Bootstrap Estimates Research Articles

How many bootstrap replications are necessary for estimating remote sensing-assisted, model-based standard errors?

When probability samples are not available, the model-based framework may be the only option for constructing inferences in the form of prediction intervals for population means. Further, for machine learning and some non-parametric and nonlinear regression prediction techniques, resampling methods such as the bootstrap may be the only option for obtaining the standard errors necessary for constructing those prediction intervals.All bootstrap approaches entail repeatedly sampling from the original sample, estimating the parameter of interest for each replication, and estimating the standard error of the estimate of the parameter as the standard deviation of the bootstrap estimates over replications. The objective of the study was to develop a procedure for terminating resampling such that the resulting number of replications assures, at least in probability, that the estimate of the standard error stabilizes to the standard error corresponding to one million replications. The analyses used a variety of datasets: five forest inventory datasets with either volume or aboveground biomass as the dependent variable and metrics from either airborne laser scanning or Landsat as independent variables, three from Europe, one from Southwest Asia, and one from Africa; and two forest/non-forest versus Landsat datasets, one from Minnesota and one from Wisconsin, both in the USA. The primary contribution of the study was development and demonstration of a procedure that specifies criteria for terminating resampling that assure in probability that the bootstrap estimate of the standard error stabilizes to the estimate obtained with one million replications.

Hypotheses Testing from Complex Survey Data Using Bootstrap Weights: A Unified Approach

ABSTRACT Standard statistical methods without taking proper account of the complexity of a survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In particular, the Type I error rates of hypotheses tests using standard methods can be much larger than the nominal significance level. Methods incorporating design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests that involve estimated covariance matrices of parameter estimates. In this article, we present a unified approach to hypothesis testing without requiring estimated covariance matrices or design effects, by constructing bootstrap approximations to quasi-likelihood ratio statistics and quasi-score statistics and establishing its asymptotic validity. The proposed method can be easily implemented without a specific software designed for complex survey sampling. We also consider hypothesis testing for categorical data and present a bootstrap procedure for testing simple goodness of fit and independence in a two-way table. In simulation studies, the Type I error rates of the proposed approach are much closer to their nominal significance level compared with the naive likelihood ratio test and quasi-score test. An application to an educational survey under a logistic regression model is also presented. Supplementary materials for this article are available online.

Bootstrapping Clustered Data in R using lmeresampler

Linear mixed-effects models are commonly used to analyze clustered data structures. There are numerous packages to fit these models in R and conduct likelihood-based inference. The implementation of resampling-based procedures for inference are more limited. In this paper, we introduce the lmeresampler package for bootstrapping nested linear mixed-effects models fit via lme4 or nlme. Bootstrap estimation allows for bias correction, adjusted standard errors and confidence intervals for small samples sizes and when distributional assumptions break down. We will also illustrate how bootstrap resampling can be used to diagnose this model class. In addition, lmeresampler makes it easy to construct interval estimates of functions of model parameters.

Long‐term stability of periodic smooth irrotational flows to the electrons Euler–Poisson system in three dimensions

We are concerned with the one‐fluid Euler–Poisson system for the electrons on the cubes in three dimensions. With the bootstrap estimates, we prove long‐term stability of periodic solutions of this system with small smooth irrotational perturbations of a constant background. Our main result is that the solutions are well‐posed for a time at least , where is the size of the initial data, the sufficiently large is the side length of the cubes, and is the index of the classical Sobolev spaces .

Mid-Holocene expansion of the Indian Ocean warm pool documented in coral Sr/Ca records from Kenya

Proxy reconstructions suggest that mid-Holocene East African temperatures were warmer than today between 8 and 5 ka BP, but climate models cannot replicate this warming. Precessional forcing caused a shift of maximum insolation from boreal spring to fall in the mid-Holocene, which may have favored intense warming at the start of the warm season. Here, we use three Porites corals from Kenya that represent time windows from 6.55 to 5.87 ka BP to reconstruct past sea surface temperature (SST) seasonality from coral Sr/Ca ratios in the western Indian Ocean during the mid-Holocene. Although the Indian monsoon was reportedly stronger in the mid-Holocene, which should have amplified the seasonal cycle of SST in the western Indian Ocean, the corals suggest reduced seasonality (mean 3.2 °C) compared to the modern record (mean 4.3 °C). Warming in austral spring is followed by a prolonged period of warm SSTs, suggesting that an upper limit of tropical SSTs under mid-Holocene conditions was reached at the start of the warm season, and SSTs then remained stable. Similar changes are seen at the Seychelles. Bootstrap estimates suggest a reduction in SST seasonality of 1.3 ± 0.22 °C at Kenya and 1.7 ± 0.32 °C at the Seychelles. SST seasonality at Kenya corresponds to present-day SST seasonality at 55° E–60° E, while SST seasonality at the Seychelles corresponds to present day SST seasonality at ~ 65° E. This implies a significant westward expansion of the Indian Ocean warm pool. Furthermore, the coral data suggests that SST seasonality deviates from seasonal changes in orbital insolation due to ocean–atmosphere interactions.

