Pre 1990 Publications - David R. Brillinger
"A justification of some common laws of mortality," Transactions
of the Society of Actuaries, Vol. 13 (1961), pp. 116-119.
"A note on the definition of asymptotic normality for multi-dimensional
random variables," Estadistica, Vol. 20 (1961), pp. 371.
"Asymptotic means and variances in the k-dimensional case," Ph.D.
Thesis, Princeton University, (1961), 70 pp.
"Examples bearing on the definition of fiducial probability with
a bibliography," Annals of Mathematical Statistics, Vol. 33
(1962), pp. 1349-1355.
"A note on the rate of convergence of a mean," Biometrika,
Vol. 49 (1962), pp. 574-576.
"A note on the re-use of samples," Annals of Mathematical
Statistics, Vol. 34 (1963), pp. 341-343.
"Necessary and sufficient conditions for a statistical problem to
be invariant under the action of a Lie group," Annals of
Mathematical Statistics, Vol. 34 (1963), pp. 492-500.
"A technique for measuring the spectral density matrix of two
signals," Proceedings of the Institute of Electrical and
Electronic Engineers, Vol. 52 (1964), pp. 103-104.
"The asymptotic behavior of Tukey's general method of setting
approximate confidence limits (the jackknife) when applied
to maximum likelihood estimates," Review of the International
Statistical Institute, Vol. 32 (1964), pp. 202-206.
"A property of low-pass filters," SIAM Review, Vol. 7 (1965),
"A moving average representation for random variables covariance
stationary on a finite time interval," Biometrika, Vol. 52 (1964), pp= 295-297.
"An introduction to polyspectra," Annals of Mathematical
Statistics, Vol. 36 (1965), pp. 1351-1374.
"The analyticity of the roots of a polynomial as functions of the
coefficients," Mathematics Magazine, Vol. 39 (1966), pp. 145-147.
"The application of the jackknife to the analysis of sample
surveys,"J. Market Research Soc., Vol. 8 (1966), pp. 74-80.
"An extremal property of the conditional expectation,"
Biometrika, Vol. 53 (1966), pp. 574-595.
D.R. Brillinger and M. Rosenblatt, "Asymptotic theory of estimates
of k-th order spectra," Proceedings on the National Academy of Sciences of
the U.S.A., Vol. 57 (1967) pp. 206-210.
D.R. Brillinger and M. Rosenblatt, "Asymptotic theory of estimates
of k-th order spectra," Advanced Seminar on Spectral Analysis (ed. B.
Harris), New York, Wiley (1967), pp. 153-188.
D.R. Brillinger and M. Rosenblatt, "Computation and interpretation
of k-th order spectra," pp. 189-232, Ibid.
"Bounded polymeasures and associated translation commutative
polynomial operators," Proceedings of the American Mathematical Society,
Vol. 18 (1967), pp. 487-491.
"Estimation of the cross-spectrum of a stationary bivariate
Gaussian process from its zeros," Journal of the Royal Statistical
Society, B, Vol. 30 (1968), pp. 145-159.
D.R. Brillinger and M. Hatanaka, "An harmonic analysis of
non-stationary multivariate economic processes," Econometrica, Vol. 7
(1969), pp. 131-141.
"The calculation of cumulants via conditioning, Annals of the
Institute of Statistical Mathematics, Vol. 21 (1969), pp. 215-218.
"The canonical analysis of stationary time series," pp. 331-350 in
Multivariate Analysis - II (ed. P.R. Krishnaiah), New York, Academic
"An asymptotic representation of the sample distribution
function," Bulletin of the American Mathematical Society, Vol. 75 (1969),
"Asymptotic properties of spectral estimates of second
order," Biometrika, Vol. 56 (1969), pp. 375-390.
"A search for a relationship between monthly sunspot numbers and
certain climatic series," Bul. Inter. Statist. Inst., Vol. 43 (1969),
Book 1, pp. 293-307.
"The identification of polynomial systems by means of higher
order spectra," Journal of Sound and Vibration, Vol. 12, (1970), pp.
D.R. Brillinger and M. Hatanaka, "A permanent income
hypothesis relating to the aggregate demand for money," Economic
Studies Quarterly, Vol. 21 (1970), pp. 44-71.
"The frequency analysis of relations between stationary spatial
series," Proceedings of the Twelfth Biennial Seminar of the Canadian
Mathematical Congress, (ed. R. Pyke), Montreal, Canadian Math. Congress.
(1970), pp. 39-81.
"On the number of solutions of systems of random equations," Annals
of Mathematical Statistics, Vol. 43 (1972), 534-540.
