arXiv subjects

J. Miguel Marín

Publications and source records attributed to J. Miguel Marín.

3 recordsLinked to original sources

arXiv2026

Unifying small area estimators based on area-level and unit-level models through calibration

When estimating area means, direct estimators based on area-specific data, are usually consistent under the sampling design without model assumptions. However, they are inefficient if the area sample size is small. In small area estimation, model assumptions linking the areas are used to "borrow strength" from other areas. The basic area-level model provides design-consistent estimators but error variances are assumed to be known. In practice, they are estimated with the (scarce) area-specific data. These estimators are inefficient, and their error is not accounted for in the associated mean squared error estimators. Unit-level models do not require to know the error variances but do not account for the survey design. Here we describe a unified estimator of an area mean that may be obtained both from an area-level model or a unit-level model and based on consistent estimators of the model error variances as the number of areas increases. We propose bootstrap mean squared error estimators that account for the uncertainty due to the estimation of the error variances. We show a better performance of the new small area estimators and our bootstrap estimators of the mean squared error. We apply the results to education data from Colombia.

stat.ME↗

arXiv2025

Small Area Estimation of General Indicators in Off-Census Years

We propose small area estimators of general indicators in off-census years, which avoid the use of deprecated census microdata, but are nearly optimal in census years. The procedure is based on replacing the obsolete census file with a larger unit-level survey that adequately covers the areas of interest and contains the values of useful auxiliary variables. However, the minimal data requirement of the proposed method is a single survey with microdata on the target variable and suitable auxiliary variables for the period of interest. We also develop an estimator of the mean squared error (MSE) that accounts for the uncertainty introduced by the large survey used to replace the census of auxiliary information. Our empirical results indicate that the proposed predictors perform clearly better than the alternative predictors when census data are outdated, and are very close to optimal ones when census data are correct. They also illustrate that the proposed total MSE estimator corrects for the bias of purely model-based MSE estimators that do not account for the large survey uncertainty.

stat.ME↗

arXiv2014

Bayesian modeling of bacterial growth for multiple populations

Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this study, we develop two models to describe bacterial growth for multiple populations under both equal and different environmental conditions. First, a semi-parametric model based on the Gompertz equation is proposed. Assuming that the parameters of the Gompertz equation may vary in relation to the running conditions under which the experiment is performed, we use feedforward neural networks to model the influence of these environmental factors on the growth parameters. Second, we propose a more general model which does not assume any underlying parametric form for the growth function. Thus, we consider a neural network as a primary growth model which includes the influencing environmental factors as inputs to the network. One of the main disadvantages of neural networks models is that they are often very difficult to tune, which complicates fitting procedures. Here, we show that a simple Bayesian approach to fitting these models can be implemented via the software package WinBugs. Our approach is illustrated using real experimental Listeria monocytogenes growth data.

stat.AP↗