Percentile Bootstrap Interval on Univariate Local Polynomial Regression Prediction

This study offers a new technique for constructing percentile bootstrap intervals to predict the regression of univariate local polynomials. Bootstrap regression uses resampling derived from paired and residual bootstrap methods. The main objective of this study is to perform a comparative analysis between the two resampling methods by considering the nominal coverage probability. Resampling uses a nonparametric bootstrap technique with the return method, where each sample point has an equal chance of being selected. The principle of nonparametric bootstrapping uses the original sample data as a source of diversity in contrast to parametric bootstrapping, where the variety comes from generating a particular distribution. The simulation results show that the paired and residual bootstrap interval coverage probabilities are close to nominal coverage. The results showed no significant difference between paired bootstrap interval and percentile residual. Increasing the bootstrap sample size sufficiently large gives the scatterplot smoothness of the confidence interval. Applying the smoothing parameter by choice gives a second-order polynomial regression with a smoother distribution than the first-order polynomial regression. The scatterplot shows that the second-degree polynomial regression can capture the data curvature feature compared to the first-degree polynomial. The bands made from second-degree polynomials give a narrower width than first-degree polynomials. In contrast, applying optimal smoothing parameters to the model provides different conclusions by using smoothing parameters based on choice. In addition to the differences based on the scatterplot, the bootstrap estimates of the coverage probability are also other. Selecting smoothing parameters based on a particular value provides probability coverage with the paired bootstrap method for the first-degree local polynomial regression is 0.93, while the second-degree local polynomial is 0.96. The probability of coverage based on the residual bootstrap method for the first-degree local polynomial regression is 0.95, while the second-degree local polynomial is 0.96. The probability coverage based on the optimal parameters of the paired bootstrap method for the first-degree local polynomial regression is 0.945, while the second-degree local polynomial is 0.93. The residual bootstrap method gives the first-degree local polynomial regression of 0.95, while the second-degree local polynomial is 0.93. In general, both bootstrap methods work well for estimating prediction confidence intervals.

Statistical inference for the Power Rayleigh distribution based on adaptive progressive Type-II censored data

<abstract><p>The Power Rayleigh distribution (PRD) is a new extension of the standard one-parameter Rayleigh distribution. To employ this distribution as a life model in the analysis of reliability and survival data, we focused on the statistical inference for the parameters of the PRD under the adaptive Type-II censored scheme. Point and interval estimates for the model parameters and the corresponding reliability function at a given time are obtained using likelihood, Bootstrap and Bayesian estimation methods. A simulation study is conducted in different settings of the life testing experiment to compare and evaluate the performance of the estimates obtained. In addition, the estimation procedure is also investigated in real lifetimes data. The results indicated that the obtained estimates gave an accurate and efficient estimation of the model parameters. The Bootstrap estimates are better than the estimates obtained by the likelihood estimation approach, and estimates obtained using the Markov Chain Monte Carlo method by the Bayesian approach under both the squared error and the general entropy loss functions have priority over other point and interval estimates. Under the adaptive Type-II censoring scheme, concluding results confirmed that the PRD can be effectively used to model the lifetimes in survival and reliability analysis.</p></abstract>

Effects of interactivity affordance on user stickiness in livestream shopping：identification and gratification as mediators

In this day and age, livestream shopping is developing by leaps and bounds in China. It has been proved that livestream shopping is efficient in attracting customers and boosting the sales of products. However, very little research has been carried out on user stickiness, which plays a valuable role in business success. In light of the stimulus–organism–response framework (S–O–R), a multiple-mediation model (identification and gratification as mediators) was established to examine the effect of interactivity affordance (S) on the user stickiness (R) of a sample of 489 Chinese livestream viewers. Structural equation modeling with bootstrapping estimation was performed to examine the mediating roles of identification (O-cognitive) and gratification (O-affective). The modeling results revealed that the relationship between interactivity affordance and user stickiness was partially mediated by identification combined with utilitarian gratification and fully mediated by identification combined with hedonic gratification. The findings stress the importance of categorizing gratifications. In addition, these findings offer new perspectives for understanding the effects of IT affordance on user stickiness.

