Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-28T16:08:15.827Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of Model Selection on Inference

Published online by Cambridge University Press:  11 February 2009

B.M. Pötscher
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic properties of parameter estimators which are based on a model that has been selected by a model selection procedure are investigated. In particular, the asymptotic distribution is derived and the effects of the model selection process on subsequent inference are illustrated.

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 2 , June 1991 , pp. 163 - 185
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Akaike, H. Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics 21 (1969): 243–247.10.1007/BF02532251CrossRefGoogle Scholar
2. Akaike, H. Statistical predictor identification. Annals of the Institute of Statistical 22 (1970): 203–217.10.1007/BF02506337Google Scholar
3. Akaike, H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (1974): 716–723.10.1109/TAC.1974.1100705Google Scholar
4. Akaike, H. Comments on “On model structure testing in system identification.” International Journal of Control 27 (1977): 323–324.10.1080/00207177808922371Google Scholar
5. Amemiya, T. Selection of regressors. International Economic Review 21 (1980): 331–354.10.2307/2526185Google Scholar
6. An, H.Z. & Gu., L. On selection of regression variables. Acta Mathematicae Applicandae Sinica 2 (1985): 27–36.Google Scholar
7. Anderson, T.W. The choice of the degree of a polynomial regression as a multiple decision problem. Annals of Mathematical Statistics 33 (1962): 255–265.10.1214/aoms/1177704729CrossRefGoogle Scholar
8. Bauer, P. Potscher, B.M. & Hackl, P.. Model selection by multiple test procedures. Statistics 19 (1988): 39–44.10.1080/02331888808802068Google Scholar
9. Brownstone, D. How to “data mine” if you must: bootstrapping Stein-rule model selection procedures. Technical Report MBS 90–08, Irvine Research Unit in Mathematical Behavioral Sciences, UC Irvine, 1990.Google Scholar
10. Ensor, K.B. & Newton, H.J.. The effect of order estimation on estimating the peak frequency of an autoregressive spectral density. Biometrika 75 (1988): 587–589.10.1093/biomet/75.3.587Google Scholar
11. Geweke, J. & Meese, R.. Estimating regression models of finite but unknown order. International Economic Review 22 (1981): 55–70.10.2307/2526135Google Scholar
12. Hannan, E.J. The estimation of the order of an ARMA process. Annals of Statistics 8 (1980): 1071–1081.10.1214/aos/1176345144Google Scholar
13. Hannan, E.J. Estimating the dimension of a linear system. Journal of Multivariate Analysis 11 (1981): 459–473.10.1016/0047-259X(81)90089-0CrossRefGoogle Scholar
14. Hannan, E.J. & Quinn, B.G.. The determination of the order of an autoregression. Journal of the Royal Statistical Society B 41 (1979): 190–195.Google Scholar
15. Hosoya, Y. Information criteria and tests for time series models. In Anderson, O.D. (ed.), Time Series Analysis: Theory and Practice 5, pp. 39–52. Amsterdam: North-Holland, 1984.Google Scholar
16. Hosoya, Y. Hierarchical statistical models and a generalized likelihood ratio test. Journal of the Royal Statistical Society B 51 (1989): 435–447.Google Scholar
17. Judge, G.G. & Bock, M.E.. The Statistical Implications of Pre-Test and Stein-Rule Estimators in Econometrics. Amsterdam: North-Holland, 1978.Google Scholar
18. Judge, G.G. & Yancey, T.A.. Improved Methods of Inference in Econometrics. Amsterdam: North-Holland, 1986.Google Scholar
19. Lehmann, E.L. Theory of Point Estimation. New York: Wiley, 1983.10.1007/978-1-4757-2769-2Google Scholar
20. Mallows, C.L. Some comments on C p. Technometrics 15 (1973): 661–675.Google Scholar
21. Paulsen, J. Order determination of multivariate autoregressive time series with unit roots. Journal of Time Series Analysis 5 (1984): 115–127.10.1111/j.1467-9892.1984.tb00381.xCrossRefGoogle Scholar
22. Paulsen, J. & Tjøstheim, D.. Least squares estimates and order determination procedures for autoregressive processes with a time dependent variance. Journal of Time Series Analysis 6 (1985): 117–133.Google Scholar
23. Pötscher, B.M. Order estimation in ARMA-models by Lagrangian multiplier tests. Annals of Statistics 11 (1983): 872–885.10.1214/aos/1176346253Google Scholar
24. Pötscher, B.M. The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model. Metrika 32 (1985): 129–150.10.1007/BF01897808CrossRefGoogle Scholar
25. Pötscher, B.M. Model selection under nonstationarity: autoregressive models and stochastic linear regression models. Annals of Statistics 17 (1989): 1257–1274.10.1214/aos/1176347267CrossRefGoogle Scholar
26. Pötscher, B.M. Effects of model selection on inference. Working Paper, Institut für Ökonometrie, Operations Research und Systemtheorie, Technische Universitat Wien, 1989.Google Scholar
27. Quinn, B.G. Order determination for multivariate autoregression. Journal of the Royal Statistical Society B 42 (1980): 182–185.Google Scholar
28. Schwarz, G. Estimating the dimension of a model. Annals of Statistics 6 (1978): 461–464.10.1214/aos/1176344136Google Scholar
29. Sen, P.K. Asymptotic properties of maximum likelihood estimators based on conditional specification. Annals of Statistics 7 (1979): 1019–1033.10.1214/aos/1176344785CrossRefGoogle Scholar
30. Shibata, R. Selection of the order of an autoregressive model by Akaike's information criterion. Biometrika 63 (1976): 117–126.10.1093/biomet/63.1.117CrossRefGoogle Scholar
31. Shibata, R. Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Annals of Statistics 8 (1980): 147–164.10.1214/aos/1176344897Google Scholar
32. Shibata, R. A theoretical view of the use of AIC. In Anderson, O.D. (ed.), Time Series Analysis: Theory and Practice 4, pp. 237–244. Amsterdam: North-Holland, 1983.Google Scholar
33. Shibata, R. Consistency of model selection and parameter estimation. In Gani, J. and Priestley, M.B. (eds.), Essays in Time Series and Allied Processes, pp. 127–141. Sheffield: Applied Probability Trust, 1986.Google Scholar
34. Söderstrom, T. On model structure testing in system identification. International Journal of Control 26 (1977): 1–18.10.1080/00207177708922285CrossRefGoogle Scholar
35. Tsay, R.S. Order selection in nonstationary autoregressive models. Annals of Statistics 12 (1984): 1425–1433.10.1214/aos/1176346801Google Scholar