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A new way of parametric bootstrapping allows similar construction of confidence ellipses applicable on all results from Multiple Factor Analysis obtained from the FactoMineR package in the statistical program R. With this procedure, a similar approach will be applied to Multiple Factor Analysis results regardless of the origin of data and the nature of the original variables. The approach is suitable for getting an overview of product confidence intervals and also applicable for data obtained from ‘one repetition’ evaluations. Furthermore, it is a convenient way to get an overview of variations in different studies performed on the same set of products. In addition, the graphical display of confidence ellipses eases interpretation and communication of results.

The Coccotremataceae is a small family including two genera: Coccotrema with a crustose, granulate to verrucose thallus and Lepolichen with terete lobes and rhizines. The generic concept based on this morphological difference was re-evaluated using three molecular markers, mt SSU rDNA, nu LSU rDNA, and the nu ITS region. The analysis of the ITS region does not provide sufficient resolution within the Coccotremataceae, while the other two data sets contradict the current generic concept. The mt SSU and nu LSU data sets and the combined analysis of the two data sets all place Lepolichen within Coccotrema. However, an alternative topology with monophyletic Coccotrema cannot be rejected when the ITS data set is included in the combined analyses. This shortcoming of the ITS data set can be overcome by the combined analysis of all three data sets, where monophyletic Coccotrema can be rejected using parametric bootstrapping, as in the mt SSU and nu LSU data sets and combination thereof. It is proposed to reduce Lepolichen into synonymy with Coccotrema. The correct name for the only species previously placed in Lepolichen is Coccotrema coccophontm (Mont.) I. Schmitt, Messuti & Lumbsch.

Motivation: The Dss statistic was proposed by (Mol. Biol. Evol., 14, 1125–1131, McGuire et al. (1997)) for scanning data sets for the presence of recombination, an important step in some phylogenetic analyses. The statistic, however, could not distinguish well between among-site rate variation and recombination, and had no statistical test for significant values. This paper addresses these shortfalls. Results: A modification to the Dss statistic is proposed which accounts for rate variation to a large extent. A statistical test, based on parametric bootstrapping, is also suggested. Availability: The TOPAL package (version 2) may be accessed from http://www.bioss.sari.ac.uk/~frank/Geneticsand by anonymous ftp from ftp://ftp.bioss.sari.ac.ukin the directory pub/phylogeny/topal. Contact: frank@bioss.sari.ac.uk

SUMMARY Recent papers have questioned the appropriateness of the circular confidence regions often drawn around group mean points in canonical variate analysis and proposed improved elliptical regions. This paper develops new theoretical and bootstrap regions of an alternative type, with those constructed using parametric bootstrapping being shown by simulation to perform consistently well.

SUMMARY A large deviation result is established for the bootstrap empirical distribution in a finite sample space, thereby validating both nonparametric and parametric bootstrapping in certain phylogenetic inference problems. The bias previously observed in the bootstrap distribution of the estimated tree topology is shown to stem from dispersion effects in the joint distribution of sample and bootstrap empirical distributions. Both results are examined for maximum likelihood estimation in a three-taxon model having particularly simple geometry. They are also applicable to discrete parameter problems outside of phylogenetic inference.

Bootstrapping has gained popularity in different tests of hypotheses as an alternative in using asymptotic distribution if one is not sure of the distribution of the test statistic under a null hypothesis. This method, in general, has two variants – the parametric and the nonparametric approaches. However, issues on reliability of this method always arise in many applications. This paper addresses the issue on reliability by establishing a reliability measure in terms of quantiles with respect to asymptotic distribution, when this is approximately correct. The test of hypotheses used is Ftest. The simulated results show that using nonparametric bootstrapping in F-test gives better reliability than parametric bootstrapping with relatively higher degrees of freedom., {"references":["S. Amiri, D. von Rosen, and S. Zwanzig, \"On the comparison of\nparametric and nonparametric bootstrap,\" Uppsala University\nDepartment of Mathematics Report 2008:15. Uppsala University,\nUppsala, Sweden, 2008, unpublished.","R. Barlow and F. Proschan, Mathematical Theory of Reliability, SIAM\nClassics edition, 1996, pp. 5-6.","A. Davison and D. Hinkley, Bootstrap Methods and their Applications.\nCambridge, United Kingdom: Cambridge University Press, 1997, ch. 1.","P. Good and J. Hardin, Common Errors in Statistics: How to Avoid\nThem. New Jersey: John Wiley & Sons, 2005.","J. MacKinnon, \"Bootstrap hypothesis testing,\" Queen-s Economics\nDepartment Working Paper No. 1127, Queen-s University, Ontario,\nCanada, 2007, unpublished.","J. MacKinnon and R. Davidson, \"Improving the reliability of bootstrap\ntests with the fast double bootstrap,\" Queen-s Economics Department\nWorking Paper No. 1044. Queen-s University, Ontario, Canada, 2006,\nunpublished.","B. Efron and R. Tibshirani, An Introduction to the Bootstrap, New York:\nChapman & Hall, 1993, pp. 31-32.","D. Politis, \"The impact of bootstrap methods in time series,\" Statistical\nScience, Vol. 18, No. 2, 2003, pp. 219-230."]}

This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic "expected improvement" (EI) in "efficient global optimization" (EGO) through the introduction of an improved estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are compared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer. We thank the anonymous referee for a very detailed report that lead to the additional experiments in Table 1 aimed at investigating the effects of different initial sample sizes, the example in the Appendix, a simpler notation, and many other minor improvements. We also thank Emmanuel Vazquez (SUPÉLEC) for bringing Abt (1999) and Müller and Pronzato (2009) to our attention.