Benzodiazepine-related dementia risks and protopathic biases revealed by multiple-kernel learning with electronic medical records.

To simultaneously estimate how the risk of incident dementia nonlinearly varies with the administration period and cumulative dose of benzodiazepines, the duration of disorders with an indication for benzodiazepines, and other potential confounders, with the goal of settling the controversy over the role of benzodiazepines in the development of dementia. The classical hazard model was extended using the techniques of multiple-kernel learning. Regularised maximum-likelihood estimation, including determination of hyperparameter values with 10-fold cross-validation, bootstrap goodness-of-fit test, and bootstrap estimation of confidence intervals, was applied to cohorts retrospectively extracted from electronic medical records of our university hospitals between 1 November 2004 and 31 July 2020. The analysis was mainly focused on 8160 patients aged 40 or older with new onset of insomnia, affective disorders, or anxiety disorders, who were followed up for years. Besides previously reported risk associations, we detected significant nonlinear risk variations over 2-4 years attributable to the duration of insomnia and anxiety disorders, and to the administration period of short-acting benzodiazepines. After nonlinear adjustment for potential confounders, we observed no significant risk associations with long-term use of benzodiazepines. The pattern of the detected nonlinear risk variations suggested reverse causation and confounding. Their putative bias effects over 2-4 years suggested similar biases in previously reported results. These results, together with the lack of significant risk associations with long-term use of benzodiazepines, suggested the need to reconsider previous results and methods for future analysis.

Robust Inference for Partially Observed Functional Response Data.

Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in quantitative ultrasound signal analysis, this paper investigates a class of robust M-estimators for partially observed functional data including functional location and quantile estimators. Consistency of the estimators is established under general conditions on the partial observation process. Under smoothness conditions on the class of M-estimators, asymptotic Gaussian process approximations are established and used for large sample inference. The large sample approximations justify a bootstrap approximation for robust inferences about the functional response process. The performance is demonstrated in simulations and in the analysis of irregular functional data from quantitative ultrasound analysis.

Emotion regulation strategies and mental health symptoms during COVID-19: the mediating role of insomnia.

COVID-19 has become a major source of stress for people around the world. Stressful life events play a role in the pathogenesis of sleep disorders such as insomnia which is considered a risk factor for anxiety and depression. Emotion regulation is an important factor linked with sleep and mental health problems. Therefore, the main goal of the present study was to examine whether insomnia could constitute a mediation mechanism that explains the relationship between emotion regulation strategies (rumination, reappraisal, suppression) and stress-induced mental health outcomes during the COVID-19 pandemic. The cross-sectional study was conducted among young (M±SD 24.8±2.24) individuals (N = 281, 85.4% women) during the time of the third wave of infections in Poland. Data were collected by means of selfreport questionnaires, including the Emotion Regulation Questionnaire; Cognitive Emotion Regulation Questionnaire; Athens Insomnia Scale; Depression, Anxiety and Stress Scale. The direct and indirect effects of emotion regulation strategies on depression, anxiety, and stress were calculated using a bootstrap estimation technique. All analyzed indirect effects were significant. The results show that insomnia mediates the relationships between all 3 emotion regulation strategies and stress, anxiety and depression. The presented results shed the light on the role of insomnia on the relationships between emotion regulation strategies and emotional states experienced during the COVID-19 pandemic. Additionally, the present study suggests that educational and therapeutic interventions aimed at improving emotion regulation might be useful for improving symptoms of insomnia and, through it, symptoms of affective disorders. Int J Occup Med Environ Health. 2023;36(1):151-59.

Quantification of vascular pathology in the retina through probability distributions of central artery and vein width equivalent

AbstractPurpose: A semi‐automated method of measuring the Central Retinal Artery Equivalent (CRAE) and Central Retinal Vein Equivalent (CRVE) has been developed. The method was used to calculate parametric probability distribution for CRAE and CRVE in healthy retinas in order to quantify possible vascular pathology degree.Methods: Using the ARIA software (MATLAB), the diameters of the retinal vessels located in a ring with radii 0.5 and 1 diameter of the optic disc were quantified. A measurement of CRAE and CRVE was obtained for two data base of healthy retinas (15 and 52 patients) measured with different retinal cameras. Subsequently, the probability distribution of CRAE and CRVE was calculated, as well as the bootstrap estimators of the mean, standard deviation, skewness, and kurtosis. MATLAB functions were used to select the parametric distribution that best fits the data. The Mahalanobis distance of each retina to healthy distribution was obtained. This classification distance was applied to healthy and glaucoma retinas.Results: The fits to theoretical distributions were good for a Generalized Extreme Value Distribution (gev) characterized by three parameters (scale, mean and standard deviation). They appear to be consistent across different databases. In retinas with glaucoma, the Mahalanobis distance allows the degree of pathology to be quantified. Moreover, the method can be used to classify the healthy retinas.Conclusions: The possible existence of parametric probability distributions for values of vascular calibres opens the possibility of quantifying the degree of vascular pathology.

