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  • 1. "Optimal" calibration weights under unit nonresponse in survey sampling
    Articles and reports: 12-001-X201900300006
    Description:

    High nonresponse is a very common problem in sample surveys today. In statistical terms we are worried about increased bias and variance of estimators for population quantities such as totals or means. Different methods have been suggested in order to compensate for this phenomenon. We can roughly divide them into imputation and calibration and it is the latter approach we will focus on here. A wide spectrum of possibilities is included in the class of calibration estimators. We explore linear calibration, where we suggest using a nonresponse version of the design-based optimal regression estimator. Comparisons are made between this estimator and a GREG type estimator. Distance measures play a very important part in the construction of calibration estimators. We show that an estimator of the average response propensity (probability) can be included in the “optimal” distance measure under nonresponse, which will help to reduce the bias of the resulting estimator. To illustrate empirically the theoretically derived results for the suggested estimators, a simulation study has been carried out. The population is called KYBOK and consists of clerical municipalities in Sweden, where the variables include financial as well as size measurements. The results are encouraging for the “optimal” estimator in combination with the estimated average response propensity, where the bias was reduced for most of the Poisson sampling cases in the study.

    Release date: 2019-12-17
  • 2. An optimal calibration distance leading to the optimal regression estimator Archived
    Articles and reports: 12-001-X20050018092
    Description:

    When there is auxiliary information in survey sampling, the design based "optimal (regression) estimator" of a finite population total/mean is known to be (at least asymptotically) more efficient than the corresponding GREG estimator. We will illustrate this by some simulations with stratified sampling from skewed populations. The GREG estimator was originally constructed using an assisting linear superpopulation model. It may also be seen as a calibration estimator; i.e., as a weighted linear estimator, where the weights obey the calibration equation and, with that restriction, are as close as possible to the original "Horvitz-Thompson weights" (according to a suitable distance). We show that the optimal estimator can also be seen as a calibration estimator in this respect, with a quadratic distance measure closely related to the one generating the GREG estimator. Simple examples will also be given, revealing that this new measure is not always easily obtained.

    Release date: 2005-07-21
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Articles and reports (2)

Articles and reports (2) ((2 results))

  • 1. "Optimal" calibration weights under unit nonresponse in survey sampling
    Articles and reports: 12-001-X201900300006
    Description:

    High nonresponse is a very common problem in sample surveys today. In statistical terms we are worried about increased bias and variance of estimators for population quantities such as totals or means. Different methods have been suggested in order to compensate for this phenomenon. We can roughly divide them into imputation and calibration and it is the latter approach we will focus on here. A wide spectrum of possibilities is included in the class of calibration estimators. We explore linear calibration, where we suggest using a nonresponse version of the design-based optimal regression estimator. Comparisons are made between this estimator and a GREG type estimator. Distance measures play a very important part in the construction of calibration estimators. We show that an estimator of the average response propensity (probability) can be included in the “optimal” distance measure under nonresponse, which will help to reduce the bias of the resulting estimator. To illustrate empirically the theoretically derived results for the suggested estimators, a simulation study has been carried out. The population is called KYBOK and consists of clerical municipalities in Sweden, where the variables include financial as well as size measurements. The results are encouraging for the “optimal” estimator in combination with the estimated average response propensity, where the bias was reduced for most of the Poisson sampling cases in the study.

    Release date: 2019-12-17
  • 2. An optimal calibration distance leading to the optimal regression estimator Archived
    Articles and reports: 12-001-X20050018092
    Description:

    When there is auxiliary information in survey sampling, the design based "optimal (regression) estimator" of a finite population total/mean is known to be (at least asymptotically) more efficient than the corresponding GREG estimator. We will illustrate this by some simulations with stratified sampling from skewed populations. The GREG estimator was originally constructed using an assisting linear superpopulation model. It may also be seen as a calibration estimator; i.e., as a weighted linear estimator, where the weights obey the calibration equation and, with that restriction, are as close as possible to the original "Horvitz-Thompson weights" (according to a suitable distance). We show that the optimal estimator can also be seen as a calibration estimator in this respect, with a quadratic distance measure closely related to the one generating the GREG estimator. Simple examples will also be given, revealing that this new measure is not always easily obtained.

    Release date: 2005-07-21
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