Some Asymptotics for Localized Principal Components and Curves

The asymptotic behavior of localized principal components applying kernels as weights is investigated. In particular, we show that the first-order approximation of the first localized principal component at any given point only depends on the bandwidth parameter(s) and the density at that point. This result is extended to the context of local principal curves, where the characteristics of the points at which the curve stops at the edges are identified. This is used to provide a method which allows the curve to proceed beyond its natural endpoint if desired.     

Statistical Discrimination Analysis Using the Maximum Function

The maximum of k functions defined on R ⁿ , n ≥ 1, by f _max (x) = max{f ₁ (x),…, f _k (x)}, ? x ? R ⁿ , can have important roles in Statistics, particularly in Classification. Through its relation with the Bayes error, which is the reference error in classification, it can serve to compute numerical bounds for errors in other classification schemes. It can also serve to define the joint L¹-distance between more than two densities, which, in turn, will serve as a useful tool in Classification and Cluster Analyses. It has a vast potential application in digital image processing too. Finally, its versatile role can be seen in several numerical examples, related to the analysis of Fisher's classical iris data in multidimensional spaces.     

Consistency of non parametric estimators of the area under the ROC curve

ABSTRACT

The area under the receiver operating characteristic (ROC) curve is a popular summary index that measures the accuracy of a continuous-scale diagnostic test to measure its accuracy. Under certain conditions on estimators of distribution functions, we prove a theorem on strong consistency of the non parametric “plugin” estimators of the area under the ROC curve. Based on this theorem, we construct some new “plugin” consistent estimators. The performance of the non parametric estimators considered is illustrated numerically and the estimators are compared in terms of bias, variance, and mean square error.     

Reanalyzing Ultimatum Bargaining—Comparing Nondecreasing Curves Without Shape Constraints

We employ a hierarchical Bayesian method with exchangeable prior distributions to estimate and compare similar nondecreasing response curves. A Dirichlet process distribution is assigned to each of the response curves as a first stage prior. A second stage prior is then used to model the hyperparameters. We define parameters which will be used to compare the response curves. A Markov chain Monte Carlo method is applied to compute the resulting Bayesian estimates. To illustrate the methodology, we re-examine data from an experiment designed to test whether experimenter observation influences the ultimatum game. A major restriction of the original analysis was the shape constraint that the present technique allows us to greatly relax. We also consider independent priors and use Bayes factors to compare various models.     

Nonparametric Predictive Inference for diagnostic accuracy

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine and health care. Good methods for determining diagnostic accuracy provide useful guidance on selection of patient treatment, and the ability to compare different diagnostic tests has a direct impact on quality of care. In this paper Nonparametric Predictive Inference (NPI) methods for accuracy of diagnostic tests with continuous test results are presented and discussed. For such tests, Receiver Operating Characteristic (ROC) curves have become popular tools for describing the performance of diagnostic tests. We present the NPI approach to ROC curves, and some important summaries of these curves. As NPI does not aim at inference for an entire population but instead explicitly considers a future observation, this provides an attractive alternative to standard methods. We show how NPI can be used to compare two continuous diagnostic tests.     

Empirical likelihood confidence regions for comparison distributions and roc curves

Abstract: The authors derive empirical likelihood confidence regions for the comparison distribution of two populations whose distributions are to be tested for equality using random samples. Another application they consider is to ROC curves, which are used to compare measurements of a diagnostic test from two populations. The authors investigate the smoothed empirical likelihood method for estimation in this context, and empirical likelihood based confidence intervals are obtained by means of the Wilks theorem. A bootstrap approach allows for the construction of confidence bands. The method is illustrated with data analysis and a simulation study.     

On Broadening Failure Rate Distributions in PRA Uncertainty Analyses

Several recent nuclear power plant probabilistic risk assessments (PRAs) have utilized broadened Reactor Safety Study (RSS) component failure rate population variability curves to compensate for such things as expert "overvaluation bias" in the estimates upon which the curves are based.
A simple two-components of variation empirical Bayes model is proposed for use in estimating the between-expert variability curve in the presence of such biases. Under certain conditions this curve is a population variability curve. Comparisons are made with the existing method.
The popular procedure appears to be generally much more conservative than the empirical Bayes method in removing such biases. In one case the broadened curve based on the popular method is more than two orders of magnitude broader than the empirical Bayes curve. In another case it is found that the maximum justifiable degree of broadening of the RSS curve is to increase α from 5% to 12%, which is significantly less than the 20% value recommended in the popular approach.     

The South Oaks Gambling Screen-revised Adolescent (SOGS-RA) Revisited: A Cut-point Analysis

The lack of a criterion validity gold standard defining adolescent pathological gambling represents a major limitation of the adolescent gambling literature. The present study employed Receiver Operating Characteristic curve analysis (ROC) to examine the performance of the South Oaks Gambling Screen-Revised Adolescent (SOGS-RA) recommended cut-point of 4 against two-proxy gold standards: self-identified need for, or receipt of, help for gambling. Logistic regression analysis examined the correlates of self-identified need for help with gambling. The sample was comprised of 12990 adolescents from Atlantic Canada whose average age was 15 years and 50% of whom were male. The SOGS-RA performed as well or better with these proxy gold standards than with proxies used in previous studies. We concluded that the proxy gold standards based on self-identified need for or receipt of help represent a pragmatic solution to the lack of an adolescent-specific definition of problem or pathological gambling. Students in grade seven and SOGS-RA scores of 4 or greater were independent predictors of self-identifying a need for help.     

Risk analysis of fast spreading species in a Kashmir Himalayan National Park (Dachigam) for better monitoring and management

Huge economic costs and ecological impacts of invasive alien species (IAS) in the protected areas (PAs) worldwide make their timely prediction and potential risk assessment of central importance for effective management. While the preborder weed risk assessment framework has been extensively evaluated and implemented, the postborder species risk assessment framework has not been subjected to the same degree of scrutiny. Here we used a rather more realistic modified version of the Australian Weed Risk framework (AWRM) for Dachigam National Park (DNP) in Kashmir Himalaya against 84 plant species, including 55 alien species and 29 fast spreading native species, for risk analysis. We found two very high-risk species, three high-risk species, 10 medium-risk species, 29 low-risk species, and 40 negligible-risk species in the DNP. The containment scores accordingly ranged from 14.4 to 293.5 comprising of 27 species that can be contained with very high feasibility, 23 species with high feasibility, 14 species with medium feasibility, and 12 species which cannot be contained easily thereby having low feasibility of containment (FOC) score. However, eight species which have a negligible FOC score are difficult to contain within their infestation sites. Our results demonstrate the merit of the AWRM with a caution that the necessary region-specific modifications may help in its better implementation. Overall, these results provide quite a promising tool in the hands of protected area managers to timely and effectively deal with the problem of plant invasions.