Genomic and Transcriptomic Predictors of Response to Immune Checkpoint Inhibitors in Melanoma Patients: A Machine Learning Approach.

Immune checkpoint inhibitors (ICIs) became one of the most revolutionary cancer treatments, especially in melanoma. While they have been proven to prolong survival with lesser side effects compared to chemotherapy, the accurate prediction of response remains to be an unmet gap. Thus, we aim to identify accurate clinical and transcriptomic biomarkers for ICI response in melanoma. We also provide mechanistic insight into how high-performing markers impose their effect on the tumor microenvironment (TME). Clinical and transcriptomic data were retrieved from melanoma studies administering ICIs from cBioportal and GEO databases. Four machine learning models were developed using random-forest classification (RFC) entailing clinical and genomic features (RFC7), differentially expressed genes (DEGs, RFC-Seq), survival-related DEGs (RFC-Surv) and a combination model. The xCELL algorithm was used to investigate the TME. A total of 212 ICI-treated melanoma patients were identified. All models achieved a high area under the curve (AUC) and bootstrap estimate (RFC7: 0.71, 0.74; RFC-Seq: 0.87, 0.75; RFC-Surv: 0.76, 0.76, respectively). Tumor mutation burden, GSTA3, and VNN2 were the highest contributing features. Tumor infiltration analyses revealed a direct correlation between upregulated genes and CD8+, CD4+ T cells, and B cells and inversely correlated with myeloid-derived suppressor cells. Our findings confirmed the accuracy of several genomic, clinical, and transcriptomic-based RFC models, that could further support the use of TMB in predicting response to ICIs. Novel genes (GSTA3 and VNN2) were identified through RFC-seq and RFC-surv models that could serve as genomic biomarkers after robust validation.

The Pricing of Skewness Over Different Return Horizons

While recent theoretical and empirical work suggests that the physical skewness of a stock’s future discrete return distribution prices stocks, it does not tell us over which return horizon(s) that physical skewness is priced. Developing a novel block bootstrap estimator that allows us to calculate realized return skewness over arbitrary horizons, we aim to identify those return horizons. In doing so, we first show that our block bootstrap estimator produces more accurate realized skewness estimates than other recent estimators do. Next, we report that the existing skewness proxies used in the empirical asset pricing literature differ in how well they predict skewness over short or long return horizons. Finally, we reveal that the skewness pricing evidence documented in the empirical asset pricing literature is mostly driven by skewness over short (and not long) return horizons.

The Arcsine Kumaraswamy-Generalized Family: Bayesian and Classical Estimates and Application

In this paper, by including a trigonometric function, we propose a family of heavy-tailed distribution called the arcsine Kumaraswamy generalized-X family of distributions. Based on the proposed approach, a four-parameter extension of the Lomax distribution called the arcsine Kumaraswamy generalized Lomax (ASKUG-LOMAX) distribution is discussed in detail. Maximum likelihood, bootstrap, and Bayesian estimation are used to estimate the model parameters. A simulation study is used to evaluate ASKUG-LOMAX performance. The flexibility and usefulness of the proposed ASKUG-LOMAX distribution to predict unique symmetric and asymmetric patterns is demonstrated by analyzing real data. The results show that the ASKUG-LOMAX model is a good candidate for analyzing claims based on heavy-tailed data.

Understanding the effect of organizational innovation environment and customer participation in virtual communities on customer creativity: A study of mediating and moderating influences.

The importance of enterprises significantly improving their innovation performance by working closely with customers throughout the innovation process has been emphasized in recent literature. However, the role of organizational innovation environment in customer creativity and the impact of customer knowledge matching on the innovation environment are not sufficiently explored. Based on the Social cognitive theory and Flow theory, his investigate the factors that influence enterprise innovation performance in the context of customer participation in innovation, as well as how businesses can foster an online innovation environment that fosters customer creativity. The mixed-methods study, which combines qualitative and quantitative research, is used to create the scale item that measures the study's main variables. Structural equation modeling and bootstrapping estimation was performed on survey data collected via questionnaire from 392 consumers who participated in online service innovation in an online virtual brand community between June 2018 and May 2019. The study obtain the following main results. First, the innovative environment of customer online participation in service innovation fosters customer creativity. Second, two mediation interactions exist: creative self-efficacy and positive emotions, both of which partially mediate the relationship between customer creativity and the innovation environment. Third, while customer knowledge matching influences the intermediary effect of creative self-efficacy on innovation environment and customer creativity, it has no effect on the intermediary effect of positive emotion on innovation environment and customer creativity.

