A Modified Score Test Statistic Having Chi-Squared Distribution to Order n -1

Biometrika ◽  
1991 ◽  
Vol 78 (3) ◽  
pp. 573 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Silvia L. de Paula Ferrari
Keyword(s):  
Score Test ◽  
Test Statistic ◽  
Chi Squared ◽  
Chi Squared Distribution

A modified score test statistic having chi-squared distribution to order n−1

Biometrika ◽  
1991 ◽  
Vol 78 (3) ◽  
pp. 573-582 ◽  
Author(s):  
GAUSS M. CORDEIRO ◽  
SILVIA L. DE PAULA FERRARI
Keyword(s):  
Score Test ◽  
Test Statistic ◽  
Chi Squared ◽  
Chi Squared Distribution

scholarly journals Nonparametric test for spatial geometric anisotropy

2010 ◽  
Vol 51 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lina Dreižienė
Keyword(s):  
Spatial Data ◽  
Nonparametric Test ◽  
Test Statistics ◽  
Simple Test ◽  
Test Statistic ◽  
Simulation Experiments ◽  
Chi Squared ◽  
Geometric Anisotropy ◽  
Chi Squared Distribution

Paper deals with a problem of testing isotropy against geometric anisotropy for Gaussian spatial data. The original simple test statistic based on directional empirical semivariograms is proposed. Under the assumption of independence of the classical semivariogram estimators and for increasing domain asymptotics, the distribution of test statistics is approximated by chi-squared distribution. The simulation experiments demonstrate the efficacy of the proposed test.

scholarly journals TESTING FOR NEGLECTED NONLINEARITY USING EXTREME LEARNING MACHINES

2013 ◽  
Vol 21 (supp02) ◽  
pp. 117-129
Author(s):  
KYULEE SHIN ◽  
JIN SEO CHO
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Linear Models ◽  
Regularity Conditions ◽  
Extreme Learning Machines ◽  
Test Statistic ◽  
Learning Machines ◽  
Monte Carlo Experiments ◽  
Chi Squared ◽  
Chi Squared Distribution

We introduce a statistic testing for neglected nonlinearity using extreme learning machines and call it ELMNN test. The ELMNN test is very convenient and can be widely applied because it is obtained as a by-product of estimating linear models. For the proposed test statistic, we provide a set of regularity conditions under which it asymptotically follows a chi-squared distribution under the null. We conduct Monte Carlo experiments and examine how it behaves when the sample size is finite. Our experiment shows that the test exhibits the properties desired by our theory.

scholarly journals Components of the Pearson-Fisher chi-squared statistic

2002 ◽  
Vol 6 (4) ◽  
pp. 241-254
Author(s):  
G. D. Raynery
Keyword(s):  
Null Hypothesis ◽  
Goodness Of Fit ◽  
Score Test ◽  
Continuous Distribution ◽  
Continuous Data ◽  
Test Statistic ◽  
Chi Squared ◽  
Distribution Parameters ◽  
The Relationship

The Pearson-Fisher chi-squared test can be used to evaluate the goodness-of-fit of categorized continuous data with known bin endpoints compared to a continuous distribution, in the presence of unknown (nuisance) distribution parameters. Rayner and McAlevey [11] and Rayner and Best [9],[10] demonstrate that in this case, component tests of the Pearson-Fisher chi-squared test statistic can be obtained by equating it to the Neyman smooth score test for a categorized composite null hypothesis under certain restrictions. However, only Rayner and McAlevey [11] provide even brief details as to how these restrictions can be used to obtain any kind of decomposition. More importantly, the relationship between the range of possible decompositions and the interpretation of the corresponding test statistic components has not previously been investigated. This paper provides the necessary details, as well as an overview of the decomposition options available, and revisits two published examples.

scholarly journals RL-SKAT: An exact and efficient score test for heritability and set tests

2017 ◽  
Author(s):  
Regev Schweiger ◽  
Omer Weissbrod ◽  
Elior Rahmani ◽  
Martina Müller-Nurasyid ◽  
Sonja Kunze ◽  
...  
Keyword(s):  
Variance Component ◽  
Association Studies ◽  
Score Test ◽  
Small Samples ◽  
Phenotypic Variance ◽  
Test Statistic ◽  
Entire Genome ◽  
P Values ◽  
Continuous Response ◽  
Efficient Score Test

AbstractTesting for the existence of variance components in linear mixed models is a fundamental task in many applicative fields. In statistical genetics, the score test has recently become instrumental in the task of testing an association between a set of genetic markers and a phenotype. With few markers, this amounts to set-based variance component tests, which attempt to increase power in association studies by aggregating weak individual effects. When the entire genome is considered, it allows testing for the heritability of a phenotype, defined as the proportion of phenotypic variance explained by genetics. In the popular score-based Sequence Kernel Association Test (SKAT) method, the assumed distribution of the score test statistic is uncalibrated in small samples, with a correction being computationally expensive. This may cause severe inflation or deflation of p-values, even when the null hypothesis is true. Here, we characterize the conditions under which this discrepancy holds, and show it may occur also in large real datasets, such as a dataset from the Wellcome Trust Case Control Consortium 2 (n=13,950) study, and in particular when the individuals in the sample are unrelated. In these cases the SKAT approximation tends to be highly over-conservative and therefore underpowered. To address this limitation, we suggest an efficient method to calculate exact p-values for the score test in the case of a single variance component and a continuous response vector, which can speed up the analysis by orders of magnitude. Our results enable fast and accurate application of the score test in heritability and in set-based association tests. Our method is available in http://github.com/cozygene/RL-SKAT.

scholarly journals Estimation of the Non-Centrality Parameter of a Chi Squared Distribution

1982 ◽  
Vol 10 (3) ◽  
pp. 1012-1016 ◽  
Author(s):  
K. M. Lal Saxena ◽  
Khursheed Alam
Keyword(s):  
Chi Squared ◽  
Chi Squared Distribution

Chi-Squared Distribution

1968 ◽  
pp. 178-200 ◽  
Author(s):  
H. Mulholland ◽  
C. R. Jones
Keyword(s):  
Chi Squared ◽  
Chi Squared Distribution
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