메뉴 건너뛰기




Volumn 65, Issue 1, 1996, Pages 69-80

Strong convergence of sums of α-mixing random variables with applications to density estimation

Author keywords

mixing; Kernel density estimators; Strong convergence; Triangular array

Indexed keywords


EID: 0030582828     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(96)00096-8     Document Type: Article
Times cited : (106)

References (31)
  • 1
    • 51249182479 scopus 로고
    • A note on nonparametric density estimation for dependent variables using a delta sequence
    • I.A. Ahmad, A note on nonparametric density estimation for dependent variables using a delta sequence, Ann. Inst. Statist. Math. Part A 33 (1981) 247-254.
    • (1981) Ann. Inst. Statist. Math. Part A , vol.33 , pp. 247-254
    • Ahmad, I.A.1
  • 2
    • 0001917727 scopus 로고
    • Probability inequalities for the sum of independent random variables
    • G. Bennett, Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc. 57 (1962) 33-45.
    • (1962) J. Amer. Statist. Assoc. , vol.57 , pp. 33-45
    • Bennett, G.1
  • 4
    • 0343171028 scopus 로고
    • Estimation of a multivariate density
    • T. Cacoullos, Estimation of a multivariate density, Ann. Inst. Statist. Math. 18 (1966) 179-190.
    • (1966) Ann. Inst. Statist. Math. , vol.18 , pp. 179-190
    • Cacoullos, T.1
  • 5
    • 0001261147 scopus 로고
    • Inégalité de bernstein pour les processus fortement mélangeants, non nécessairement stationnaires
    • M. Carbon, Inégalité de Bernstein pour les processus fortement mélangeants, non nécessairement stationnaires, C. R. Acad. Sci. Paris 297 I (1983) 303-306.
    • (1983) C. R. Acad. Sci. Paris , vol.297 , Issue.1 , pp. 303-306
    • Carbon, M.1
  • 6
    • 0000448413 scopus 로고
    • The invariance principle for stationary processes
    • Yu. A. Davydov, The invariance principle for stationary processes, Theory Probab. Appl. 15 (1970) 487-498.
    • (1970) Theory Probab. Appl. , vol.15 , pp. 487-498
    • Davydov, Y.A.1
  • 7
    • 0003155075 scopus 로고
    • Mixing: Properties and examples
    • Springer, Berlin
    • P. Doukhan, Mixing: properties and examples, Lecture Notes in Statistics, Vol. 85 (Springer, Berlin 1994).
    • (1994) Lecture Notes in Statistics , vol.85
    • Doukhan, P.1
  • 9
    • 11744346809 scopus 로고
    • Density estimation for nonstationary Markov processes
    • H. Gillert and A. Wartenberg, Density estimation for nonstationary Markov processes, Statistics 15 (1984) 261-275.
    • (1984) Statistics , vol.15 , pp. 261-275
    • Gillert, H.1    Wartenberg, A.2
  • 10
    • 0000272104 scopus 로고
    • Data-driven bandwidth choice for density estimation based on dependent data
    • J.D. Hart and P. Vieu, Data-driven bandwidth choice for density estimation based on dependent data, Ann. Statist. 18 (1990) 873-890.
    • (1990) Ann. Statist. , vol.18 , pp. 873-890
    • Hart, J.D.1    Vieu, P.2
  • 11
    • 84973043789 scopus 로고
    • Kernel estimators for probability densities with discontinuities
    • E. Liebscher, Kernel estimators for probability densities with discontinuities, Statistics 21 (1990) 185-196.
    • (1990) Statistics , vol.21 , pp. 185-196
    • Liebscher, E.1
  • 12
    • 0011558948 scopus 로고
    • Density estimation for Markov chains
    • E. Liebscher, Density estimation for Markov chains, Statistics 23 (1992) 27-48
    • (1992) Statistics , vol.23 , pp. 27-48
    • Liebscher, E.1
  • 13
    • 0000765308 scopus 로고
    • Strong convergence of sums of φ-mixing random variables
    • E. Liebscher, Strong convergence of sums of φ-mixing random variables, Math. Methods Statist. 4 (1995) 216-229.
    • (1995) Math. Methods Statist. , vol.4 , pp. 216-229
    • Liebscher, E.1
  • 14
    • 0020827762 scopus 로고
    • Probability density estimation from sampled data
    • E. Masry, Probability density estimation from sampled data, IEEE Trans. Inform. Theory IT-29 (1983) 696-709.
    • (1983) IEEE Trans. Inform. Theory IT-29 , pp. 696-709
    • Masry, E.1
  • 16
    • 0000953196 scopus 로고
    • ∞ norm for mixing processes
    • Série I
    • ∞ norm for mixing processes (in French), C.R. Acad. Sci. Paris, 320, Série I (1995) 1259-1262.
    • (1995) C.R. Acad. Sci. Paris , vol.320 , pp. 1259-1262
    • Nze, P.A.1    Rios, R.2
  • 17
    • 0001473437 scopus 로고
    • On estimating a probability density function and the mode
    • E. Parzen, On estimating a probability density function and the mode, Ann. Math. Statist. 33 (1962) 1065-1076.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 18
