scholarly journals Spacing and shape of random peaks in non-parametric spectrum estimates

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140101 ◽  
Author(s):  
D. J. Thomson ◽  
C. L. Haley
Keyword(s):  
Solar Wind ◽  
Gaussian Process ◽  
Permutation Test ◽  
Coincidence Detection ◽  
Expected Number ◽  
True Nature ◽  
Significance Level ◽  
Large Sets ◽  
Frequency Unit ◽  
Expected Width

In this paper, expressions are derived for the expected number of spurious peaks in a spectrum estimate, that is, crossings above a given significance level per frequency unit, as well as the expected width of these peaks. In numerous scientific applications, spectrum estimates are used for the purpose of identifying sinusoidal or modal components, often thinning large sets of candidate frequencies with coincidence detection. Because one always expects numerous false peaks in a spectrum estimate, knowing the expected rate of false peaks helps to decide whether the number observed is abnormal and hence determine the true nature of the process. An example using solar wind data from the Advanced Composition Explorer is given where spectra display pathological numbers of significant peaks, while temporally permuted versions of the data possess spectra with the number expected for a white, Gaussian process. The permutation test is a valuable diagnostic for processes suspected to contain many line components.

The Clinical Use of Statistical Permutation Test Methodology: A Tool for Identifying Predictive Variables of Outcome

2014 ◽  
Vol 94 (3) ◽  
pp. 262-269 ◽  
Author(s):  
M. Racioppi ◽  
L. Salmaso ◽  
C. Brombin ◽  
R. Arboretti ◽  
D. D''Agostino ◽  
...  
Keyword(s):  
Bladder Cancer ◽  
Medical History ◽  
Missing Values ◽  
Permutation Test ◽  
Regional Lymph Node ◽  
Testing Procedure ◽  
Small Sample ◽  
Clinical Staging ◽  
Significance Level ◽  
Predictive Variables

Objectives: To identify the predictive variables affecting the outcome after radical surgery for bladder cancer by a newer statistical methodology, i.e. nonparametric combination (NPC). Methods: A multicenter study enrolled 1,312 patients who had undergone radical cystectomy for bladder cancer in 11 Italian oncological centers from January 1982 to December 2002. A statistical analysis of their medical history and diagnostic, pathological and postoperative variables was performed using a NPC test. The patients were included in a comprehensive database with medical history and clinical and pathological data. Five-year survival was used as the dependent variable, and p values were corrected for multiplicity using a closed testing procedure. The newer nonparametric approach was used to evaluate the prognostic importance of the variables. All of the analyses were performed using routines developed in MATLAB© and the significance level was set at α = 0.05. Results: A significant prognostic predictive value (p < 0.01) for tumor clinical staging, hydronephrosis, tumor pathological staging, grading, presence of concomitant carcinoma in situ, regional lymph node involvement, corpora cavernosa invasion, microvascular invasion, lymphatic invasion and prostatic stroma involvement was found. Conclusions: The NPC test could handle any type of variable (categorical and quantitative) and take into account the multivariate relation among variables. This newer methodology offers a significant contribution in biomedical studies with several endpoints and is recommended in presence of non-normal data and missing values, as well as solving high-dimensional data and problems relating to small sample sizes.

scholarly journals The growth of the expected number of real zeros of a random polynomial

1989 ◽  
Vol 46 (1) ◽  
pp. 100-121
Author(s):  
Richard Glendinning
Keyword(s):  
Gaussian Process ◽  
Sufficient Conditions ◽  
Stationary Gaussian Process ◽  
Random Polynomial ◽  
Expected Number ◽  
Real Zeros ◽  
Number Of Real Zeros

AbstractLet X0, X1…Xn,… be a stationary Gaussian process. We give sufficient conditions for the expected number of real zeros of the polynomial Qn (z) = Σnj =o X jzj to be (2/ π)log n as n tends to infinity.

scholarly journals Tidal triggering evidence of intermediate depth earthquakes in the Vrancea zone (Romania)

2007 ◽  
Vol 7 (6) ◽  
pp. 733-740 ◽  
Author(s):  
N. Cadicheanu ◽  
M. van Ruymbeke ◽  
P. Zhu
Keyword(s):  
Phase Angle ◽  
Phase Distribution ◽  
Permutation Test ◽  
Angle Distribution ◽  
Seismic Zone ◽  
Data Set ◽  
Significance Level ◽  
Tidal Triggering ◽  
Eastern Carpathians ◽  
Set Up

Abstract. Tidal triggering evidence of intermediate earthquakes in the Vrancea region (Romania) is investigated. The Vrancea seismic zone is located in the bend region of the South-Eastern Carpathians (45°–46° N, 25.5°–27.5° E) and is known as one of the most active seismic zones in Europe. We selected earthquakes occurred between 1981 and 2005 from the RomPlus catalog provided by the Institute of Earth Physics of Bucharest with Mω≥2.5 and focal depths between 60 and 300 Km. We assigned a tidal component phase angle for each event which is computed from the earthquake occurrence time. Then the phase angle distribution was obtained by stacking every angle value in a 360 degree coordinate. Main lunar and solar semidiurnal tidal components M2 and S2 are considered. The phase angle distributions are tested by Permutation test which are introduced for the first time to a tidal triggering study. We compared results with classical Schuster's test. Both tests produce one value, pp for Permutation test and ps for Schuster's test, which represent the significance level for rejecting the null hypothesis that earthquakes occur randomly irrespective of tidal activities M2 and S2 phase distribution are random for the complete data set. However, when we set up a one year window and slide it by 30 d step, significant correlations were found in some windows. As a result of the sliding window, data set systematic temporal patterns related to the decrease of the pp and ps values seem to precede the occurrence of larger earthquakes.

