scholarly journals Bootstrap Statistical Inference for the Variance Based on Fuzzy Data

2016 ◽  
Vol 38 (2) ◽  
Author(s):  
Mohammad Ghasem Akbari ◽  
Abdolhamid Rezaei
Keyword(s):  
Hypothesis Testing ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Nonparametric Estimation ◽  
Bootstrap Method ◽  
Estimation Problem ◽  
Fuzzy Data ◽  
Signed Distance ◽  
Straightforward Method ◽  
Statistical Hypotheses

The bootstrap is a simple and straightforward method for calculating approximated biases, standard deviations, confidence intervals, testing statistical hypotheses, and so forth, in almost any nonparametric estimation problem. In this paper we describe a bootstrap method for variance that is designed directly for hypothesis testing in case of fuzzy data based on Yao-Wu signed distance.

Statistical inference

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Hypothesis Testing ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Random Sample ◽  
Statistical Power ◽  
Short Term Memory ◽  
Multiple Comparisons ◽  
Estimation Bias ◽  
Short Term ◽  
Term Memory

This chapter begins with a very successful demonstration that illustrates many of the general principles of statistical inference, including estimation, bias, and the concept of the sampling distribution. Students each take a “random” sample of different size candies, weigh them, and estimate the total weight of all candies. Then various demonstrations and examples are presented that take the students on the transition from probability to hypothesis testing, confidence intervals, and more advanced concepts such as statistical power and multiple comparisons. These activities include use an inflatable globe, short-term memory test, first digits of street addresses, and simulated student IQs.

STATISTICAL INFERENCE AND UNCERTAINTY ASSESSMENT FOR MULTI-STATE SYSTEMS

2009 ◽  
Vol 16 (05) ◽  
pp. 453-467
Author(s):  
LANCE FIONDELLA
Keyword(s):  
Hypothesis Testing ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Testing Procedure ◽  
Uncertainty Assessment ◽  
Point Estimation ◽  
Confidence Bounds ◽  
Confidence Levels ◽  
Hypothesis Testing Procedure

Most of the existing research in multi-state systems relies on point estimation for modeling and optimization. The assessment of uncertainty during design is essential, yet variability in system performance is commonly ignored. Unfortunately, unlimited testing which could provide these arbitrarily accurate estimates is not economical. This paper describes a statistical inference technique to quantify the uncertainties inherent in limited testing. The methodology enables estimation of joint confidence intervals for both system and component performance distributions and subsequently provides a hypothesis testing procedure to perform objective assessments. This builds on previous research which has only addressed confidence bounds for system reliability. Instead of dichotomizing systems into acceptable and unacceptable classes, our approach can handle the case when a system exhibits three or more distinct performance levels. Thus, the method does not place restrictions on the flexibility of the underlying multi-state system concept. The value of the approach is illustrated using a case study and several experiments. The results indicate that joint confidence intervals produced by this procedure are accurate for a range of common confidence levels and sample sizes. It is also demonstrated how hypothesis testing and uncertainty assessment may be used to objectively measure system readiness.

scholarly journals Insights in Hypothesis Testing and Making Decisions in Biomedical Research

2016 ◽  
Vol 10 (1) ◽  
pp. 196-200 ◽  
Author(s):  
Varin Sacha ◽  
Demosthenes B. Panagiotakos
Keyword(s):  
Confidence Interval ◽  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Biomedical Research ◽  
Bootstrap Method ◽  
Resampling Methods ◽  
Effect Measure ◽  
Social Fields ◽  
The Bootstrap Method

It is a fact that p values are commonly used for inference in biomedical and other social fields of research. Unfortunately, the role of p value is very often misused and misinterpreted; that is why it has been recommended the use of resampling methods, like the bootstrap method, to calculate the confidence interval, which provides more robust results for inference than does p value. In this review a discussion is made about the use of p values through hypothesis testing and its alternatives using resampling methods to develop confidence intervals of the tested statistic or effect measure.

scholarly journals Evaluation of Inter-Observer Reliability of Animal Welfare Indicators: Which Is the Best Index to Use?

Animals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1445
Author(s):  
Mauro Giammarino ◽  
Silvana Mattiello ◽  
Monica Battini ◽  
Piero Quatto ◽  
Luca Maria Battaglini ◽  
...  
Keyword(s):  
Animal Welfare ◽  
Confidence Intervals ◽  
Bootstrap Method ◽  
Dairy Goat ◽  
Microsoft Excel ◽  
Bootstrap Methods ◽  
Welfare Indicators ◽  
Observer Reliability ◽  
High Concordance ◽  
Variance Estimates

