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Theory and Methods

Nonparametric Spectral Density Estimation Using Penalized Whittle Likelihood

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Pages 600-610 | Received 01 Jul 1992, Published online: 27 Feb 2012

References

  • Brillinger , D. 1981 . Time Series: Data Analysis and Theory , San Francisco : Holden Day .
  • Beltrao , I. I. and Bloomfield , P. 1987 . “Determining the Bandwidth of a Kernel Spectrum Estimate,” . Journal of Time Series Analysis , 8 : 21 – 38 .
  • Chow , Y. and Grenander , U. 1985 . “A Sieve Method for Spectral Density,” . The Annals of Statistics , 13 : 998 – 1010 .
  • Cogburn , R. and David , H. T. 1974 . “Periodic Spline and Spectral Estimation,” . The Annals of Statistics , 2 : 1108 – 1126 .
  • Cox , D. D. and O'Sullivan , F. 1990 . “Asymptotic Analysis of Penalized Likelihood-Type Estimators,” . The Annals of Statistics , 18 : 1676 – 1695 .
  • Cox , D. D. and O'Sullivan , F. 1993 . “Generalized Nonparametric Regression Via Penalized Likelihood,” , University of Washington, Dept. of Statistics . Technical Report No. 170
  • Davies , R. B. 1973 . “Asymptotic Inference in Stationary Gaussian Time Series,” . Advances in Applied Probability , 5 : 469 – 497 .
  • Good , I. J. and Gaskin , R. A. 1971 . “Nonparametric Roughness Penalty for Probability Densities,” . Biometrika , 58 : 255 – 277 .
  • Gu , C. 1990 . “Adaptive Spline Smoothing in Non-Gaussian Regression Models,” . Journal of the American Statistical Association , 85 : 801 – 807 .
  • Hannan , E. J. 1973 . “The Asymptotic Theory of Linear Time Series Models,” . Journal of Applied Probability , 10 : 130 – 145 .
  • Hurvich , C. M. 1985 . “Data-Driven Choice of a Spectrum Estimate: Extending the Applicability of Cross-Validation Methods,” . Journal of the American Statistical Association , 80 : 933 – 940 .
  • Kulperger , R. 1985 . “On an Optimality of Whittle's Gaussian Estimation of the Parameter of the Spectrum of a Time Series,” . Journal of Time Series Analysis , 6 : 253 – 259 .
  • McCullagh , P. and Nelder , J. A. 1989 . Generalized Linear Models , London : Chapman and Hall .
  • Mélard , G. 1984 . “A Fast Algorithm for the Exact Likelihood of Auto-regressive Moving Average Models,” . Applied Statistics , 33 : 104 – 114 .
  • Natterer , F. 1986 . Mathematics of Computerized Tomography , Chichester , , UK : John Wiley .
  • Priestley , M. B. 1987 . Spectral Analysis and Time Series , London : Academic Press .
  • Shumway , R. H. 1988 . Applied Statistical Time Series Analysis , Englewood Cliffs , NJ : Prentice-Hall .
  • Silverman , B. W. 1982 . “On the Estimation of a Probability Density Function by the Maximum Penalised Likelihood Method,” . The Annals of Statistics , 10 : 795 – 810 .
  • Silverman , B. W. 1985 . “Some Aspect of Spline Smoothing Approach to Nonparametric Regression Curve Fitting,” . Journal of the Royal Statistical Society , 47 : 1 – 50 . Ser. B
  • Tibshirani , R. and Hastie , T. 1987 . “Local Likelihood Estimation,” . Journal of the American Statistical Association , 82 : 559 – 567 .
  • Wahba , G. 1980 . “Automatic Smoothing of the Log Periodogram,” . Journal of the American Statistical Association , 75 : 122 – 132 .
  • Wahba , G. Spline Models in Statistics . CBMS Regional Conference Series in Applied Mathematics . Philadelphia : SIAM .
  • Whittle , P. 1962 . “Gaussian Estimation in Stationary Time Series,” . Bulletin of the International Statistical Institute , 39 : 105 – 129 .
  • Wichman , B. A. and Hill , I. D. 1982 . “An Efficient and Portable Pseudo-Random Number Generator,” . Applied Statistics , 31 : 188 – 190 .

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