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References
Anderson, T. W.: On asymptotic distributions of estimates of parameters of stochastic difference equations. Ann. math. Statistics 30, 676–687 (1959).
Chanda, K. C.: A note on the consistency and maxima of the roots of likelihood equations. Biometrika 41, 56–61 (1954).
Cramér, H.: Mathematical methods of statistics. Princeton: Princeton University Press 1946.
Erdös, P., and M. Kac: On certain limit theorems in the theory of probability. Bull. Amer. math. Soc. 52, 292–302 (1946).
Gnedenko, B. V., and A. N. Kolmogorov: Limit distributions for sums of independent random variables (Translation). Cambridge, Mass.: Addison-Wesley 1954.
Grenander, U.: Stochastic processes and statistical inference. Ark. Mat. 1, 195–277 (1950).
Hoeffding, W., and H. Robbins: The central limit theorem for dependent random variables. Duke math. J., 15, 773–780 (1948).
Hurwicz, L.: Variable parameters in stochastic processes. Cowles Commission Monograph, 10, New York: Wiley 1950.
Jordan, C.: Calculus of finite differences. Budapest: Röttig and Romwalter 1939.
Kraft, C., and L. Le Cam: A remark on the roots of the maximum likelihood equation. Ann. math. Statistics 27, 1174–1177 (1956).
Kulldorff, G.: On the conditions for consistency and asymptotic efficiency of maximum likelihood estimates. Skand. Aktuarietidskr. 40, 129–144 (1958).
LeCam, L.: On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates. Univ. California Publ. Statistics 1, 277–330 (1953).
—: On the asymptotic theory of estimation and testing hypotheses. Proc. Third Berkeley Sympos. math. Statist. Probab. 1, 129–156 (1956).
Mann, H. B., and A. Wald: On the statistical treatment of linear stochastic difference equations. Econometrica 11, 173–220 (1943).
Rao, M. M.: Consistency and limit distributions of estimators of parameters in explosive stochastic difference equations. Ann. math. Statistics 32, 195–218 (1961).
—: Inference in stochastic processes — I. Teor. Verojatn. Primen. 8, 282–298 (1963).
—: Inference in stochastic processes — II: Asymptotic properties of maximum likelihood estimators. Notices Amer. math. Soc. 6, 849 (1959).
- Inference in stochastic processes — III: Nonlinear prediction, filtering and sampling theorems. (To appear.)
—: Some infernece theorems in stochastic processes. Bull. Amer. math. Soc. 69, 72–77 (1963).
Rubin, H.: Consistency of maximum likelihood estimates in the explosive case. Cowles Commission Monograph, 10, 356–364. New York: Wiley 1950.
Wald, A.: Asymptotic properties of the maximum likelihood estimate of an unknown parameter of a discrete stochastic process. Ann. math. Statistics 19, 40–46 (1948).
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Supported in part by the National Science Foundation under grants NSF-G 14832 and GP-1349.
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Rao, M.M. Inference in stochastic processes. II. Z. Wahrscheinlichkeitstheorie verw Gebiete 5, 317–335 (1966). https://doi.org/10.1007/BF00535362
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DOI: https://doi.org/10.1007/BF00535362