Bootstrap Selector for the Smoothing Parameter of Beran’s Estimator

This work proposes a resampling technique to approximate the smoothing parameter of Beran’s estimator. It is based on resampling by the smoothed bootstrap and minimising the bootstrap approximation of the mean integrated squared error to find the bootstrap bandwidth. The behaviour of this method has been tested by simulation on several models. Bootstrap confidence intervals are also addressed in this research and their performance is analysed in the simulation study.

Nutritional Inadequacy: Unraveling the Methodological Challenges for the Application of the Probability Approach or the EAR Cut-Point Method—A Pregnancy Perspective

The aim of this study was to unravel the methodological challenges when exploring nutritional inadequacy, involving 608 healthy pregnant women. The usual intake of twenty-one nutrients was recorded by employing a validated FFQ. Simulated datasets of usual intake were generated, with randomly imposed uncertainty. The comparison between the usual intake and the EAR was accomplished with the probability approach and the EAR cut-point method. Point estimates were accompanied by bootstrap confidence intervals. Bootstrap intervals applied on the risk of inadequacy for raw and simulated data tended in most cases to overlap. A detailed statistical analysis, aiming to predict the level of inadequacy, as well as the application of the EAR cut-point method, along with bootstrap intervals, could effectively be used to assess nutrient inadequacy. However, the final decision for the method used depends on the distribution of nutrient-intake under evaluation. Irrespective of the applied methodology, moderate to high levels of inadequacy, calculated from FFQ were identified for certain nutrients (e.g. vitamins C, B6, magnesium, vitamin A), while the highest were recorded for folate and iron. Considering that micronutrient-poor, obesogenic diets are becoming more common, the underlying rationale may help towards unraveling the complexity characterizing nutritional inadequacies, especially in vulnerable populations.

On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.

On the Construction of Bootstrap Confidence Intervals for Estimating the Correlation Between Two Time Series Not Sampled on Identical Time Points

Two important issues characterize the design of bootstrap methods to construct confidence intervals for the correlation between two time series sampled (unevenly or evenly spaced) on different time points: (i) ordinary block bootstrap methods that produce bootstrap samples have been designed for time series that are coeval (i.e., sampled on identical time points) and must be adapted; (ii) the sample Pearson correlation coefficient cannot be readily applied, and the construction of the bootstrap confidence intervals must rely on alternative estimators that unfortunately do not have the same asymptotic properties. In this paper it is argued that existing proposals provide an unsatisfactory solution to issue (i) and ignore issue (ii). This results in procedures with poor coverage whose limitations and potential applications are not well understood. As a first step to address these issues, a modification of the bootstrap procedure underlying existing methods is proposed, and the asymptotic properties of the estimator of the correlation are investigated. It is established that the estimator converges to a weighted average of the cross-correlation function in a neighborhood of zero. This implies a change in perspective when interpreting the results of the confidence intervals based on this estimator. Specifically, it is argued that with the proposed modification of the bootstrap, the existing methods have the potential to provide a useful lower bound for the absolute correlation in the non-coeval case and, in some special cases, confidence intervals with approximately the correct coverage. The limitations and implications of the results presented are demonstrated with a simulation study. The extension of the proposed methodology to the problem of estimating the cross-correlation function is straightforward and is illustrated with a real data example. Related applications include the estimation of the autocorrelation function and the periodogram of a time series.

Patient-level detection of grade group ≥2 prostate cancer using quantitative diffusion MRI

Purpose: Multiparametric MRI (mpMRI) improves detection of clinically significant prostate cancer (csPCa), but the qualitative PI-RADS system and quantitative apparent diffusion coefficient (ADC) yield inconsistent results. An advanced Restrictrion Spectrum Imaging (RSI) model may yield a better quantitative marker for csPCa, the RSI restriction score (RSIrs). We evaluated RSIrs for patient-level detection of csPCa. Materials and Methods: Retrospective analysis of men who underwent mpMRI with RSI and prostate biopsy for suspected prostate cancer from 2017-2019. Maximum RSIrs within the prostate was assessed by area under the receiver operating characteristic curve (AUC) for discriminating csPCa (grade group ≥2) from benign or grade group 1 biopsies. Performance of RSIrs was compared to minimum ADC and PI-RADS v2-2.1via bootstrap confidence intervals and bootstrap difference (two-tailed α=0.05). We also tested whether the combination of PI-RADS and RSIrs (PI-RADS+RSIrs) was superior to PI-RADS, alone. Results: 151 patients met criteria for inclusion. AUC values for ADC, RSIrs, and PI-RADS were 0.50 [95% confidence interval: 0.41, 0.60], 0.76 [0.68, 0.84], and 0.78 [0.71, 0.85], respectively. RSIrs (p=0.0002) and PI-RADS (p<0.0001) were superior to ADC for patient-level detection of csPCa. The performance of RSIrs was comparable to that of PI-RADS (p=0.6). AUC for PI-RADS+RSIrs was 0.84 [0.77, 0.90], superior to PI-RADS or RSIrs, alone (p=0.008, p=0.009). Conclusions: RSIrs was superior to conventional ADC and comparable to (routine, clinical) PI-RADS for patient-level detection of csPCa. The combination of PI-RADS and RSIrs was superior to either alone. RSIrs is a promising quantitative marker worthy of prospective study in the setting of csPCa detection.