    • 0001507728 scopus 로고
    • The functional law of the iterated logarithm for stationary strongly mixing sequences
    • E. Rio, The functional law of the iterated logarithm for stationary strongly mixing sequences, Ann. Probab. 23 (1995) 1188-1203.
    • (1995) Ann. Probab. , vol.23 , pp. 1188-1203
    • Rio, E.1
  • 19
    • 84986849734 scopus 로고
    • Nonparametric estimators for time series
    • P.M. Robinson, Nonparametric estimators for time series, J. Time Series Anal. 4 No. 3 (1983) 185-207.
    • (1983) J. Time Series Anal. , vol.4 , Issue.3 , pp. 185-207
    • Robinson, P.M.1
  • 20
    • 0001529784 scopus 로고
    • Remarks on some nonparametric estimates of a density function
    • M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. 27 (1956) 823-835.
    • (1956) Ann. Math. Statist. , vol.27 , pp. 823-835
    • Rosenblatt, M.1
  • 21
    • 0000661887 scopus 로고
    • Density estimates and Markov sequences
    • Cambridge University Press, Cambridge
    • M. Rosenblatt, Density estimates and Markov sequences, in: Nonparametric Techniques in Statistical Inference (Cambridge University Press, Cambridge, 1970) pp. 199-210.
    • (1970) Nonparametric Techniques in Statistical Inference , pp. 199-210
    • Rosenblatt, M.1
  • 22
    • 84950440675 scopus 로고
    • Nonparametric estimation in markov processes
    • G.G. Roussas, Nonparametric estimation in Markov processes, Ann. Inst. Statist. Math. 21 (1969) 73-87.
    • (1969) Ann. Inst. Statist. Math. , vol.21 , pp. 73-87
    • Roussas, G.G.1
  • 23
    • 38249032193 scopus 로고
    • Nonparametric estimation in mixing sequences of random variables
    • G.G. Roussas, Nonparametric estimation in mixing sequences of random variables, J. Statist. Plann. Inference 18 (1988) 135-149.
    • (1988) J. Statist. Plann. Inference , vol.18 , pp. 135-149
    • Roussas, G.G.1
  • 24
    • 38249019654 scopus 로고
    • Asymptotic normality of the kernel estimate under dependence conditions: Application to hazard rate
    • G.G. Roussas, Asymptotic normality of the kernel estimate under dependence conditions: application to hazard rate, J. Statist. Plann. Inference 25 (1990) 81-104.
    • (1990) J. Statist. Plann. Inference , vol.25 , pp. 81-104
    • Roussas, G.G.1
  • 25
    • 0011621958 scopus 로고
    • Consistency of estimators for multivariate density functions and for the mode
    • Series A
    • L. Rüschendorf, Consistency of estimators for multivariate density functions and for the mode, Sankhya 39 (1977) Series A 243-250.
    • (1977) Sankhya , vol.39 , pp. 243-250
    • Rüschendorf, L.1
  • 26
    • 0001212258 scopus 로고
    • Empirical distribution function for mixing random variables
    • P. Sarda and P. Vieu, Empirical distribution function for mixing random variables, Statistics 20 (1989) 559-571.
    • (1989) Statistics , vol.20 , pp. 559-571
    • Sarda, P.1    Vieu, P.2
  • 27
    • 38249020988 scopus 로고
    • Kernal density estimation under dependence
    • L.T. Tran, Kernal density estimation under dependence, Statist. Probab. Lett. 10 (1990) 193-201.
    • (1990) Statist. Probab. Lett. , vol.10 , pp. 193-201
    • Tran, L.T.1
  • 28
    • 38149148069 scopus 로고
    • Density estimation for time series by histograms
    • L.T. Tran, Density estimation for time series by histograms, J. Statist. Plann. Inference 40 (1994) 61-79.
    • (1994) J. Statist. Plann. Inference , vol.40 , pp. 61-79
    • Tran, L.T.1
  • 29
    • 0001158445 scopus 로고
    • Quadratic errors for nonparametric estimates under dependence
    • P. Vieu, Quadratic errors for nonparametric estimates under dependence, J. Multivariate Anal. 39 (1991) 324-347.
    • (1991) J. Multivariate Anal. , vol.39 , pp. 324-347
    • Vieu, P.1
  • 30
    • 38249021954 scopus 로고
    • Nonparametric density and regression estimation for Markov sequences without mixing assumption
    • S. Yakowitz, Nonparametric density and regression estimation for Markov sequences without mixing assumption, J. Multivariate Anal. 30 (1989) 124-136.
    • (1989) J. Multivariate Anal. , vol.30 , pp. 124-136
    • Yakowitz, S.1
  • 31
    • 0001494739 scopus 로고
    • ∞ norm for dependent data with applications to the Gibbs sampler
    • ∞ norm for dependent data with applications to the Gibbs sampler, Ann. Statist. 21 (1993) 711-735.
    • (1993) Ann. Statist. , vol.21 , pp. 711-735
    • Yu, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.