Polygenic Inheritance of Bracts Number in Sunflower

Helia ◽  
2019 ◽  
Vol 42 (71) ◽  
pp. 221-228
Author(s):  
A. I. Soroka ◽  
V. A. Lyakh
Keyword(s):  
Degrees Of Freedom ◽  
Mean Value ◽  
Actual Number ◽  
Expected Number ◽  
Chi Square ◽  
Polygenic Inheritance ◽  
Significance Level ◽  
Average Value ◽  
The Mean ◽  
4 Degrees Of Freedom

Abstract Two inbreds of mutant origin, differing in the number of bracts, were crossed to obtain the F1 hybrid. One mutant line had 24.5 ± 1.01 bracts, while the other, 78.6 ± 1.69 bracts. The F1 hybrid had an average value between parents, which practically did not differ from the mean value in the F2 population. The variability of the trait under study in the F2 population was continuous, varying from 20 to 84 bracts. This indicated the probable participation of several genes with an additive effect in the control of the number of bracts. Assuming that the differences between the parental lines are due to two pairs of genes, the F2 plant population, grown in 2016, was divided into 5 classes. In that population the observed classes ratio turned out to be close to the theoretically expected ratio of 1 : 4 : 6 : 4 : 1. Over the next two years F2 populations were tested in a similar way. In all the cases, the calculated chi-square value did not exceed the critical value for 4 degrees of freedom and 5 % significance level. This gave reason to talk about the two-loci control of a such quantitative trait as the number of bracts. The participation of two non-allelic genes in the control of this trait is also proved by matching the actual number of plants in the parental classes to the theoretically expected number of plants. Thus, the number of bracts depends on the number of dominant alleles of two different genes in the genotype.

Millennial- to centennial-scale climate periodicities and forcing mechanisms in the westernmost Mediterranean for the past 20,000 yr

2014 ◽  
Vol 81 (1) ◽  
pp. 78-93 ◽  
Author(s):  
Marta Rodrigo-Gámiz ◽  
Francisca Martínez-Ruiz ◽  
Francisco J. Rodríguez-Tovar ◽  
Francisco J. Jiménez-Espejo ◽  
Eulogio Pardo-Igúzquiza
Keyword(s):  
North Atlantic ◽  
North Atlantic Ocean ◽  
Permutation Test ◽  
Significance Level ◽  
The North ◽  
Low Latitudes ◽  
Monsoon System ◽  
North Atlantic Climate ◽  
Marine Productivity ◽  
Forcing Mechanisms

AbstractCyclostratigraphic analysis conducted on a continuous high-resolution marine record from the western most Mediterranean reveals well-identified paleoclimate cycles for the last 20,000 yr. The detrital proxies used (Si/Al, Ti/Al, Zr/Al, Mg/Al, K/Al, Rb/Al) are related to different sediment-transport mechanisms, including eolian dust and fluvial runoff, which involve fluctuations in the atmosphere–hydrosphere systems. These fluctuations are accompanied by changes in marine productivity (supported by Ba/Al) and bottom-water redox conditions (Cu/Al, V/Al, Zn/Al, Fe/Al, Mn/Al, U/Th). Spectral analysis conducted using the Lomb–Scargle periodogram and the achieved significance level implemented with the permutation test allowed us to establish major periodicities at 1300, 1515, 2000, and 5000 yr, and secondary peaks at 650, 1087, and 3000 yr. Some of these cycles also agree with those previously described in the North Atlantic Ocean and circum-Mediterranean records. The periodicities obtained at 2000 and 5000 yr support a global connection with records distributed at high, mid, and low latitudes associated with solar activity, monsoonal regime and orbital forcing. The 1300- and 1515-yr cycles appear to be linked with North Atlantic climate variability and the African monsoon system. Thus, the analyzed record provides evidence of climate cycles and plausible forcing mechanisms coupled with ocean–atmosphere fluctuations.

A view of niche overlap amenable to statistical analysis

1989 ◽  
Vol 67 (1) ◽  
pp. 55-60 ◽  
Author(s):  
L. R. Linton ◽  
E. S. Edgington ◽  
Ronald W. Davies
Keyword(s):  
Statistical Analysis ◽  
Confidence Intervals ◽  
Permutation Test ◽  
Test Procedure ◽  
Niche Overlap ◽  
Data Handling ◽  
Data Presentation ◽  
Statistical Procedures ◽  
Large Sets ◽  
Point Estimates

Published values of niche overlap (similarity) are generally point estimates of the similarity between population centroids. A number of shortcomings are associated with this method of data presentation: (i) confidence intervals on the estimates are lacking, (ii) no statistical procedures are used to test for significant differences between estimates, and (iii) the estimates tend to be biased. These problems arise primarily as a result of the manner in which data are pooled for the calculations. We illustrate an alternative method of data handling, involving calculation of similarity between individuals, which is more biologically reasonable and which eliminates these problems. A permutation test procedure is also introduced for use on large sets of data.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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