This paper concerns the asymptotic validity of the bootstrap method in a non-regular model. Specifically, it is shown that the parametric bootstrap of the change-point parameter in the change-point hazard rate model works.

• Input data included ageand sex-specific population, ageand sexspecific all-cause mortality, and cubic spline interpolation of sizeand sex-specific relative risk (RR) of death estimates for persons with AAA compared with persons without AAA, adjusted for age, ethnicity, height, weight, smoking, and cardiovascular disease history. Confidence intervals were calculated via a monte carlo simulation (parametric bootstrapping). Results • There were 2,347,339 (90% CI: 2,178,188–2,519,827) prevalent cases of AAA in the United States in 2013, resulting in 41,371 (90% CI: 34,888–47,102) deaths attributable to AAA. • Prevalence of AAA was greatest in the 60–64 years age group for both men and women, while AAA-attributable deaths peaked in the 80–84 years age group for both men and women (Fig 1). • Small AAAs (infrarenal diameter 3.0–3.9 cm) accounted for 72.7% of the total prevalent cases and 59.1% of attributable deaths, compared with large AAAs (infrarenal diameter ≥4.0 cm) accounting for 27.3% of the total prevalent cases and 40.9% of deaths (Fig 2, Fig 3). • Females constituted 21.1% of prevalent cases and 45.2% of deaths, compared with males constituting 79.0% of prevalent cases and 54.8% of deaths (Fig 2, Fig 3). • Among men ≥55 years of age, 2.01% of all-cause deaths (90% CI: 1.67%–2.32%) were attributable to AAA, compared with 1.34% of allcause deaths among women ≥55 years of age (90% CI: 1.18%–1.48%) (data not shown).

Publisher Summary This chapter discusses the standard approaches that have been used to estimate variation in landmark data and explains why these methods do not properly estimate variation in biological forms. Though some of these approaches have become rather mathematically involved, their suitability to the realities of biological data has not improved in parallel. The chapter presents a generalized model for variation in landmark data. It has been shown that only certain features of this model can be consistently estimated. This model and the estimators are used in morphometric analysis as the basis for parametric bootstrapping procedures to test for differences in form using landmark data. Recognizing the limitation of the ability to estimate only certain features of this general model of variation, it discusses the need for the development of less general models that may reasonably characterize variation in landmark data. The chapter shows how biological knowledge pertaining to the organisms under study can be used to impose certain constraints on the models of variance–covariance structure. It suggests ways to integrate such constraints into the proposal of several less generalized models, some statistically convenient but biologically improbable, others less streamlined statistically but more biologically reasonable.

The problem of distinguishing density-independent (DI) from density-dependent (DD) demographic time series has been addressed in the past via hypothesis testing based on parametric bootstrapping (PBLR) and, in later works, by Information Criteria such as FPE or SIC. Here, we address the problem in a novel way using Structural Risk Minimization (SRM). DI and DD time series corrupted with noise are extensively simulated using a drift (DI) and a Ricker (DD) model; on each generated time series, both models are identified, and then one is selected by FPE, SIC and SRM. The probability of density-[in]dependence recognition is statistically assessed and compared with the results obtained via PBLR in a previous work.

This paper describes a new methodology for equipment fault detection. This methodology consists of fitting a thin-plate spline to post-process spatial data in order to construct a virtual wafer surface. The virtual wafer surface is then compared to an established baseline process surface, and the resulting spatial signature is used to detect equipment faults. Statistical distributional studies of signature metrics using a parametric bootstrapping technique provide the justification of determining the significance of the signature. Data collected from a Rapid Thermal Chemical Vapor Deposition (RTCVD) process is used to illustrate the procedures. This method detected equipment faults for all 11 wafers that were subjected to induced equipment faults.

In recent years, likelihood ratio tests (LRTs) based on DNA and protein sequence data have been proposed for testing various evolutionary hypotheses. Because conducting an LRT requires an evolutionary model of nucleotide or amino acid substitution, which is almost always unknown, it becomes important to investigate the robustness of LRTs to violations of assumptions of these evolutionary models. Computer simulation was used to examine performance of LRTs of the molecular clock, transition/transversion bias, and among-site rate variation under different substitution models. The results showed that when correct models are used, LRTs perform quite well even when the DNA sequences are as short as 300 nt. However, LRTs were found to be biased under incorrect models. The extent of bias varies considerably, depending on the hypotheses tested, the substitution models assumed, and the lengths of the sequences used, among other things. A preliminary simulation study also suggests that LRTs based on parametric bootstrapping may be more sensitive to substitution models than are standard LRTs. When an assumed substitution model is grossly wrong and a more realistic model is available, LRTs can often reject the wrong model; thus, the performance of LRTs may be improved by using a more appropriate model. On the other hand, many factors of molecular evolution have not been considered in any substitution models so far built, and the possibility of an influence of this negligence on LRTs is often overlooked. The dependence of LRTs on substitution models calls for caution in interpreting test results and highlights the importance of clarifying the substitution patterns of genes and proteins and building more realistic models.

The video lottery terminal dataset contains observations on the three windows of an electronic slot machine for 345 plays together with the prize paid out for each play. The prize payout distribution is so badly skewed that confidence intervals for expected payout based on the central limit theorem are not accurate. This dataset can be used at the graduate or upper undergraduate level to illustrate parametric bootstrapping. The dataset can also be used in a graduate course to illustrate tests of independence for two and three-way contingency tables involving random zeroes, or these tables may be collapsed and used as examples in an introductory course.