Analytic and bootstrap confidence intervals for the common-language effect size estimate

Evaluating how an effect-size estimate performs between two continuous variables based on the common-language effect size (CLES) has received increasing attention. While Blomqvist (1950; https://doi.org/10.1214/aoms/1177729754) developed a parametric estimator (q') for the CLES, there has been limited progress in further refining CLES. This study: a) extends Blomqvist’s work by providing a mathematical foundation for Bp (a non-parametric version of CLES) and an analytic approach for estimating its standard error; and b) evaluates the performance of the analytic and bootstrap confidence intervals (CIs) for Bp. The simulation shows that the bootstrap bias-corrected-and-accelerated interval (BCaI) has the best protected Type 1 error rate with a slight compromise in Power, whereas the analytic-t CI has the highest overall Power but with a Type 1 error slightly larger than the nominal value. This study also uses a real-world data-set to demonstrate the applicability of the CLES in measuring the relationship between age and sexual compulsivity.

Anger Rumination and Mindfulness: Mediating Effects on Forgiveness

(1) Background: Different investigations relate mindfulness practice as a strategy to cope with and improve negative repetitive thinking states and forgiveness. (2) Methods: The aim is to analyze the mediating processes of mindfulness as a trait and the changes in the anger rumination on forgiveness. This sample comprised 264 undergraduate students (M = 24.13 years, SD = 11.39). The instruments used were the Anger Rumination Scale (ARS), the Five Facet Mindfulness Questionnaire (FFMQ) and the Heartland Forgiveness Scale (HFS). For data analysis, the spillover effect was calculated using 10,000 bootstrap samples for the bootstrap confidence intervals (CI). (3) Conclusions: The results confirm that the relationship between mindfulness practice and forgiveness is mediated by changes in mindfulness trait and anger rumination. Given the results obtained, it is considered appropriate to extend the study to samples from other countries, as well as to contexts of depressive rumination or anxiety.

Accuracy assessment of the joint CloudSat-CALIPSO global cloud amount based on the bootstrap confidence intervals

&lt;p&gt;Vertically-resolved cloud amount is essential for understanding the Earth&amp;#8217;s radiation budget. Joint CloudSat-CALIPSO, lidar-radar cloud climatology remains the only dataset providing such information globally. However, a specific sampling scheme (pencil-like swath, 16-day revisit) introduces an uncertainty to CloudSat-CALIPSO cloud amounts. In the research we assess those uncertainties in terms of a bootstrap confidence intervals. Five years (2006-2011) of the 2B-GEOPROF-LIDAR (version P2_R05) cloud product was examined, accounting for &amp;#160;typical spatial resolutions of a global grids (1.0&amp;#176;, 2.5&amp;#176;, 5.0&amp;#176;, 10.0&amp;#176;), four confidence levels of confidence interval (0.85, 0.90, 0.95, 0.99), and three time scales of mean cloud amount (annual, seasonal, monthly). Results proved that cloud amount accuracy of 1%, or 5%, is not achievable with the dataset, assuming a 5-year mean cloud amount, high (&gt;0.95) confidence level, and fine spatial resolution (1&amp;#186;&amp;#8211;2.5&amp;#186;). The 1% requirement was only met by ~6.5% of atmospheric volumes at 1&amp;#186; and 2.5&amp;#186;, while more tolerant criterion (5%) was met by 22.5% volumes at 1&amp;#186;, or 48.9% at 2.5&amp;#186; resolution. In order to have at least 99% of volumes meeting an accuracy criterion, the criterion itself would have to be lowered to ~20% for 1&amp;#186; data, or to ~8% for 2.5&amp;#186; data. Study also quantified the relation between confidence interval width, and spatial resolution, confidence level, number of observations. Cloud regime (mean cloud amount, and standard deviation of cloud amount) was found the most important factor impacting the width of confidence interval. The research has been funded by the National Science Institute of Poland grant no. UMO-2017/25/B/ST10/01787. This research has been supported in part by PL-Grid Infrastructure (a computing resources).&lt;/p&gt;