A Review of Bootstrap Methods in Ranked Set Sampling

This chapter provides a brief review of the existing resampling methods for RSS and its implementation to construct a bootstrap confidence interval for the mean parameter. The authors present a brief comparison of these existing methods in terms of their flexibility and consistency. To construct the bootstrap confidence interval, three methods are adopted, namely, bootstrap percentile method, bias-corrected and accelerated method, and method based on monotone transformation along with normal approximation. Usually, for the second method, the accelerated constant is computed by employing the jackknife method. The authors discuss an analytical expression for the accelerated constant, which results in reducing the computational burden of this bias-corrected and accelerated bootstrap method. The usefulness of the proposed methods is further illustrated by analyzing real-life data on shrubs.

Generalized Inference on Stress-Strength Reliability in Generalized Pareto Model

The article focuses on the inference of stress-strength reliability in generalized Pareto model using the generalized variable approach and bootstrap percentile method. Simulation studies are conducted to obtain expected lengths and coverage probabilities of confidence intervals constructed using the generalized variable and the bootstrap percentile methods. An example consisting of real stress-strength data is also presented for illustrative purposes.

A Data Mining Approach Identified Salivary Biomarkers That Discriminate between Two Obesity Measures

Background. A key mechanism of obesity involves dysregulation of metabolic and inflammatory markers. This study aimed to identify salivary biomarkers and other factors associated with obesity using an ensemble data mining approach. Methods. For a random cohort of over 700 subjects from 8137 Kuwait children (10.00 ± 0.67 years), four data mining methods were applied to identify important variables associated with obesity, including logistic regression by lasso regularization (Lasso), multivariate adaptive regression spline (MARS), random forests (RF), and boosting classification trees (BT). Each algorithm generated a variable importance rank list, based on an internal cross-validation procedure. An aggregated importance ranking was constructed by averaging the rank ordering of variables from individual list, weighted by the classification performance of respective models. Subsequently, the subset of top-ranking variables that were identified with at least three algorithms was evaluated by classification performance using receiver operating characteristic (ROC) analysis with bootstrap percentile resampling. Results. Obesity was defined either by the waist circumference (OBW) or by the body mass index (BMI) (OBWHO). We identified C-reactive protein (CRP), insulin, leptin, adiponectin, as salivary biomarkers associated with OBW, plus a clinical feature fitness level. A similar set of biomarkers was identified for OBWHO, but not including leptin. Tree-based clustering analysis revealed patterns that were significantly different between the OBW and OBWHO subjects. Conclusion. A data mining approach based on multiple algorithms is useful for identifying factors associated with phenotypes, especially in cases where relationships are not salient, and a consensus from multiple methods can help produce a more generalizable subset of features. In this case, we have demonstrated that evaluation using the waist circumference includes association with high levels of salivary leptin, which is not seen with evaluation by BMI.

Bootstrap Prediction Intervals for Small Area Means from Unit-Level Nonlinear Models

For analyses based on nonlinear models, agencies and policy makers are often interested in prediction intervals for small area means. We give statistics for small area predictions that can be used to construct prediction intervals in the same way that standard errors and degrees of freedom are used to construct prediction intervals based on the Student-t distribution. In a simulation study, the new parametric bootstrap prediction interval has good coverage properties and much better coverage than the bootstrap percentile prediction interval. The methods are applied in a study of soil erosion and water runoff conducted by the US Department of Agriculture.

Percentile and Percentile-t Bootstrap Confidence Intervals: A Practical Comparison

This paper employs a Monte Carlo study to compare the performance of equal-tailed bootstrap percentile-