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Functional limit theorems for random quadratic forms

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  • Mikosch, T.

Abstract

We prove a functional central limit theorem and a functional law of the iterated logarithm for quadratic forms in independent random variables.

Suggested Citation

  • Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    • Handle: RePEc:eee:spapps:v:37:y:1991:i:1:p:81-98
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    Cited by:

    1. Linton, Oliver, 1996. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 12(1), pages 30-60, March.
    2. Ellison, Glenn & Ellison, Sara Fisher, 2000. "A simple framework for nonparametric specification testing," Journal of Econometrics, Elsevier, vol. 96(1), pages 1-23, May.
    3. Lili Xia & Tingyu Lai & Zhongzhan Zhang, 2023. "An Adaptive-to-Model Test for Parametric Functional Single-Index Model," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    4. Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
    5. R. Bárcenas & J. Ortega & A. J. Quiroz, 2017. "Quadratic forms of the empirical processes for the two-sample problem for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 503-526, September.
    6. Liudas Giraitis & Masanobu Taniguchi & Murad S. Taqqu, 2017. "Asymptotic normality of quadratic forms of martingale differences," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 315-327, October.
    7. Zhang, Tonglin & Lin, Ge, 2016. "On Moran’s I coefficient under heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 83-94.
    8. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    9. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Approximations and limit theory for quadratic forms of linear processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 71-95, January.
    10. Matthias Arnold & Dominik Wied, 2014. "Improved GMM estimation of random effects panel data models with spatially correlated error components," Papers in Regional Science, Wiley Blackwell, vol. 93(1), pages 77-99, March.
    11. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Convergence of quadratic forms with nonvanishing diagonal," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 726-734, April.
    12. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    13. Zhang, Tonglin, 2019. "General Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 234-247.

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