$L_p$-Approximable sequences of vectors and limit distribution of quadratic forms of random variables
AbstractThe properties of $L_2$-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are "two-wing" averages of martingale differences. The results constitute the first significant advancement in the theory of $L_2$-approximable sequences since 1976 when Moussatat introduced a narrower notion of $L_2$-generated sequences. The method relies on a study of certain linear operators in the spaces $L_p$ and $l_p$. A criterion of $L_p$-approximability is given. The results are new even when the weights generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 18447.
Date of creation: 2000
Date of revision: 2001
linear operators in $L_p$ spaces; central limit theorem; quadratic forms of random variables;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Mynbaev, Kairat T. & Ullah, Aman, 2008. "Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 245-277, February.
- Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005.
- Mynbaev, Kairat & Ullah, Aman, 2006. "A Remark on the Asymptotic Distribution of the OLS Estimator for a Purely Autoregressive Spatial Model," MPRA Paper 3318, University Library of Munich, Germany.
- Mynbaev, Kairat, 2009.
"Regressions with Asymptotically Collinear Regressor,"
31315, University Library of Munich, Germany.
- Kairat T. Mynbaev, 2011. "Regressions with asymptotically collinear regressors," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 304-320, 07.
- Mynbaev, Kairat, 2007. "Comment on "Regression with slowly varying regressors and nonlinear trends" by P.C.B. Phillips," MPRA Paper 8838, University Library of Munich, Germany, revised 23 May 2008.
- Mynbaev, Kairat T., 2010. "Asymptotic distribution of the OLS estimator for a mixed spatial model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 733-748, March.
- Mynbaev, Kairat, 2006. "Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model," MPRA Paper 4411, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.