Search results for "Statistical Hypothesis Testing"
showing 10 items of 110 documents
On Mardia’s Tests of Multinormality
2004
Classical multivariate analysis is based on the assumption that the data come from a multivariate normal distribution. The tests of multinormality have therefore received very much attention. Several tests for assessing multinormality, among them Mardia’s popular multivariate skewness and kurtosis statistics, are based on standardized third and fourth moments. In Mardia’s construction of the affine invariant test statistics, the data vectors are first standardized using the sample mean vector and the sample covariance matrix. In this paper we investigate whether, in the test construction, it is advantageous to replace the regular sample mean vector and sample covariance matrix by their affi…
Locally optimal invariant detector for testing equality of two power spectral densities
2018
This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT do…
Statistical Techniques for Validation of Simulation and Analytic Stochastic Models
2014
In this paper, we consider the problem of statistical validation of multivariate stationary response simulation and analytic stochastic models of observed systems (say, transportation or service systems), which have p response variables. The problem is reduced to testing the equality of the mean vectors for two multivariate normal populations. Without assuming equality of the covariance matrices, it is referred to as the Behrens–Fisher problem. The main purpose of this paper is to bring to the attention of applied researchers the satisfactory tests that can be used for testing the equality of two normal mean vectors when the population covariance matrices are unknown and arbitrary. To illus…
Comparison of differences in resolution and sources of controlling factors for gully erosion susceptibility mapping
2018
Abstract Gully erosion has been identified as an important soil degradation process and sediment source, especially in arid and semiarid areas. Thus, it is useful to identify the spatial occurrence of this form of water erosion in the landscape and the most vulnerable areas. In this study, we explored the effects of different pixel sizes on some controlling factors extracted from a digital elevation model and remote sensing data when producing a gully erosion susceptibility map (GESM) of Ekbatan Dam Basin, Hamadan, Iran. An inventory map of the gully landforms was prepared based on global positioning system routes of the gullies, extensive field surveys, and visual interpretations of satell…
Rank scores tests of multivariate independence
2004
New rank scores test statistics are proposed for testing whether two random vectors are independent. The tests are asymptotically distribution-free for elliptically symmetric marginal distributions. Recently, Gieser and Randles (1997), Taskinen, Kankainen and Oja (2003) and Taskinen, Oja and Randles (2005) introduced and discussed different multivariate extensions of the quadrant test, Kendall's tau and Spearman's rho statistics. In this paper, standardized multivariate spatial signs and the (univariate) ranks of the Mahalanobis-type distances of the observations from the origin are combined to construct ranks cores tests of independence. The limiting distributions of the test statistics ar…
Surrogate Data Analysis for Assessing the Significance of the Coherence Function
2004
In cardiovascular variability analysis, the significance of the coupling between two time series is commonly assessed by setting a threshold level in the coherence function. While traditionally used statistical tests consider only the parameters of the adopted estimator, the required zero-coherence level may be affected by some features of the observed series. In this study, three procedures, based on the generation of surrogate series sharing given properties with the original but being structurally uncoupled, were considered: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR). IID surrogates maintained the distribution of the original series, while …
Were the chaotic ELMs in TCV the result of an ARMA process?
2004
The results of a previous paper claiming the demonstration that edge localized mode (ELM) dynamics on TCV are chaotic in a number of cases has recently been called into question, because the statistical test employed was found to also identify linear auto regressive—moving average (ARMA) models as chaotic. The TCV ELM data has therefore been re-examined with an improved method that is able to make this distinction, and the ARMA model is found to be an inappropriate description of the dynamics on TCV. The hypothesis that ELM dynamics are chaotic on TCV in a number of cases is therefore still favoured.
Manipulating the alpha level cannot cure significance testing
2018
We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple in…
Manual segmentation qualification platform for the EADC-ADNI harmonized protocol for hippocampal segmentation project
2015
The use of hippocampal volumetry as a biomarker for Alzheimer's disease (AD) requires that tracers from different laboratories comply with the same segmentation method. Here we present a platform for training and qualifying new tracers to perform the manual segmentation of the hippocampus on magnetic resonance images (MRI) following the European Alzheimer's Disease Consortium and Alzheimer's Disease Neuroimaging Initiative (EADC-ADNI) Harmonized Protocol (HarP). Our objective was to demonstrate that the training process embedded in the platform leads to increased compliance and qualification with the HarP.Thirteen new tracers' segmentations were compared with benchmark images with respect t…
A statistical study of the quality of surface water intended for human consumption near Valencia (Spain)
2007
Water quality in the European Union is subject to legislation through directives that are applicable in all Member States. The directives specify a set of physical and chemical parameters that should be regularly controlled using a network of sampling points, with sampling based on the intended use of the water. This paper presents the results of a statistical comparison of the quality of water intended for human consumption at two different locations (the Canal de Benagéber and the Canal Júcar-Turia) near the town of Valencia (Spain). These are currently the only canals that could supply Valencia and other nearby towns with drinking water. The parameters considered in this paper are the on…