A Bootstrap Variance Procedure for the Generalised Regression Estimator

SummaryThe generalised regression estimator (GREG) uses auxiliary data that are available from the finite population to improve the efficiency of the estimator of a total (mean). Estimators of the variance of GREG that have been proposed in the sampling literature include those based on Taylor linearisation and the jackknife techniques. Approximations based on Taylor expansions are reasonable for large samples. However, when the sample size is small, the Taylor‐based variance estimator has a large negative bias. The jackknife variance estimators overestimate the variance of GREG for small sample sizes. We offset these setbacks using a bootstrap procedure for estimating the variance of the GREG. The method uses a bootstrap population constructed with the model underlying the GREG estimator. Repeated samples are selected in the bootstrap population according to the design used to select the initial sample, and the variability associated with these bootstrap samples is used to compute the proposed bootstrap variance estimator. Simulations show that the new bootstrap estimator has a small bias for samples that have few observations.

Probabilistic Pairwise Model Comparisons Based on Bootstrap Estimators of the Kullback-Leibler Discrepancy.

When choosing between two candidate models, classical hypothesis testing presents two main limitations: first, the models being tested have to be nested, and second, one of the candidate models must subsume the structure of the true data-generating model. Discrepancy measures have been used as an alternative method to select models without the need to rely upon the aforementioned assumptions. In this paper, we utilize a bootstrap approximation of the Kullback–Leibler discrepancy (BD) to estimate the probability that the fitted null model is closer to the underlying generating model than the fitted alternative model. We propose correcting for the bias of the BD estimator either by adding a bootstrap-based correction or by adding the number of parameters in the candidate model. We exemplify the effect of these corrections on the estimator of the discrepancy probability and explore their behavior in different model comparison settings.

The mediating effect of self-directed learning in the relationship between caring and resilience among Chinese nursing students: A multi-center cross-sectional study

BackgroundDespite the proliferation of literature focusing on resilience, a paucity of research has attempted a thorough and accurate examination of factors that contribute to resilience among nursing students. ObjectivesTo examine the mediating effect of self-directed learning in the relationship between caring and resilience in Chinese nursing students. DesignA cross-sectional design. SettingsFive universities in China. ParticipantsUndergraduate nursing students (N = 511). MethodsThe Caring Ability Inventory, Self-Rating Scale of Self-Directed Learning, and Connor-Davidson Resilience Scale (CD-RISC) were administered. Socio-demographic and academic data were collected from nursing students after obtaining their informed consent. A multiple linear regression analysis was performed to assess factors associated with resilience. A structural equation model with bootstrapping estimation was conducted to further explore the potential mediating role of self-directed learning in the relationship between caring and resilience. ResultsThe average score of CD-RISC for nursing students was 92.96 ± 14.85. Multiple linear regression analyses indicated that caring and self-directed learning were significantly positively associated with resilience. Self-directed learning (β = 0.327, 95% Confidence Interval [CI]: 0.049–6.667, p < 0.001) had a significant mediating effect on the relationship between caring and resilience in nursing students, explaining 67.1% of the total effect of caring on resilience. ConclusionsInterventions that enhance students' self-directed learning have the potential to enhance resilience level. Innovative pedagogical approaches, strategic reinforcement, and nursing curriculum transformation are recommended to promote self-directed learning awareness and internalize self-directed learning skills.

Comparisons between Resampling Techniques in Linear Regression: A Simulation Study

The classic methods used in estimating the parameters in linear regression need to fulfill some assumptions. If the assumptions are not fulfilled, the conclusion is questionable. Resampling is one of the ways to avoid such problems. The study aims to compare resampling techniques in linear regression. The original data used in the study is clean, without any influential observations, outliers and leverage points. The ordinary least square method was used as the primary method to estimate the parameters and then compared with resampling techniques. The variance, p-value, bias, and standard error are used as a scale to estimate the best method among random bootstrap, residual bootstrap and delete-one Jackknife. After all the analysis took place, it was found that random bootstrap did not perform well while residual and delete-one Jackknife works quite well. Random bootstrap, residual bootstrap, and Jackknife estimate better than ordinary least square. Is was found that residual bootstrap works well in estimating the parameter in the small sample. At the same time, it is suggested to use Jackknife when the sample size is big because Jackknife is more accessible to apply than residual bootstrap and Jackknife works well when the sample size is big.