| Title:
|
Rate of convergence for a class of RCA estimators (English) |
| Author:
|
Vaněček, Pavel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
42 |
| Issue:
|
6 |
| Year:
|
2006 |
| Pages:
|
699-709 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established. (English) |
| Keyword:
|
RCA |
| Keyword:
|
parameter estimation |
| Keyword:
|
rate of convergence |
| MSC:
|
60F05 |
| MSC:
|
60G10 |
| MSC:
|
62F10 |
| MSC:
|
62M09 |
| MSC:
|
62M10 |
| MSC:
|
91B84 |
| idZBL:
|
Zbl 1249.60034 |
| idMR:
|
MR2296509 |
| . |
| Date available:
|
2009-09-24T20:20:12Z |
| Last updated:
|
2015-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135745 |
| . |
| Reference:
|
[1] Basu A. K., Roy S. Sen: On rates of convergence in the central limit theorem for parameter estimation in general autoregressive model.Statistics 21 (1990), 461–470 MR 1062852, 10.1080/02331889008802256 |
| Reference:
|
[2] Basu A. K., Roy S. Sen: On rates of convergence in the central limit theorem for parameter estimation in random coefficient autoregressive models.J. Indian Statist. Assoc. 26 (1988), 19–25 MR 1002100 |
| Reference:
|
[3] Davidson J.: Stochastic Limit Theory.(Advanced Texts in Econometrics.) Oxford University Press, New York, Reprinted 2002 Zbl 0904.60002, MR 1430804 |
| Reference:
|
[5] Janečková H., Prášková Z.: CWLS and ML estimates in a heteroscedastic RCA(1) model.Statist. Decisions 22 (2004), 245–259 Zbl 1057.62071, MR 2125611, 10.1524/stnd.22.3.245.57064 |
| Reference:
|
[6] Kato Y.: Rates of convergence in central limit theorem for martingale differences.Bull. Math. Statist 18 (1979), 1–8 MR 0517156 |
| Reference:
|
[7] Michel R., Pfanzagl J.: The accuracy of the normal approximation for minimum contrast estimate.Z. Wahrsch. Verw. Gebiete 18 (1971), 73–84 MR 0288897, 10.1007/BF00538488 |
| Reference:
|
[8] Nicholls D. F., Quinn B. G.: Random Coefficient Autoregressive Models: An Introduction.(Lecture Notes in Statistics 11.) Springer, New York 1982 Zbl 0497.62081, MR 0671255, 10.1007/978-1-4684-6273-9 |
| Reference:
|
[9] Phillips P. C. B., Solo V.: Asymptotics for linear processes.Ann. Statist. 20 (1992), 971–1001 Zbl 0759.60021, MR 1165602, 10.1214/aos/1176348666 |
| Reference:
|
[10] Schick A.: $\sqrt{n}$-consistent estimation in a random coefficient autoregressive model.Austral. J. Statist. 38 (1996), 155–160 MR 1442543, 10.1111/j.1467-842X.1996.tb00671.x |
| Reference:
|
[12] Vaněček P.: Estimators of generalized RCA models.In: Proc. WDS’04 Part I (2004), pp. 35–40 |
| . |
