Time-domain procedures for testing that a stationary time-series is Gaussian

Moulines, Éric; Choukri, Karim

doi:10.1109/78.533722

Cited by 31 publications

(10 citation statements)

References 27 publications

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“…We use a Gaussianity test based on the sample estimates of the first three moments I, '2, 13 of the prediction errors as in [13]. Estimates of the moments are given by:…”

Section: Adaptive Filtering Based Gaussianity Testsmentioning

confidence: 99%

<title>2D adaptive prediction-based Gaussianity tests in microcalcification detection</title>

Gürcan¹,

Yardımcı

Cetin

1998

SPIE Proceedings

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With increasing use of Picture Archiving and Communication Systems (PACS), Computeraided Diagnosis (CAD) methods will be more widely utilized. In this paper, we develop a CAD method for the detection of microcalcification clusters in mammograms, which are an early sign of breast cancer. The method we propose makes use of two-dimensional (2-D) adaptive filtering and a Gaussianity test recently developed by Ojeda et al. for causal invertible time series. The first step of this test is adaptive linear prediction. It is assumed that the prediction error sequence has a Gaussian distribution as the mammogram images do not contain sharp edges. Since microcalcifications appear as isolated bright spots, the prediction error sequence contains large outliers around microcalcification locations. The second step of the algorithm is the computation of a test statistic from the prediction error values to determine whether the samples are from a Gaussian distribution. The Gaussianity test is applied over small, overlapping square regions. The regions, in which the Gaussianity test fails, are marked as suspicious regions. Experimental results obtained from a mammogram database are presented.

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“…We use a Gaussianity test based on the sample estimates of the first three moments I, '2, 13 of the prediction errors as in [13]. Estimates of the moments are given by:…”

Section: Adaptive Filtering Based Gaussianity Testsmentioning

confidence: 99%

<title>2D adaptive prediction-based Gaussianity tests in microcalcification detection</title>

Gürcan¹,

Yardımcı

Cetin

1998

SPIE Proceedings

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“…observations (see Thode (2002) for an extensive review), a number of tests which are valid for dependent data have also been proposed. These include tests based on empirical standardized cumulants (Lobato and Velasco (2004), Bai and Ng (2005)), moment conditions of various types (e.g., Epps (1987), Moulines and Choukri (1996), Bontemps and Meddahi (2005)), the bispectral density function (e.g., Hinich (1982), Nusrat and Harvill (2008), Berg et al (2010)), and the empirical distribution function (Psaradakis and Vávra (2017)). Unlike normality tests for i.i.d.…”

Section: Introductionmentioning

confidence: 99%

Normality tests for dependent data: large-sample and bootstrap approaches

Psaradakis

Vávra

2018

Communications in Statistics - Simulation and Computation

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The paper considers the problem of testing for normality of the one-dimensional marginal distribution of a strictly stationary and weakly dependent stochastic process. The possibility of using an autoregressive sieve bootstrap procedure to obtain critical values and P-values for normality tests is explored. The smallsample properties of a variety of tests are investigated in an extensive set of Monte Carlo experiments. The bootstrap version of the classical skewness-kurtosis test is shown to have the best overall performance in small samples.

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“…(Epps, 1987), of the skewness and kurtosis (Lobato and Velasco, 2004, the so-called Jarque-Bera test), of both the empirical ch.f. and the skewness and kurtosis (Moulines and Choukri, 1996) and the bispectral density function (Rao and Gabr, 1980). An important drawback of these tests is that they only consider a finite order marginal of the process (generally order one).…”

Section: Introductionmentioning

confidence: 99%

A random-projection based test of Gaussianity for stationary processes

Nieto-Reyes¹,

Cuesta-Albertos²,

Gamboa³

2014

Computational Statistics & Data Analysis

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Gaussianity tests have being widely studied in the literature. Regarding the study of Gaussianity tests for stationary processes, these only verify the Gaussianity of a marginal at a fixed finite order, generally order one. Therefore, they do not reject stationary non-Gaussian processes with the one-dimensional Gaussian marginal. Thus, a consistent test is proposed for Gaussianity of stationary processes when a finite sample path of the process is observed. Using random projections, decision rules are applied to the whole distribution of the process and not only on its marginal distribution at a fixed order, as in previous tests. The main idea is to test the Gaussianity of the one-dimensional marginal distribution of some random linear transformations of the process. Note that testing the one-dimensional marginal distribution can be done with previous tests of Gaussianity for stationary processes. It is shown by both theoretical and empirical studies that the proposed test procedure has good properties for a wide range of alternatives.

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Time-domain procedures for testing that a stationary time-series is Gaussian

Cited by 31 publications

References 27 publications

<title>2D adaptive prediction-based Gaussianity tests in microcalcification detection</title>

<title>2D adaptive prediction-based Gaussianity tests in microcalcification detection</title>

Normality tests for dependent data: large-sample and bootstrap approaches

A random-projection based test of Gaussianity for stationary processes

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