Estimating with partial statistics the parameters of ergodic finite Markov sources

Parameter estimation based on data emitted from a finite ergodic Markov source is discussed. This can be considered an extension of the memoryless case. First, an asymptotically optimal estimator is suggested for the case where the parametric model is completely known. For an unknown parametric model (e.g unknown noise distribution with training sequences available) a necessary condition is given for the existence of a universally optimum estimate. A universal estimate is then suggested that is asymptotically nearly optimal. The results hold under fairly mild regularity conditions. >

[1]  Jacob Ziv,et al.  Some lower bounds on signal parameter estimation , 1969, IEEE Trans. Inf. Theory.

[2]  W. J. R. Eplett Rank Tests Generated by Continuous Piecewise Linear Functions , 1982 .

[3]  R. Zieliński,et al.  Robust statistical procedures: A general approach , 1983 .

[4]  J. Wolfowitz,et al.  Asymptotically efficient non-parametric estimators of location and scale parameters , 1970 .

[5]  J. Wolfowitz,et al.  Asymptotically efficient non-parametric estimators of location and scale parameters. II , 1970 .

[6]  V. Fabian Asymptotically Efficient Stochastic Approximation; The RM Case , 1973 .

[7]  Seymour Sherman,et al.  Non-mean-square error criteria , 1958, IRE Trans. Inf. Theory.

[8]  W. J. Hall,et al.  Information and Asymptotic Efficiency in Parametric-Nonparametric Models , 1983 .

[9]  Constance Van Eeden,et al.  Efficiency-Robust Estimation of Location , 1970 .

[10]  R. Beran An Efficient and Robust Adaptive Estimator of Location , 1978 .

[11]  C. J. Stone,et al.  Adaptive Maximum Likelihood Estimators of a Location Parameter , 1975 .

[12]  R. Hogg Some Observations on Robust Estimation , 1967 .

[13]  J. L. Hodges,et al.  Estimates of Location Based on Rank Tests , 1963 .

[14]  A. Kester,et al.  Large Deviations of Estimators , 1986 .

[15]  S. Natarajan Large deviations, hypotheses testing, and source coding for finite Markov chains , 1985, IEEE Trans. Inf. Theory.

[16]  Louise Dionne Efficient Nonparametric Estimators of Parameters in the General Linear Hypothesis , 1981 .

[17]  S. J. Merhav,et al.  Performance of Predictors with Non-Gaussian Inputs , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[18]  Giuseppe Longo,et al.  The error exponent for the noiseless encoding of finite ergodic Markov sources , 1981, IEEE Trans. Inf. Theory.

[19]  Stephen M. Stigler An Edgeworth Curiosum , 1980 .

[20]  R. Hogg On adaptive statistical inferences , 1982 .

[21]  C. Stein Efficient Nonparametric Testing and Estimation , 1956 .

[22]  Louis A. Jaeckel Some Flexible Estimates of Location , 1971 .

[23]  Rudolf Beran,et al.  Asymptotically Efficient Adaptive Rank Estimates in Location Models , 1974 .

[24]  Jerome Sacks,et al.  AN ASYMPTOTICALLY EFFICIENT SEQUENCE OF ESTIMATORS OF A LOCATION PARAMETER , 1975 .

[25]  Kei Takeuchi,et al.  A Uniformly Asymptotically Efficient Estimator of a Location Parameter , 1971, Contributions on Theory of Mathematical Statistics.

[26]  P. Bickel On Adaptive Estimation , 1982 .

[27]  Wei-Yin Loh,et al.  Partially-adaptive robust estimators of location via exponential embedding , 1984 .

[28]  A. Wyner,et al.  On communication of analog data from a bounded source space , 1969 .

[29]  Pranab Kumar Sen,et al.  The extended two-sample problem: nonparametric case , 1979 .

[30]  P. K. Bhattacharya Efficient Estimation of a Shift Parameter From Grouped Data , 1967 .

[31]  C. C. Lee,et al.  Nonparametric estimation algorithms based on input quantization , 1985, IEEE Trans. Inf. Theory.

[32]  M. V. Johns,et al.  Nonparametric Estimation of Location , 1974 .