7. Quadratic Forms of the Quantile Process, Weighted Spacings and Testing for Composite Goodness-of-Fit

1983 ◽  
pp. 75-113
Keyword(s):  
Quadratic Forms ◽  
Goodness Of Fit ◽  
Quantile Process

Pearson’s chi-squared statistics: approximation theory and beyond

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 716-723
Author(s):  
Mengyu Xu ◽  
Danna Zhang ◽  
Wei Biao Wu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Approximation Theory ◽  
Quadratic Forms ◽  
Degrees Of Freedom ◽  
Goodness Of Fit ◽  
High Dimensional ◽  
Goodness Of Fit Test ◽  
Chi Squared

Summary We establish an approximation theory for Pearson’s chi-squared statistics in situations where the number of cells is large, by using a high-dimensional central limit theorem for quadratic forms of random vectors. Our high-dimensional central limit theorem is proved under Lyapunov-type conditions that involve a delicate interplay between the dimension, the sample size, and the moment conditions. We propose a modified chi-squared statistic and introduce an adjusted degrees of freedom. A simulation study shows that the modified statistic outperforms Pearson’s chi-squared statistic in terms of both size accuracy and power. Our procedure is applied to the construction of a goodness-of-fit test for Rutherford’s alpha-particle data.

Quadratic forms in order statistics used as goodness-of-fit criteria

Biometrika ◽  
1972 ◽  
Vol 59 (3) ◽  
pp. 605-611 ◽  
Author(s):  
H. O. HARTLEY ◽  
R. C. PFAFFENBERGER
Keyword(s):  
Order Statistics ◽  
Quadratic Forms ◽  
Goodness Of Fit

scholarly journals THE JOINT MOMENT GENERATING FUNCTION OF QUADRATIC FORMS IN MULTIVARIATE AUTOREGRESSIVE SERIES

2001 ◽  
Vol 17 (1) ◽  
pp. 222-246 ◽  
Author(s):  
Karim M. Abadir ◽  
Rolf Larsson
Keyword(s):  
Generating Function ◽  
Quadratic Forms ◽  
Goodness Of Fit ◽  
Moment Generating Function ◽  
Joint Moment ◽  
Finite Sample ◽  
Sufficient Statistic ◽  
Deterministic Components ◽  
Non Gaussian ◽  
Autoregressive Series

Let {Xt} follow a discrete Gaussian vector autoregression with deterministic components. We derive the exact finite-sample joint moment generating function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of functionals involving multivariate and univariate Ornstein–Uhlenbeck processes, drifts, and time trends. Such processes arise asymptotically from more general non-Gaussian processes and also from the Gaussian {Xt} and have also been used in areas other than time series, such as the “goodness of fit” literature.

Applying the Anderson-Darling Test to Suicide Clusters

Crisis ◽  
2013 ◽  
Vol 34 (6) ◽  
pp. 434-437 ◽  
Author(s):  
Donald W. MacKenzie
Keyword(s):  
Poisson Process ◽  
Goodness Of Fit ◽  
Small Samples ◽  
Massachusetts Institute Of Technology ◽  
Homogeneous Poisson Process ◽  
Cornell University ◽  
The Difference ◽  
Suicide Clusters ◽  
Institute Of Technology ◽  
Anderson Darling

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

Confirmatory Factor Analysis of the Long and Short Forms of the Worry Domains Questionnaire

2009 ◽  
Vol 25 (4) ◽  
pp. 239-243
Author(s):  
Roberto Nuevo ◽  
Andrés Losada ◽  
María Márquez-González ◽  
Cecilia Peñacoba
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Factor Structure ◽  
Goodness Of Fit ◽  
Factorial Validity ◽  
Fit Indices ◽  
Short Forms ◽  
Confirmatory Factor ◽  
Positive Correlations ◽  
Future Work

The Worry Domains Questionnaire was proposed as a measure of both pathological and nonpathological worry, and assesses the frequency of worrying about five different domains: relationships, lack of confidence, aimless future, work, and financial. The present study analyzed the factor structure of the long and short forms of the WDQ (WDQ and WDQ-SF, respectively) through confirmatory factor analysis in a sample of 262 students (M age = 21.8; SD = 2.6; 86.3% females). While the goodness-of-fit indices did not provide support for the WDQ, good fit indices were found for the WDQ-SF. Furthermore, no source of misspecification was identified, thus, supporting the factorial validity of the WDQ-SF scale. Significant positive correlations between the WDQ-SF and its subscales with worry (PSWQ), anxiety (STAI-T), and depression (BDI) were found. The internal consistency was good for the total scale and for the subscales. This work provides support for the use of the WDQ-SF, and potential uses for research and clinical purposes are discussed.

Finding Goodness of Fit When You are Black, Poor, Male, and Disturbed

1988 ◽  
Vol 33 (10) ◽  
pp. 885-886
Author(s):  
Judith K. Grosenick
Keyword(s):  
Goodness Of Fit ◽  
Black Poor
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