A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate

1990 ◽  
Vol 86 (1) ◽  
pp. 87-104 ◽  
Author(s):  
L. Giraitis ◽  
D. Surgailis
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quadratic Forms ◽  
Asymptotical Normality

A central limit theorem for generalized quadratic forms

1987 ◽  
Vol 75 (2) ◽  
pp. 261-277 ◽  
Author(s):  
Peter de Jong
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quadratic Forms

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.

scholarly journals Central limit theorem for quadratic forms for sparse tables

1987 ◽  
Vol 22 (2) ◽  
pp. 258-277 ◽  
Author(s):  
Prabir Burman
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quadratic Forms

A Central Limit Theorem for the Sum of Generalized Linear and Quadratic Forms

Statistics ◽  
1999 ◽  
Vol 33 (1) ◽  
pp. 85-91 ◽  
Author(s):  
R. L. Eubank ◽  
Suojin Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quadratic Forms ◽  
Linear And Quadratic Forms

Asymptotic expansion in the central limit theorem for quadratic forms

2007 ◽  
Vol 147 (4) ◽  
pp. 6891-6911 ◽  
Author(s):  
F. Götze ◽  
A. N. Tikhomirov ◽  
V. A. Yurchenko
Keyword(s):  
Asymptotic Expansion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Quadratic Forms ◽  
The Central Limit Theorem

Applets Demonstrating the Central Limit Theorem and Statistical Power

2007 ◽  
Author(s):  
Amanda Saw ◽  
Dale E. Berger ◽  
Giovanni Sosa
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Statistical Power ◽  
The Central Limit Theorem

Central limit theorem for weakly dependent random fields with values in $l_p$ ($1 \lep \le2$) and $c_0$ spaces

2020 ◽  
Vol 2020 (1) ◽  
pp. 116-122
Author(s):  
D.S. Ruzieva ◽  
O.Sh. Sharipov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Weakly Dependent
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