Maximal inequalities for U-processes of strongly mixing random variables

• Autorzy: Sancetta A.
• Języki publikacji: EN

Abstrakty

EN

Maximal inequalities for U-processes are required in order to achieve a reduction to the first nonvanishing term in their Hoeffding’s decomposition, which is the relevant quantity for statistical inference. This paper proves new maximal inequalities under strong mixing for U-processes in some function spaces. As an application we derive a uniform central limit theorem.

Słowa kluczowe

EN

Besov space; Hoeffding decomposition; stochastic equicontinuity; strong mixing; U-process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2009
• Tom: Vol. 29, Fasc. 1
• Strony: 155--167
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Sancetta A.

• FIRST, BNP Paribas, 10 Harewood Avenue, London NW1 6AA

Bibliografia

• [1] R. A. Adams and J. J. F. Fournier, Sobolev Spaces, Academic Press, Amsterdam 2003.
• [2] M. A. Arcones and E. Giné, On the bootstrap of U and V statistics, Ann. Statist. 20 (1992), pp. 655-674.
• [3] M. A. Arcones and E. Giné, Limit theorems for U-processes, Ann. Probab. 21 (1993), pp. 1494-1542.
• [4] M. A. Arcones and B. Y u, Central limit theorems for empirical and U-processes of stationary mixing sequences, J. Theoret. Probab. 7 (1994), pp. 47-71.
• [5] L. Birgé and P. Massart, An adaptive compression algorithm in Besov spaces, Constr. Approx. 16 (2000), pp. 1-36.
• [6] S. Borovkova, R. Burton and H. Dehling, Limit theorems for functionals of mixing processes with applications to U-statistics and dimension estimation, Trans. Amer. Math. Soc. 353 (2001), pp. 4261-4318.
• [7] C. Cavanagh and R. P. Sherman, Rank estimators for monotonic index models, J. Econometrics 84 (1998), pp. 351-381.
• [8] M. Denker and G. Keller, Rigorous statistical procedures for data from dynamical systems, J. Statist. Phys. 44 (1986), pp. 67-93.
• [9] R. A. DeVore and B. J. Lucier, Wavelets, Acta Numer. 1 (1992), pp. 1-56.
• [10] Y. Fan and Q. Li, Central limit theorem for degenerate U-statistics of absolutely regular processes with applications to model specification testing, J. Nonparametr. Stat. 10 (1999), pp. 245-271.
• [11] Y. Fan and A. Ullah, On goodness-of-fit tests for weakly dependent processes using kernel methods, J. Nonparametr. Stat. 11 (1999), pp. 337-360.
• [12] S. Ghosal, A. Sen and A. W. Van der Vaart, Testing monotonicity of regression, Ann. Statist. 28 (2000), pp. 1054-1082.
• [13] A. K. Han, A non-parametric analysis of transformations, J. Econometrics 35 (1987), pp. 191-209.
• [14] B. E. Honore and J. L. Powell, Pairwise difference estimators of censored and truncated regression models, J. Econometrics 64 (1994), pp. 241-278.
• [15] Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge 1992.
• [16] E. Rio, Théorie asymptotique des processus aléatoires faiblement dépendants, Springer, Paris 2000.
• [17] J. R. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York 1980.
• [18] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel 1983.
• [19] A. Van der Vaart and J. A. Wellner, Weak Convergence of Empirical Processes, Springer, New York 2000.