Nonparametric Statistical Inference

Gibbons, Jean Dickinson; Chakraborti, S.

doi:10.1007/978-3-642-04898-2_420

Cited by 540 publications

(286 citation statements)

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“…As is well known, a parametric family of distributions is defined by a finite number of parameters (e.g., the family of Gaussian distributions); on the contrary, a nonparametric family of distributions [3][4][5][6][7][8] cannot be defined by a finite number of parameters (e.g., the family of all continuous distributions).…”

Section: Optimum Permutation Testsmentioning

confidence: 99%

“…It is worth noting that permutation test (6) can be interpreted as a test with adaptive threshold x k (x) } because we have to compute the threshold for each new sample vector x before comparing it with the statistic T(X). In order to obtain threshold x k (x) in (6), we have to compute statistic T(X) for all permutations of x and, after, ordering (sorting) them according to (3). Then, the computation problem of the permutation test is apparent for large n-values (e.g., if n = 16, we have approximately 2 x 10 13 computations of the statistic).…”

Section: Optimum Permutation Testsmentioning

confidence: 99%

“…where X 0 is the threshold (a fixed value), and X{r) is the rank test statistic that, in general, it does not have a closed-form expression, and a computable suboptimum rank statistic is more practical (e.g., the well-known Wilcoxon rank statistic [3][4][5][6]). Finally, according to the above, the family of rank test can be considered as a subfamily of the family of permutation tests.…”

Section: Relationship Between Permutation Tests and Rank Testsmentioning

confidence: 99%

“…Most contributions on nonparametric statistics are referred to rank tests [3][4][5][6]. Basic introductions to rank tests are given in [3,4], and more advanced treatments are in [5,6]. Also, the rank tests can be considered as a particular case of the family of permutation tests [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…Hoeffding [12] demonstrates that many FT are asymptotically as powerful as their parametric counterparts. For analyzing contributions on nonparametric permutation tests in the 2nd half of the 20th century, we can consult books [3][4][5][6][7][8][9], papers [12][13][14][15], and references therein. After the 1950s, fundamental contributions to nonparametric statistics have been scarce.…”

Section: Introductionmentioning

confidence: 99%

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Permutation tests for nonparametric detection

2012

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In this paper, the authors provide a methodology to design nonparametric permutation tests and, in particular, nonparametric rank tests for applications in detection. In the first part of the paper, the authors develop the optimization theory of both permutation and rank tests in the Neyman-Pearson sense; in the second part of the paper, they carry out a comparative performance analysis of the permutation and rank tests (detectors) against the parametric ones in radar applications.First, a brief review of some contributions on nonparametric tests is realized. Then, the optimum permutation and rank tests are derived. Finally, a performance analysis is realized by Monte-Carlo simulations for the corresponding detectors, and the results are shown in curves of detection probability versus signal-to-noise ratio.

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Section: Optimum Permutation Testsmentioning

confidence: 99%

Section: Optimum Permutation Testsmentioning

confidence: 99%

Section: Relationship Between Permutation Tests and Rank Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Permutation tests for nonparametric detection

2012

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Friction weakening in granular flows deduced from seismic records at the Soufrière Hills Volcano, Montserrat

et al. 2015

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Accurate modeling of rockfalls and pyroclastic flows is still an open issue, partly due to a lack of measurements related to their dynamics. Using seismic data from the Soufrière Hills Volcano, Montserrat, and granular flow modeling, we show that the power laws relating the seismic energy Es to the seismic duration ts and relating the loss of potential energy ΔEp to the flow duration tf are very similar, like the power laws observed at Piton de la Fournaise, Reunion Island. Observations showing that tf≃ts suggest a constant ratio Es/ΔEp≃10−5. This similarity in these two power laws can be obtained only when the granular flow model uses a friction coefficient that decreases with the volume transported. Furthermore, with this volume‐dependent friction coefficient, the simulated force applied by the flow to the ground correlates well with the seismic energy, highlighting the signature of this friction weakening effect in seismic data.

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Assessment of earthquake locations in 3‐D deterministic velocity models: A case study from the Altotiberina Near Fault Observatory (Italy)

et al. 2016

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The accuracy of earthquake locations and their correspondence with subsurface geology depends strongly on the accuracy of the available seismic velocity model. Most modern methods to construct a velocity model for earthquake location are based on the inversion of passive source seismological data. Another approach is the integration of high‐resolution geological and geophysical data to construct deterministic velocity models in which earthquake locations can be directly correlated to the geological structures. Such models have to be kinematically consistent with independent seismological data in order to provide precise hypocenter solutions. We present the Altotiberina (AT) seismic model, a three‐dimensional velocity model for the Upper Tiber Valley region (Northern Apennines, Italy), constructed by combining 300 km of seismic reflection profiles, six deep boreholes (down to 5 km depth), detailed data from geological surveys and direct measurements of P and S wave velocities performed in situ and in laboratory. We assess the robustness of the AT seismic model by locating 11,713 earthquakes with a nonlinear, global‐search inversion method and comparing the probabilistic hypocenter solutions to those calculated in three previously published velocity models, constructed by inverting passive seismological data only. Our results demonstrate that the AT seismic model is able to provide higher‐quality hypocenter locations than the previous velocity models. Earthquake locations are consistent with the subsurface geological structures and show a high degree of spatial correlation with specific lithostratigraphic units, suggesting a lithological control on the seismic activity evolution.

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Nonparametric Statistical Inference

Cited by 540 publications

References 0 publications

Permutation tests for nonparametric detection

Permutation tests for nonparametric detection

Friction weakening in granular flows deduced from seismic records at the Soufrière Hills Volcano, Montserrat

Assessment of earthquake locations in 3‐D deterministic velocity models: A case study from the Altotiberina Near Fault Observatory (Italy)

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