Analysis

This article develops computational tools, called indicators, for judging the effectiveness of the auxiliary information used to control nonresponse bias in survey estimates, obtained in this article by calibration. This work is motivated by the survey environment in a number of countries, notably in northern Europe, where many potential auxiliary variables are derived from reliable administrative registers for household and individuals. Many auxiliary vectors can be composed. There is a need to compare these vectors to assess their potential for reducing bias. The indicators in this article are designed to meet that need. They are used in surveys at Statistics Sweden. General survey conditions are considered: There is probability sampling from the finite population, by an arbitrary sampling design; nonresponse occurs. The probability of inclusion in the sample is known for each population unit; the probability of response is unknown, causing bias. The study variable (the y-variable) is observed for the set of respondents only. No matter what auxiliary vector is used in a calibration estimator (or in any other estimation method), a residual bias will always remain. The choice of a "best possible" auxiliary vector is guided by the indicators proposed in the article. Their background and computational features are described in the early sections of the article. Their theoretical background is explained. The concluding sections are devoted to empirical studies. One of these illustrates the selection of auxiliary variables in a survey at Statistics Sweden. A second empirical illustration is a simulation with a constructed finite population; a number of potential auxiliary vectors are ranked in order of preference with the aid of the indicators.

This paper deals with calibration estimation for surveys with nonresponse. Efficient weighting adjustment for unit nonresponse requires powerful auxiliary information. The weights in the calibration estimator are computed on information about a specified auxiliary vector. Even with the "best possible" auxiliary vector, some bias remains in the estimator. An indicator of the remaining bias is presented and analyzed.

The many potential auxiliary variables allow the statistician to compose a wide variety of possible auxiliary vectors. The need arises to compare these vectors to assess their effectiveness for bias reduction. To this end we examine an indicator useful for ranking alternative auxiliary vectors in regard to their ability to reduce the bias. The indicator is computed on the auxiliary vector values for the sampled units, responding and nonresponding. An advantage is its independence of the study variables, of which there are many in a large survey.

The properties of the indicator are examined in empirical studies. A synthetic population is constructed and potential auxiliary vectors are ranked with the aid of the indicator. Another empirical illustration illustrates how the indicator is used for selecting auxiliary variables in a large survey at Statistics Sweden.

This article develops computational tools, called indicators, for judging the effectiveness of the auxiliary information used to control nonresponse bias in survey estimates, obtained in this article by calibration. This work is motivated by the survey environment in a number of countries, notably in northern Europe, where many potential auxiliary variables are derived from reliable administrative registers for household and individuals. Many auxiliary vectors can be composed. There is a need to compare these vectors to assess their potential for reducing bias. The indicators in this article are designed to meet that need. They are used in surveys at Statistics Sweden. General survey conditions are considered: There is probability sampling from the finite population, by an arbitrary sampling design; nonresponse occurs. The probability of inclusion in the sample is known for each population unit; the probability of response is unknown, causing bias. The study variable (the y-variable) is observed for the set of respondents only. No matter what auxiliary vector is used in a calibration estimator (or in any other estimation method), a residual bias will always remain. The choice of a "best possible" auxiliary vector is guided by the indicators proposed in the article. Their background and computational features are described in the early sections of the article. Their theoretical background is explained. The concluding sections are devoted to empirical studies. One of these illustrates the selection of auxiliary variables in a survey at Statistics Sweden. A second empirical illustration is a simulation with a constructed finite population; a number of potential auxiliary vectors are ranked in order of preference with the aid of the indicators.

This paper deals with calibration estimation for surveys with nonresponse. Efficient weighting adjustment for unit nonresponse requires powerful auxiliary information. The weights in the calibration estimator are computed on information about a specified auxiliary vector. Even with the "best possible" auxiliary vector, some bias remains in the estimator. An indicator of the remaining bias is presented and analyzed.

The many potential auxiliary variables allow the statistician to compose a wide variety of possible auxiliary vectors. The need arises to compare these vectors to assess their effectiveness for bias reduction. To this end we examine an indicator useful for ranking alternative auxiliary vectors in regard to their ability to reduce the bias. The indicator is computed on the auxiliary vector values for the sampled units, responding and nonresponding. An advantage is its independence of the study variables, of which there are many in a large survey.

The properties of the indicator are examined in empirical studies. A synthetic population is constructed and potential auxiliary vectors are ranked with the aid of the indicator. Another empirical illustration illustrates how the indicator is used for selecting auxiliary variables in a large survey at Statistics Sweden.