Analysis

Description: Adaptive cluster sampling designs were proposed as a method that could be used when sampling rare populations whose units tend to appear in clusters. The resulting estimator is not based on any model assumptions and is design unbiased. It can have smaller variance than the standard estimator which does not incorporate the fact that one is dealing with a rare population. Here we will demonstrate that, when adaptive cluster sampling is appropriate, its estimator does not take into account all the available information in the design. We present a quasi Bayesian approach which incorporates the information which is now ignored. We will see that the resulting estimator is a significant improvement over the current methods.

Description:

In the standard design approach to missing observations, the construction of weight classes and calibration are used to adjust the design weights for the respondents in the sample. Here we use these adjusted weights to define a Dirichlet distribution which can be used to make inferences about the population. Examples show that the resulting procedures have better performance properties than the standard methods when the population is skewed.

Description:

Although weights are widely used in survey sampling their ultimate justification from the design perspective is often problematical. Here we will argue for a stepwise Bayes justification for weights that does not depend explicitly on the sampling design. This approach will make use of the standard kind of information present in auxiliary variables however it will not assume a model relating the auxiliary variables to the characteristic of interest. The resulting weight for a unit in the sample can be given the usual interpretation as the number of units in the population which it represents.

Description:

In finite population sampling prior information is often available in the form of partial knowledge about an auxiliary variable, for example its mean may be known. In such cases, the ratio estimator and the regression estimator are often used for estimating the population mean of the characteristic of interest. The Polya posterior has been developed as a noninformative Bayesian approach to survey sampling. It is appropriate when little or no prior information about the population is available. Here we show that it can be extended to incorporate types of partial prior information about auxiliary variables. We will see that it typically yields procedures with good frequentist properties even in some problems where standard frequentist methods are difficult to apply.

Description:

In small area estimation, one uses data from similar domains to estimate the mean in a particular small area. This borrowing of strength is justified by assuming a model that relates the small area means. Here, we suggest a non-informative or objective Bayesian approach to small area estimation. Using this approach, one can estimate population parameters other than means and find sensible estimates of their precision. AMS 1991 subject classifications Primary 62D05; secondary 62C10.

Description:

The problem of estimating the median of a finite population when an auxiliary variable is present is considered. Point and interval estimators based on a non-informative Bayesian approach are proposed. The point estimator is compared to other possible estimators and is seen to perform well in a variety of situations.

Description: Adaptive cluster sampling designs were proposed as a method that could be used when sampling rare populations whose units tend to appear in clusters. The resulting estimator is not based on any model assumptions and is design unbiased. It can have smaller variance than the standard estimator which does not incorporate the fact that one is dealing with a rare population. Here we will demonstrate that, when adaptive cluster sampling is appropriate, its estimator does not take into account all the available information in the design. We present a quasi Bayesian approach which incorporates the information which is now ignored. We will see that the resulting estimator is a significant improvement over the current methods.

Description:

In the standard design approach to missing observations, the construction of weight classes and calibration are used to adjust the design weights for the respondents in the sample. Here we use these adjusted weights to define a Dirichlet distribution which can be used to make inferences about the population. Examples show that the resulting procedures have better performance properties than the standard methods when the population is skewed.

Description:

Although weights are widely used in survey sampling their ultimate justification from the design perspective is often problematical. Here we will argue for a stepwise Bayes justification for weights that does not depend explicitly on the sampling design. This approach will make use of the standard kind of information present in auxiliary variables however it will not assume a model relating the auxiliary variables to the characteristic of interest. The resulting weight for a unit in the sample can be given the usual interpretation as the number of units in the population which it represents.

Description:

In finite population sampling prior information is often available in the form of partial knowledge about an auxiliary variable, for example its mean may be known. In such cases, the ratio estimator and the regression estimator are often used for estimating the population mean of the characteristic of interest. The Polya posterior has been developed as a noninformative Bayesian approach to survey sampling. It is appropriate when little or no prior information about the population is available. Here we show that it can be extended to incorporate types of partial prior information about auxiliary variables. We will see that it typically yields procedures with good frequentist properties even in some problems where standard frequentist methods are difficult to apply.

Description:

In small area estimation, one uses data from similar domains to estimate the mean in a particular small area. This borrowing of strength is justified by assuming a model that relates the small area means. Here, we suggest a non-informative or objective Bayesian approach to small area estimation. Using this approach, one can estimate population parameters other than means and find sensible estimates of their precision. AMS 1991 subject classifications Primary 62D05; secondary 62C10.

Description:

The problem of estimating the median of a finite population when an auxiliary variable is present is considered. Point and interval estimators based on a non-informative Bayesian approach are proposed. The point estimator is compared to other possible estimators and is seen to perform well in a variety of situations.