This study focuses on the problem of assessing inter-observer reliability (IOR) in the case of dichotomous categorical animal-based welfare indicators and the presence of two observers. Based on observations obtained from Animal Welfare Indicators (AWIN) project surveys conducted on nine dairy goat farms, and using udder asymmetry as an indicator, we compared the performance of the most popular agreement indexes available in the literature: Scott’s π, Cohen’s k, kPABAK, Holsti’s H, Krippendorff’s α, Hubert’s Γ, Janson and Vegelius’ J, Bangdiwala’s B, Andrés and Marzo’s ∆, and Gwet’s γ(AC1). Confidence intervals were calculated using closed formulas of variance estimates for π, k, kPABAK, H, α, Γ, J, ∆, and γ(AC1), while the bootstrap and exact bootstrap methods were used for all the indexes. All the indexes and closed formulas of variance estimates were calculated using Microsoft Excel. The bootstrap method was performed with R software, while the exact bootstrap method was performed with SAS software. k, π, and α exhibited a paradoxical behavior, showing unacceptably low values even in the presence of very high concordance rates. B and γ(AC1) showed values very close to the concordance rate, independently of its value. Both bootstrap and exact bootstrap methods turned out to be simpler compared to the implementation of closed variance formulas and provided effective confidence intervals for all the considered indexes. The best approach for measuring IOR in these cases is the use of B or γ(AC1), with bootstrap or exact bootstrap methods for confidence interval calculation.

scholarly journals Nonparametric bootstrap inference for the targeted highly adaptive least absolute shrinkage and selection operator (LASSO) estimator

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Weixin Cai ◽  
Mark van der Laan
Keyword(s):  
Confidence Intervals ◽  
Nonparametric Estimation ◽  
Cross Validation ◽  
Data Distribution ◽  
Average Treatment Effect ◽  
Finite Sample ◽  
Nonparametric Bootstrap ◽  
A Value ◽  
Variation Norm ◽  
Selection Operator

AbstractThe Highly-Adaptive least absolute shrinkage and selection operator (LASSO) Targeted Minimum Loss Estimator (HAL-TMLE) is an efficient plug-in estimator of a pathwise differentiable parameter in a statistical model that at minimal (and possibly only) assumes that the sectional variation norm of the true nuisance functions (i.e., relevant part of data distribution) are finite. It relies on an initial estimator (HAL-MLE) of the nuisance functions by minimizing the empirical risk over the parameter space under the constraint that the sectional variation norm of the candidate functions are bounded by a constant, where this constant can be selected with cross-validation. In this article we establish that the nonparametric bootstrap for the HAL-TMLE, fixing the value of the sectional variation norm at a value larger or equal than the cross-validation selector, provides a consistent method for estimating the normal limit distribution of the HAL-TMLE. In order to optimize the finite sample coverage of the nonparametric bootstrap confidence intervals, we propose a selection method for this sectional variation norm that is based on running the nonparametric bootstrap for all values of the sectional variation norm larger than the one selected by cross-validation, and subsequently determining a value at which the width of the resulting confidence intervals reaches a plateau. We demonstrate our method for 1) nonparametric estimation of the average treatment effect when observing a covariate vector, binary treatment, and outcome, and for 2) nonparametric estimation of the integral of the square of the multivariate density of the data distribution. In addition, we also present simulation results for these two examples demonstrating the excellent finite sample coverage of bootstrap-based confidence intervals.

scholarly journals Which particles to select, and if yes, how many?

2021 ◽  
Author(s):  
Christian Schwaferts ◽  
Patrick Schwaferts ◽  
Elisabeth von der Esch ◽  
Martin Elsner ◽  
Natalia P. Ivleva
Keyword(s):  
Confidence Intervals ◽  
Bootstrap Method ◽  
Analytical Techniques ◽  
Single Particles ◽  
Minimal Sample ◽  
Error Quantification ◽  
Measurement Algorithm ◽  
Reliable Quantification ◽  
Window Selection ◽  
Number Of Particles

AbstractMicro- and nanoplastic contamination is becoming a growing concern for environmental protection and food safety. Therefore, analytical techniques need to produce reliable quantification to ensure proper risk assessment. Raman microspectroscopy (RM) offers identification of single particles, but to ensure that the results are reliable, a certain number of particles has to be analyzed. For larger MP, all particles on the Raman filter can be detected, errors can be quantified, and the minimal sample size can be calculated easily by random sampling. In contrast, very small particles might not all be detected, demanding a window-based analysis of the filter. A bootstrap method is presented to provide an error quantification with confidence intervals from the available window data. In this context, different window selection schemes are evaluated and there is a clear recommendation to employ random (rather than systematically placed) window locations with many small rather than few larger windows. Ultimately, these results are united in a proposed RM measurement algorithm that computes confidence intervals on-the-fly during the analysis and, by checking whether given precision requirements are already met, automatically stops if an appropriate number of particles are identified, thus improving efficiency.

Testing statistical hypotheses for intuitionistic fuzzy data

2018 ◽  
Vol 23 (20) ◽  
pp. 10385-10392 ◽  
Author(s):  
Mohammad Ghasem Akbari ◽  
Gholamreza Hesamian
Keyword(s):  
Fuzzy Data ◽  
Intuitionistic Fuzzy ◽  
Statistical Hypotheses ◽  
Intuitionistic Fuzzy Data
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