Joint convergence of i.i.d. patterned matrices

2018 ◽  
pp. 187-199
Author(s):  
Arup Bose
Keyword(s):  
Patterned Matrices

On the inverses of some patterned matrices arising in the theory of stationary time series

1974 ◽  
Vol 11 (01) ◽  
pp. 63-71 ◽  
Author(s):  
R. F. Galbraith ◽  
J. I. Galbraith
Keyword(s):  
Moving Average ◽  
Autoregressive Process ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
First Order ◽  
Explicit Formulae ◽  
Patterned Matrices ◽  
Autoregressive Moving Average Process

Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ≧ p), and for the first order mixed autoregressive moving average process.

scholarly journals Algorithms for Finding Inverse of Two Patterned Matrices overZp

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaoyu Jiang ◽  
Kicheon Hong
Keyword(s):  
Circulant Matrix ◽  
Basic Properties ◽  
Hensel Lifting ◽  
Network Engineering ◽  
The Cost ◽  
Patterned Matrices ◽  
Chinese Remaindering

Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices overZpwhich include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given.

scholarly journals Convergence of joint moments for independent random patterned matrices

2011 ◽  
Vol 39 (4) ◽  
pp. 1607-1620 ◽  
Author(s):  
Arup Bose ◽  
Rajat Subhra Hazra ◽  
Koushik Saha
Keyword(s):  
Joint Moments ◽  
Patterned Matrices

On the inverses of some patterned matrices arising in the theory of stationary time series

1974 ◽  
Vol 11 (1) ◽  
pp. 63-71 ◽  
Author(s):  
R. F. Galbraith ◽  
J. I. Galbraith
Keyword(s):  
Moving Average ◽  
Autoregressive Process ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Average Process ◽  
Moving Average Process ◽  
First Order ◽  
Explicit Formulae ◽  
Patterned Matrices ◽  
Autoregressive Moving Average Process

Expressions are obtained for the determinant and inverse of the covariance matrix of a set of n consecutive observations on a mixed autoregressive moving average process. Explicit formulae for the inverse of this matrix are given for the general autoregressive process of order p (n ≧ p), and for the first order mixed autoregressive moving average process.

On Inverting a Class of Patterned Matrices

Biometrika ◽  
1956 ◽  
Vol 43 (1/2) ◽  
pp. 227
Author(s):  
S. N. Roy ◽  
A. E. Sarhan
Keyword(s):  
Patterned Matrices
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