Asymptotic formulae for the distribution of a multivariate test statistic: Power comparisons of certain multivariate tests

Biometrika ◽  
1971 ◽  
Vol 58 (3) ◽  
pp. 647-651 ◽  
Author(s):  
YOONG-SIN LEE
Keyword(s):  
Test Statistic ◽  
Multivariate Test ◽  
Multivariate Tests ◽  
Asymptotic Formulae ◽  
Power Comparisons ◽  
Multivariate Test Statistic

COMPARATIVE ANALYSIS OF SHRINKAGE COVARIANCE MATRIX USING MICROARRAYS DATA

2016 ◽  
Vol 78 (4-4) ◽  
Author(s):  
Suryaefiza Karjanto ◽  
Norazan Mohamed Ramli ◽  
Nor Azura Md Ghani
Keyword(s):  
Covariance Matrix ◽  
Activity Level ◽  
Test Statistic ◽  
Multivariate Test ◽  
Hotelling's T2 ◽  
Gene Sets ◽  
Sample Covariance ◽  
Hotelling’S T2 ◽  
Hotelling’S T2 Statistic ◽  
Multivariate Test Statistic

The DNA microarray technologies permit scientists to depict the expression of genes for related samples.  This relationship between genes is analysed using Hotelling’s T2 as a multivariate test statistic but the disadvantage of this test, when used in microarray studies is the number of samples is larger than the number of variables.  This study discovers the potential of the shrinkage approach to estimate the covariance matrix specifically when the high dimensionality problem happened.  Consequently, the sample covariance matrix in Hotelling’s T2 statistic is not positive definite and become singular thus cannot be inverted.  In this research, the Hotelling’s T2 statistic is combined with a shrinkage approach as an alternative estimation to estimate the covariance matrix to detect significant gene sets.  The multivariate test statistic of classical Hotelling's T2 is used to integrate the correlation when assessing changes in activity level across biological conditions.  The performances of the proposed methods were assessed using real data study.  Shrinkage covariance matrix approach indicates a better result for detection of differentially expressed gene sets as compared to other methods.

On some properties of the scan statistic on the circle and the line

1977 ◽  
Vol 14 (2) ◽  
pp. 272-283 ◽  
Author(s):  
Noel Cressie
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Test Statistic ◽  
Scan Statistic ◽  
Asymptotic Power ◽  
Power Comparisons ◽  
Continuous Time Stochastic Process ◽  
Parameter Distributions

The scan statistic is defined as the supremum of a particular continuous-time stochastic process, and is used as a test statistic for testing uniformity against a simple clustering type of alternative. Its distribution under the null hypothesis is investigated and weak convergence of the stochastic process to the appropriate Gaussian process is proved. An interesting link is forged between the circular scan statistic and Kuiper's statistic, which rids us of the trouble of estimating a nuisance parameter. Distributions under the alternative are then derived, and asymptotic power comparisons are made.

scholarly journals Fractional Entropy-Based Test of Uniformity with Power Comparisons

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed S. Mohamed ◽  
Haroon M. Barakat ◽  
Salem A. Alyami ◽  
Mohamed A. Abd Elgawad
Keyword(s):  
Simulation Study ◽  
Limit Distribution ◽  
Residual Entropy ◽  
Test Statistic ◽  
Percentage Points ◽  
Entropy Measures ◽  
Cumulative Residual Entropy ◽  
Power Comparisons ◽  
Fractional Entropy ◽  
Cumulative Residual

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

On some properties of the scan statistic on the circle and the line

1977 ◽  
Vol 14 (02) ◽  
pp. 272-283 ◽  
Author(s):  
Noel Cressie
Keyword(s):  
Stochastic Process ◽  
Continuous Time ◽  
Null Hypothesis ◽  
Nuisance Parameter ◽  
Test Statistic ◽  
Scan Statistic ◽  
Asymptotic Power ◽  
Power Comparisons ◽  
Continuous Time Stochastic Process ◽  
Parameter Distributions

The scan statistic is defined as the supremum of a particular continuous-time stochastic process, and is used as a test statistic for testing uniformity against a simple clustering type of alternative. Its distribution under the null hypothesis is investigated and weak convergence of the stochastic process to the appropriate Gaussian process is proved. An interesting link is forged between the circular scan statistic and Kuiper's statistic, which rids us of the trouble of estimating a nuisance parameter. Distributions under the alternative are then derived, and asymptotic power comparisons are made.

scholarly journals Asymmetric vector moving average models: estimation and testing

2021 ◽  
Author(s):  
Jan G. De Gooijer
Keyword(s):  
Moving Average ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Test Statistic ◽  
Multivariate Test ◽  
Testing Procedures ◽  
Proposed Model ◽  
Moving Average Models ◽  
Global Invertibility

AbstractWe propose the class of asymmetric vector moving average (asVMA) models. The asymmetry of these models is characterized by different MA filters applied to the components of vectors of lagged positive and negative innovations. This allows for a detailed investigation of the interrelationships among past model innovations of different sign. We derive some covariance matrix properties of an asVMA model under the assumption of Gaussianity. Related to this, we investigate the global invertibility condition of the proposed model. The paper also introduces a maximum likelihood estimation procedure and a multivariate Wald-type test statistic for symmetry versus the alternative of asymmetry. The finite-sample performance of the proposed multivariate test is studied by simulation. Furthermore, we devise an exploratory test statistic based on lagged sample cross-bicovariance estimates. The estimation and testing procedures are used to uncover asymmetric effects in two US growth rates, and in three US industrial prices.

PENGARUH LATIHAN RANGE OF MOTION (ROM) AKTIF ASSITIF TERHADAP RENTANG GERAK SENDI PADA LANSIA YANG MENGALAMI IMMOBILISASI FISIK

2019 ◽  
Vol 13 (2) ◽  
Author(s):  
Andri Setyorini ◽  
Niken Setyaningrum
Keyword(s):  
Range Of Motion ◽  
Human Life ◽  
The Elderly ◽  
General Purpose ◽  
Test Statistic ◽  
Physical Mobility ◽  
Motion Exercise ◽  
The One ◽  
The Individual ◽  
Active Training

Background: Elderly is the final stage of the human life cycle, that is part of the inevitable life process and will be experienced by every individual. At this stage the individual undergoes many changes both physically and mentally, especially setbacks in various functions and abilities he once had. Preliminary study in Social House Tresna Wreda Yogyakarta Budhi Luhur Units there are 16 elderly who experience physical immobilization. In the social house has done various activities for the elderly are still active, but the elderly who experienced muscle weakness is not able to follow the exercise, so it needs to do ROM (Range Of Motion) exercise.   Objective: The general purpose of this research is to know the effect of Range Of Motion (ROM) Active Assitif training to increase the range of motion of joints in elderly who experience physical immobility at Social House of Tresna Werdha Yogyakarta unit Budhi Luhur.   Methode: This study was included in the type of pre-experiment, using the One Group Pretest Posttest design in which the range of motion of the joints before (pretest) and posttest (ROM) was performed  ROM. Subjects in this study were all elderly with impaired physical mobility in Social House Tresna Wreda Yogyakarta Unit Budhi Luhur a number of 14 elderly people. Data analysis in this research use paired sample t-test statistic  Result: The result of this research shows that there is influence of ROM (Range of Motion) Active training to increase of range of motion of joints in elderly who experience physical immobility at Social House Tresna Wredha Yogyakarta Unit Budhi Luhur.  Conclusion: There is influence of ROM (Range of Motion) Active training to increase of range of motion of joints in elderly who experience physical immobility at Social House Tresna Wredha Yogyakarta Unit Budhi Luhur.

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