Conditional independence, conditional mixing and conditional association

Annals of the Institute of Statistical Mathematics

Volumn 61, Issue 2, 2009, Pages 441-460

  Prakasa Rao, B L S ^a  

^a UNIVERSITY OF HYDERABAD   (India)

Author keywords

Conditional association; Conditional Borel Cantelli lemma; Conditional H jek R nyi inequality; Conditional independence; Conditional mixing; Conditional strong law of large numbers; Generalized Kolmogorov inequality

Indexed keywords

CONDITIONAL ASSOCIATION; CONDITIONAL BOREL-CANTELLI LEMMA; CONDITIONAL INDEPENDENCE; CONDITIONAL MIXING; CONDITIONAL STRONG LAW OF LARGE NUMBERS; GENERALIZED KOLMOGOROV INEQUALITY;

COMPUTATIONAL COMPLEXITY; LAWS AND LEGISLATION; RANDOM PROCESSES;

RANDOM VARIABLES;

EID: 65449179217     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-007-0152-2     Document Type: Article

References (23)

1. Basawa I.V., Prakasa Rao B.L.S. (1980). Statistical inference for stochastic processes. London, Academic
2. Basawa I.V., Scott D. (1983). Asymptotic optimal inference for non-ergodic models. Lecture Notes in Statistics, Vol. 17. New York, Springer
3. Billingsley P. (1986). Probability and measure. New York, Wiley
4. Chow Y.S., Teicher H. (1978). Probability theory: independence, interchangeability, martingales. New York, Springer
5. K.L. Chung P. Erdös 1952 On the application of the Borel-Cantelli lemma Transactions of American Mathematical Society 72 179 186
6. Doob J.L. (1953). Stochastic processes. New York, Wiley
7. Guttorp P. (1991). Statistical inference for branching processes. New York, Wiley
8. Gyires B. (1981). Linear forms in random variables defined on a homogeneous Markov chain. In: Revesz P. et al. (eds). The first pannonian symposium on mathematical statistics, Lecture Notes in Statistics, Vol. 8. New York, Springer, pp. 110-121
9. J. Hájek A. Rényi 1955 Generalization of an inequality of Kolmogorov Acta Mathematica Academiae Scientiarum Hungaricae 6 281 283
10. S. Kochen C. Stone 1964 A note on the Borel-Cantelli lemma Illinois Journal of Mathematics 8 248 251
11. Loève M. (1977). Probability theory I (4th Ed.). New York, Springer
12. D. Majerak W. Nowak W. Zieba 2005 Conditional strong law of large number International Journal of Pure and Applied Mathematics 20 143 157
13. Newman C. (1984). Asymptotic independence and limit theorems for positively and negatively dependent random variables. In: Tong Y.L. (ed). Inequalities in statistics and probability. Hayward, IMS, pp. 127-140
14. V.V. Petrov 2004 A generalization of the Borel-Cantelli lemma Statistics and Probabability Letters 67 233 239
15. B.L.S. Prakasa Rao 1987 Characterization of probability measures by linear functions defined on a homogeneous Markov chain Sankhyā, Series A 49 199 206
16. B.L.S. Prakasa Rao 1990 On mixing for flows of σ-algebras, Sankhyā Series A 52 1 15
17. Prakasa Rao B.L.S. (1999a). Statistical inference for diffusion type processes. London, Arnold and New York, Oxford University Press
18. Prakasa Rao B.L.S. (1999b). Semimartingales and their statistical inference. Boca Raton, CRC Press
19. Prakasa Rao B.L.S., Dewan I. (2001). Associated sequences and related inference problems. In: Rao C.R., Shanbag D.N. (eds). Handbook of statistics, 19, stochastic Processes: theory and methods. Amsterdam, North Holland, pp. 693-728
20. M. Rosenblatt 1956 A central limit theorem and a strong mixing condition Proceedings National Academy of Sciences U.S.A 42 43 47
21. Roussas G.G. (1999). Positive and negative dependence with some statistical applications. In Ghosh S. (ed). Asymptotics, nonparametrics and time series. New York, Marcel Dekker, pp. 757-788
22. G.G. Roussas D. Ioannides 1987 Moment inequalities for mixing sequences of random variables Stochastic Analysis and Applications 5 61 120
23. Yan, J.A. (2004). A new proof of a generalized Borel-Cantelli lemma (Preprint), Academy of Mathematics and Systems Science. Chinese Academy of Sciences, Beijing.