María del Mar Rueda

Missing data and auxiliary information in surveys

SummaryThis paper proposes estimation methods with auxiliary information when some observations are missing from the sample. These ratio, difference and regression methods are proposed for any sampling design and are compared with other complete case estimators.

New imputation methods for missing data using quantiles

The problem of missing values commonly arises in data sets, and imputation is usually employed to compensate for non-response. We propose a novel imputation method based on quantiles, which can be implemented with or without the presence of auxiliary information. The proposed method is extended to unequal sampling designs and non-uniform response mechanisms. Iterative algorithms to compute the proposed imputation methods are presented. Monte Carlo simulations are conducted to assess the performance of the proposed imputation methods with respect to alternative imputation methods. Simulation results indicate that the proposed methods perform competitively in terms of relative bias and relative root mean square error.

Mean estimation with calibration techniques in presence of missing data

The problem of estimating the population mean using calibration estimators when some observations on the study and auxiliary characteristics are missing from the sample, is considered. Some new classes of estimators are proposed for any sampling design. These new classes employ to all observation (incomplete cases too) in the estimation without using any imputation techniques. On the basis of properties derived and some simulation results, the proposed estimators are compared with other complete case estimators.

Indirect methods of imputation of missing data based on available units

One of the most difficult problems confronting investigators who analyze data from surveys is how to treat missing data. Many statistical procedures cannot be used immediately if any values are missing. Imputation of missing data before starting statistical analysis is then necessary. This paper proposes imputation methods of the mean based on indirect estimators of available cases. A complete simulation study was performed to test the proposed techniques.

The use of Quantiles of Auxiliary Variables to Estimate Medians

Summary This paper proposes the use of multi-auxiliary information using quantiles and ratio and difference type estimators of the finite population distribution function to derive confidence intervals for medians. A simulation study based on three real populations compares its behaviour to that of standard methods.

Some improved estimators of finite population quantile using auxiliary information in sample surveys

Abstract The problem of quantile estimation using quantiles Qx(α) in which the order of the auxiliary variable is different from that of the main variable to be estimated, Qy(β), is considered. Certain new estimators for the β-quantile have been proposed for any sampling design. The effect of this modification on the standard estimators, ratio, position, stratification, regression and difference type estimators which use the β-quantile of the auxiliary variable to estimate the β-quantile of the main variable, is studied. On the basis of properties derived and some simulation results, the efficiencies of these estimators are compared. It is shown that by the appropriate choice of the α order of the quantile, it is possible to obtain a considerable increase in precision with respect to standard estimators. In simple random sampling, a procedure for choosing the α value is proposed.

Estimators and Confidence Intervals for the Proportion Using Binary Auxiliary Information with Applications to Pharmaceutical Studies

Estimation of a proportion is commonly used in areas such as medicine, biopharmaceutical experiments, etc. Estimation of a proportion using auxiliary information has not been investigated in the literature. Ratio estimators of the population proportion and two-sided confidence intervals based upon auxiliary information are derived in this paper. Real data extracted from the Spanish National Health Survey are used to demonstrate the application of the proposed methods in the estimation of prevalences. Results derived from simulation studies show that proposed estimators are more efficient than the traditional estimator. Proposed confidence intervals outperform the alternative methods, especially in terms of interval width. A study on patients with hypertension is also considered to calculate various estimators and confidence intervals.

Quantile estimation in two-phase sampling

The estimation of quantiles in two-phase sampling with arbitrary sampling design in each of the two phases is investigated. Several ratio and exponentiation type estimators that provide the optimum estimate of a quantile based on an optimum exponent @a are proposed. Properties of these estimators are studied under large sample size approximation and the use of double sampling for stratification to estimate quantiles can also be seen. The real performance of these estimators will be evaluated for the three quartiles on the basis of data from two real populations using different sampling designs. The simulation study shows that proposed estimators can be very satisfactory in terms of relative bias and efficiency.

Using multiparametric auxiliary information at the estimation stage

Difference type estimators use auxiliary information based on an auxiliary parameter (specifically the parameter of interest), associated with the auxiliary variable. In practice, however, several parameters for auxiliary variables are available. This paper discusses how such estimators can be modified to improve the usual methods if information related to other parameters associated with an auxiliary variable or variables is available. Some applications estimating several such parameters are described. A proper set of simulation-based comparisons is made.

Calibration estimation in dual-frame surveys

Survey statisticians make use of auxiliary information to improve estimates. One important example is calibration estimation, which constructs new weights that match benchmark constraints on auxiliary variables while remaining “close” to the design weights. Multiple-frame surveys are increasingly used by statistical agencies and private organizations to reduce sampling costs and/or avoid frame undercoverage errors. Several ways of combining estimates derived from such frames have been proposed elsewhere; in this paper, we extend the calibration paradigm, previously used for single-frame surveys, to calculate the total value of a variable of interest in a dual-frame survey. Calibration is a general tool that allows to include auxiliary information from two frames. It also incorporates, as a special case, certain dual-frame estimators that have been proposed previously. The theoretical properties of our class of estimators are derived and discussed, and simulation studies conducted to compare the efficiency of the procedure, using different sets of auxiliary variables. Finally, the proposed methodology is applied to real data obtained from the Barometer of Culture of Andalusia survey.