scholarly journals The effect of distribution of stations upon location error: Statistical tests based on the double-difference earthquake location algorithm and the bootstrap method

2006 ◽  
Vol 58 (2) ◽  
pp. e9-e12 ◽  
Author(s):  
Ling Bai ◽  
Zhongliang Wu ◽  
Tianzhong Zhang ◽  
Ichiro Kawasaki
Keyword(s):  
Statistical Tests ◽  
Bootstrap Method ◽  
Earthquake Location ◽  
Double Difference ◽  
Location Error ◽  
Location Algorithm ◽  
The Bootstrap Method

scholarly journals Using the Bootstrap Method for a Statistical Significance Test of Differences between Summary Histograms

2006 ◽  
Vol 134 (5) ◽  
pp. 1442-1453 ◽  
Author(s):  
Kuan-Man Xu
Keyword(s):  
Euclidean Distance ◽  
Probability Distributions ◽  
Statistical Tests ◽  
Statistical Significance ◽  
Bootstrap Method ◽  
Statistical Hypothesis ◽  
Object Size ◽  
Size Category ◽  
Significance Level ◽  
The Bootstrap Method

Abstract A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries–Matusita distance, and the Kuiper distance. The data used in testing the bootstrap method are satellite measurements of cloud systems called “cloud objects.” Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object, and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.

scholarly journals Statistical tests and their application in geodesy

Tehnika ◽  
2021 ◽  
Vol 76 (2) ◽  
pp. 147-154
Author(s):  
Anastasija Martinenko ◽  
Vesna Jevremović ◽  
Petko Vranić ◽  
Jovan Popović ◽  
Marko Pejić
Keyword(s):  
Statistical Data ◽  
Statistical Tests ◽  
Bootstrap Method ◽  
Nonparametric Tests ◽  
Statistical Test ◽  
Ratio Test ◽  
Correct Conclusion ◽  
Scientific Analysis ◽  
Measurement Results ◽  
The Bootstrap Method

The correct conclusion about the assumptions concerning some phenomena can be obtained only through scientific analysis of statistical data. The scientific procedure of verifying a hypothesis using measurement results is called a statistical test. Depending on whether the hypotheses about the parameters in the feature distribution are tested or the distribution as a whole is tested, a parametric or non-parametric test is selected. The most significant representatives of parametric tests are the Probability Ratio Test, the Neumann - Pearson Lemma and the Bootstrap method, while the Pearson x2 test and the Kolmogorov test are presented as representatives of nonparametric tests. The paper presents the theoretical basis of some methods used in construction of statistical tests with given examples in geodesy.

scholarly journals Statistical Estimates of the Pulsar Glitch Activity

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Alessandro Montoli ◽  
Marco Antonelli ◽  
Brynmor Haskell ◽  
Pierre Pizzochero
Keyword(s):  
Linear Regression ◽  
Upper Bound ◽  
Bootstrap Method ◽  
Waiting Times ◽  
Statistical Estimates ◽  
Equal Variance ◽  
Linear Fit ◽  
The Moment ◽  
The Bootstrap Method

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

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