| Title:
|
On the rate of approximation in the random sum CLT for dependent variables (English) |
| Author:
|
Basu, Adhir Kumar |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1987 |
| Pages:
|
169-176 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Capital $"O"$ and lower-case $"o"$ approximations of the expected value of a class of smooth functions $(f\in C^r(R))$ of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979). (English) |
| Keyword:
|
random sums |
| Keyword:
|
central limit theorem |
| Keyword:
|
approximation theorems |
| Keyword:
|
random vectors |
| MSC:
|
41A25 |
| MSC:
|
60F05 |
| MSC:
|
60G42 |
| idZBL:
|
Zbl 0631.60024 |
| idMR:
|
MR0895875 |
| DOI:
|
10.21136/AM.1987.104248 |
| . |
| Date available:
|
2008-05-20T18:32:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104248 |
| . |
| Reference:
|
[1] A. K. Basu: On the rate of approximation in the Central limit theorem for dependent random variables and random vectors.J. Multivariate Anal. 10, (1980), 565-578. Zbl 0452.60027, MR 0599690, 10.1016/0047-259X(80)90070-6 |
| Reference:
|
[2] P. L. Butzer L. Hahn W. Westphal: On the rate of approximation in the Central limit theorem.J. Approx. Theory 13 (1975), 327-340. MR 0394809, 10.1016/0021-9045(75)90042-8 |
| Reference:
|
[3] M. Mamatov I. Nematov: On a limit theorem for sums of a random number of independent random variables.(Russian). Izv. Akad. Nauk, USSR Ser. Fiz. Mat. Nauk, 3 (1971), 18-24. MR 0295419 |
| Reference:
|
[4] H. Robbins: The asymptotic distribution of the Sum of a random number of random variables.Bull. Amer. Math. Soc. 54 (1948), 1151-1161. Zbl 0034.22503, MR 0027974, 10.1090/S0002-9904-1948-09142-X |
| Reference:
|
[5] Z. Rychlík D. Szynal: On the limit behavior of Sum of a random number of independent random variables.Coll. Math. 28 (1973), 147-159. MR 0334311, 10.4064/cm-28-1-147-159 |
| Reference:
|
[6] Z. Rychlík D. Szynal: On the rate of approximation in the random C-L.T.Theory of probability and Appl. 24 (1979), 620-625. MR 0541376 |
| Reference:
|
[7] E. Rychlík Z. Rychlík: The generalized Anscombe Condition and its applications in random sum limit theorems.Lecture Notes in Math. Probability in Banach spaces I Springer-Verlag 828 (1980), 244-250. |
| Reference:
|
[8] V. Sakalauskas: An estimate in the Multidimensional Central Limit Theorem.Lithuanian Math. Jour. (Eng. Trans.) 17, 4 (1977), 567-572. MR 0464370, 10.1007/BF00972282 |
| Reference:
|
[9] S. Kh. Sirazhdinov G. Orazov: Generalization of a theorem of Robbins.(Russian), In Limit theorems and Statistical Inferences, Tashkent 1960, 154-162. |
| . |
