated, thus assuming that any additional sampling variance associated with these controls is negligible. The goal of the research presented here is to evaluate variance estimators for stratified, multi-stage designs under estimated-control (EC) poststratification using design-unbiased controls. We compare the theoretical and empirical properties of linearization and jackknife variance estimators for a poststratified estimator of a population total. Illustrations are given of the effects on variances from different levels of precision in the estimated controls. Our research suggests (i) traditional variance estimators can seriously underestimate the theoretical variance, and (ii) two EC poststratification variance estimators can mitigate the negative bias.
Release date: 2010-06-29 - 6. Quality control and data reduction procedures for accelerometry-derived measures of physical activity ArchivedArticles and reports: 82-003-X201000111066Geography: CanadaDescription:
This article considers critical quality control and data reduction procedures that should be addressed before physical activity information is derived from accelerometry data.
Release date: 2010-01-13
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- Articles and reports: 12-001-X201000211377Description:
We consider the problem of parameter estimation with auxiliary information, where the auxiliary information takes the form of known moments. Calibration estimation is a typical example of using the moment conditions in sample surveys. Given the parametric form of the original distribution of the sample observations, we use the estimated importance sampling of Henmi, Yoshida and Eguchi (2007) to obtain an improved estimator. If we use the normal density to compute the importance weights, the resulting estimator takes the form of the one-step exponential tilting estimator. The proposed exponential tilting estimator is shown to be asymptotically equivalent to the regression estimator, but it avoids extreme weights and has some computational advantages over the empirical likelihood estimator. Variance estimation is also discussed and results from a limited simulation study are presented.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000211381Description:
Taylor linearization methods are often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, and (ii) validity under a conditional repeated sampling framework. Demnati and Rao (2004) proposed a unified approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs. When analyzing survey data, finite populations are often assumed to be generated from super-population models, and analytical inferences on model parameters are of interest. If the sampling fractions are small, then the sampling variance captures almost the entire variation generated by the design and model random processes. However, when the sampling fractions are not negligible, the model variance should be taken into account in order to construct valid inferences on model parameters under the combined process of generating the finite population from the assumed super-population model and the selection of the sample according to the specified sampling design. In this paper, we obtain an estimator of the total variance, using the Demnati-Rao approach, when the characteristics of interest are assumed to be random variables generated from a super-population model. We illustrate the method using ratio estimators and estimators defined as solutions to calibration weighted estimating equations. Simulation results on the performance of the proposed variance estimator for model parameters are also presented.
Release date: 2010-12-21 - Articles and reports: 12-001-X201000111246Description:
Many surveys employ weight adjustment procedures to reduce nonresponse bias. These adjustments make use of available auxiliary data. This paper addresses the issue of jackknife variance estimation for estimators that have been adjusted for nonresponse. Using the reverse approach for variance estimation proposed by Fay (1991) and Shao and Steel (1999), we study the effect of not re-calculating the nonresponse weight adjustment within each jackknife replicate. We show that the resulting 'shortcut' jackknife variance estimator tends to overestimate the true variance of point estimators in the case of several weight adjustment procedures used in practice. These theoretical results are confirmed through a simulation study where we compare the shortcut jackknife variance estimator with the full jackknife variance estimator obtained by re-calculating the nonresponse weight adjustment within each jackknife replicate.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111247Description:
In this paper, the problem of estimating the variance of various estimators of the population mean in two-phase sampling has been considered by jackknifing the two-phase calibrated weights of Hidiroglou and Särndal (1995, 1998). Several estimators of population mean available in the literature are shown to be the special cases of the technique developed here, including those suggested by Rao and Sitter (1995) and Sitter (1997). By following Raj (1965) and Srivenkataramana and Tracy (1989), some new estimators of the population mean are introduced and their variances are estimated through the proposed jackknife procedure. The variance of the chain ratio and regression type estimators due to Chand (1975) are also estimated using the jackknife. A simulation study is conducted to assess the efficiency of the proposed jackknife estimators relative to the usual estimators of variance.
Release date: 2010-06-29 - Articles and reports: 12-001-X201000111251Description:
Calibration techniques, such as poststratification, use auxiliary information to improve the efficiency of survey estimates. The control totals, to which sample weights are poststratified (or calibrated), are assumed to be population values. Often, however, the controls are estimated from other surveys. Many researchers apply traditional poststratification variance estimators to situations where the control totals are estimated, thus assuming that any additional sampling variance associated with these controls is negligible. The goal of the research presented here is to evaluate variance estimators for stratified, multi-stage designs under estimated-control (EC) poststratification using design-unbiased controls. We compare the theoretical and empirical properties of linearization and jackknife variance estimators for a poststratified estimator of a population total. Illustrations are given of the effects on variances from different levels of precision in the estimated controls. Our research suggests (i) traditional variance estimators can seriously underestimate the theoretical variance, and (ii) two EC poststratification variance estimators can mitigate the negative bias.
Release date: 2010-06-29 - 6. Quality control and data reduction procedures for accelerometry-derived measures of physical activity ArchivedArticles and reports: 82-003-X201000111066Geography: CanadaDescription:
This article considers critical quality control and data reduction procedures that should be addressed before physical activity information is derived from accelerometry data.
Release date: 2010-01-13
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