본문 바로가기
KERD
논문KCI 등재

Almost sure and complete consistency of the estimator in nonparametric regression model for negatively orthant dependent random variables

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function $g(\cdot)$, the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

Abstract

In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function $g(\cdot)$, the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

참고문헌 (30)

  1. A. Antoniadis, "Wavelet methods for curve estimation", J. Amer. Statist. Assoc, 89(428), pp.1340~1353 (1994)
  2. Xiaohan Bao, "On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications", Mathematica Slovaca, 69(1), pp.223~232 (2019), Walter de Gruyter GmbH[DOI]
  3. Liwang Ding, "Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples", Statistical Papers, 61(6), pp.2331~2349 (2020), Springer Science and Business Media LLC[DOI]
  4. Liwang Ding, "Berry–Esseen bound of wavelet estimators in heteroscedastic regression model with random errors", International Journal of Computer Mathematics, 96(4), pp.821~852 (2018), Informa UK Limited[DOI]
  5. A. A. Georgiev, "Mathematical statistics and applications, Vol. B", pp.141~151 (1985), Reidel
  6. Alexander A Georgiev, "Consistent nonparametric multiple regression: The fixed design case", Journal of Multivariate Analysis, 25(1), pp.100~110 (1988), Elsevier BV[DOI]
  7. Alexander A. Georgiev, "Nonparametric function recovering from noisy observations", Journal of Statistical Planning and Inference, 13, pp.1~14 (1986), Elsevier BV[DOI]
  8. P. Hall, "Formulae for mean integrated squared error of nonlinear wavelet-based density estimators", Ann. Statist, 23(3), pp.905~928 (1995)[DOI]
  9. K. Joag-Dev, "Negative association of random variables, with ap-plications", Ann. Statist, 11(1), pp.286~295 (1983)[DOI]
  10. Yongming Li, "Berry–Esseen bounds for wavelet estimator in a regression model with linear process errors", Statistics & Probability Letters, 81(1), pp.103~110 (2011), Elsevier BV[DOI]
  11. Xiaoqin Li, "The Bahadur representation for sample quantile under NOD sequence", Journal of Nonparametric Statistics, 23(1), pp.59~65 (2011), Informa UK Limited[DOI]
  12. Hanying Liang, "Asymptotic normality of wavelet estimator in heteroscedastic model with α-mixing errors", Journal of Systems Science and Complexity, 24(4), pp.725~737 (2011), Springer Science and Business Media LLC[DOI]
  13. Han-Ying Liang, "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences", Journal of Multivariate Analysis, 95(2), pp.227~245 (2005), Elsevier BV[DOI]
  14. H. -G. Muller, "Weak and universal consistency of moving weighted averages", Period. Math. Hungar, 18(3), pp.241~250 (1987)
  15. Aiting Shen, "On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables", Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 107(2), pp.257~271 (2013), Springer Science and Business Media LLC[DOI]
  16. Aiting Shen, "Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables", Metrika, 78(3), pp.295~311 (2015), Springer Science and Business Media LLC[DOI]
  17. Ronald F. Patterson, "A strong law of large numbers for arrays of rowwise negatively dependent random variables", Stochastic Analysis and Applications, 20(3), pp.643~656 (2002), Informa UK Limited[DOI]
  18. Xuejun Wang, "On consistency of least square estimators in the simple linear EV model with negatively orthant dependent errors", Electronic Journal of Statistics, 11(1), pp.1434~1463 (2017), Institute of Mathematical Statistics[DOI]
  19. Xuejun Wang, "An exponential inequality for a NOD sequence and a strong law of large numbers", Applied Mathematics Letters, 24(2), pp.219~223 (2011), Elsevier BV[DOI]
  20. Xuejun Wang, "Strong limit theorems for weighted sums of NOD sequence and exponential inequalities", 대한수학회보, 48(5), pp.923~938 (2011), 대한수학회
  21. Xuejun Wang, "Complete convergence for arrays of rowwise negatively orthant dependent random variables", Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 106(2), pp.235~245 (2012), Springer Science and Business Media LLC[DOI]
  22. Xuejun Wang, "Exponential inequalities and inverse moment for NOD sequence", Statistics & Probability Letters, 80(5-6), pp.452~461 (2010), Elsevier BV[DOI]
  23. Xuejun Wang, "Complete consistency of the estimator of nonparametric regression model under ND sequence", Statistical Papers, 56(3), pp.585~596 (2015), Springer Science and Business Media LLC[DOI]
  24. Xuejun Wang, "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models", Statistical Papers, 61(3), pp.1147~1180 (2020), Springer Science and Business Media LLC[DOI]
  25. Q. Y. Wu, "Probability Limit Theory for Mixing and Dependent Sequences" (2006), Science Press of China
  26. Q. Y. Wu, "Complete convergence for weighted sums of sequences of negatively dependent random variables", J. Probab. Stat, 2011, pp.16~ (2011)[DOI]
  27. Liu Gen Xue, "Bootstrap approximation of wavelet estimates in a semiparametric regression model", Acta Mathematica Sinica, English Series, 26(4), pp.763~778 (2010), Springer Science and Business Media LLC[DOI]
  28. Shan Chao Yang, "Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application", Acta Mathematica Sinica, English Series, 23(6), pp.1013~1024 (2007), Springer Science and Business Media LLC[DOI]
  29. Rui Zhang, "On complete consistency for the weighted estimator of nonparametric regression models", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(3), pp.2319~2333 (2019), Springer Science and Business Media LLC[DOI]
  30. Xing-cai Zhou, "Wavelet estimation in varying coefficient models for censored dependent data", Statistics & Probability Letters, 122, pp.179~189 (2017), Elsevier BV[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (18건)