References & Further Reading

References

  1. R. A. Fisher, Theory of Statistical Estimation, 1925

    Introduced the maximum likelihood principle and Fisher information.

  2. H. Cramer, Mathematical Methods of Statistics, Princeton University Press, 1946

    Classical text establishing MLE asymptotics and the CRLB.

  3. S. S. Wilks, The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses, 1938
  4. A. Wald, Note on the Consistency of the Maximum Likelihood Estimate, 1949
  5. H. B. Mann and A. Wald, On Stochastic Limit and Order Relationships, 1943
  6. S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice Hall, 1st ed., 1993
  7. H. L. Van Trees, K. L. Bell, and Z. Tian, Detection, Estimation, and Modulation Theory, Part I, Wiley, 2nd ed., 2013
  8. P. Stoica and R. Moses, Spectral Analysis of Signals, Prentice Hall, 2005
  9. R. O. Schmidt, Multiple Emitter Location and Signal Parameter Estimation, 1986
  10. R. Roy and T. Kailath, ESPRIT - Estimation of Signal Parameters via Rotational Invariance Techniques, 1989
  11. D. C. Rife and R. R. Boorstyn, Single-Tone Parameter Estimation from Discrete-Time Observations, 1974
  12. M. R. Osborne, Fisher's Method of Scoring, 1992
  13. P. McCullagh and J. A. Nelder, Generalized Linear Models, Chapman & Hall/CRC, 2nd ed., 1989
  14. E. L. Lehmann and G. Casella, Theory of Point Estimation, Springer, 2nd ed., 1998
  15. A. W. van der Vaart, Asymptotic Statistics, Cambridge University Press, 1998
  16. P. W. Zehna, Invariance of Maximum Likelihood Estimators, 1966
  17. A. Fengler, P. Jung, G. Caire, SPARCs and AMP for Unsourced Random Access, 2021

Further Reading

To go deeper on the topics of this chapter — asymptotic theory, iterative ML computation, and the signal-processing applications of ML.

  • Rigorous MLE asymptotics

    A. W. van der Vaart, Asymptotic Statistics, Chapters 5 and 7

    Modern treatment of consistency, asymptotic normality, and efficiency with minimal regularity.

  • Generalized linear models and IRLS

    McCullagh and Nelder, Generalized Linear Models, 2nd ed.

    Fisher scoring in practice: Poisson, logistic, and gamma regressions as iteratively reweighted least squares.

  • Frequency estimation techniques

    Stoica and Moses, Spectral Analysis of Signals, Chapter 4

    Exact and approximate MLE for frequency, Cramer-Rao bounds, and the $N^{-3}$ scaling law.

  • DOA estimation (MUSIC, ESPRIT, ML)

    Van Trees, Optimum Array Processing, Part IV

    Comprehensive comparison of ML and subspace DOA estimators with finite-sample analyses.

  • Bias correction and bootstrap

    Efron and Tibshirani, An Introduction to the Bootstrap

    When asymptotic normality is a poor approximation, the bootstrap provides finite-sample confidence intervals.

ExercisesCh 7 →