"The spectral analysis of stationary interval
functions," Proceedings of the Sixth Berkeley Symposium on
Mathematical Statistics and Probability, (eds. L.M. Le Cam, J. Neyman,
E.L. Scott), Berkeley, University of California Press (1972), pp. 483-513
"Estimating the mean of a stationary time series by
sampling," Journal of Applied Probability, Vol. 10, (1973), pp. 419-431.
"A power spectral estimate insensitive to transients,"
Technometrics, Vol. 15 (1973), pp. 559-562.
"The analysis of time series collected in an experimental
design," pp. 241-256 in Multivariate Analysis - III (ed. P.R.
Krishnaiah), New York, Academic (1973).
"An empirical investigation of the Chandler wobble and two
proposed excitation processes," Bulletin of the International
Statistical Institute, Vol. 45, (1973), Book 3, pp. 413-434.
"Cross-spectral analysis of processes with stationary
increments including the stationary G/G/inf queue, Annals of
Probability, Vol. 2 (1974), pp. 815-827.
"The asymptotic distribution of the Whittaker periodgram and
a related chisquared statistic for stationary processes," Biometrika,
Vol. 61 (1974), pp. 419-422.
"The Fourier analysis of stationary processes," Proceedings of
the Institute of Electrical and Electronic Engineers, Vol. 62 (1974), 1628-1643.
Time Series: Data Analysis and Theory, New York, Holt, Rinehart and
Winston, 512 pp. (1975)
"Statistical inference for stationary point processes,"
Stochastic Processes and Related Topics, (ed. M.L. Puri), New
York, Academic (1975), pp. 55-99.
"The identification of point process systems," Annals
of Probability, Vol. 3, (1975), pp. 909-924.
"Estimation of product densities," Computer Science and Statistics:
8th Annual Symposium (ed. J.W. Frane), U.C.L.A. (1975),
D.R. Brillinger, H.L. Bryant and J.P. Segundo, "Identification of
synaptic operators," Proceedings of the California Institute of Technology
Conference,(eds. J. McCann and P.Z. Marmarelis), pp. 221-226.
"Measuring the association of point processes: a case
history," American Mathematical Monthly, Vol. 83 (1976), pp. 16-22.
"Estimation of the second-order intensities of a bivariate
stationary point process," Journal of the Royal Statistical Society B
Vol. 38 (1976), pp. 60-66.
"Some history of the data analysis of time series in the United
States," History of Statistics in the United States (ed. D.B. Owen), New
York, Marcel Dekker (1976), pp. 267-280.
D.R. Brillinger, H.L. Bryant and J.P. Segundo, "Identification of
synaptic interactions," Biological Cybernetics, Vol. 22 (1976), 213-228.
"Approximate estimation of the standard errors of complex
statistics based on sample surveys," New Zealand Statistician, 1
(1976), pp. 35-41.
"The identification of a particular nonlinear time series
system," Biometrika, Vol. 64 (1977), pp. 509-515.
"Comparative aspects of the study of ordinary time series and
of point processes," Advances in Statistics, Vol. 1 (1978), pp. 33-133,
New York, Academic.
"A note on a representation for the Gauss-Poisson process," Stoch.
Proc. Appl. Vol. 6 (1978), pp. 135-137.
W.A. Silveria and D.R. Brillinger, "On maximum wave heights
of severe seas," Proc. 1978 Offshore Technology Conference, Vol.
III (1978), pp. 1563-1568.
D.R. Brillinger, A. Udias and B.A. Bolt, "Un modelo
probabilistico para la determinacion del mechanismo region de los
terremotos," II Asambla Geol. y Geof. Barcelona. IGN, (1978), pp.
W.H.K. Lee and D.R. Brillinger, "A point process analysis of Chinese
earthquake history," Proc. Conf. Seismic Gaps. Cambridge, M.I.T. (1978).
D.R. Brillinger, L.V. Jones and J.W. Tukey, The Role of
Statistics in Weather Resources Management, Vol. II, The Management of
Weather Resources, Washington, Government Printing Office (1978).
"A note on the estimation of evoked response,"
Biological Cybernetics, Vol. 31 (1978), pp. 141-144.
56a. "Obituary: Henry Scheffe 1907-1977". J. Roy. Statist. Soc. Swr. A 141, 406-407 (1978)
"Analyzing point processes subjected to random deletions," Canadian
J. Statistics, Vol. 7 (1979), pp. 21-27.
"A continuous form of post-stratification," Ann. Inst. Stat.
Math. Vol. 31 (1979), pp. 271-277.
G. Hung, D.R. Brillinger and L. Stark, "Interpretation of kernels,
Same signed lst and 2nd degree," Math. Biosciences, Vol. 46, (1979), pp. 159-187.
B.A. Bolt and D.R. Brillinger, "Estimation of uncertainties
in eigenspectral estimates from decaying geophysical time
series," Geophys. J.R. Astr. Soc., Vol. 59 (1979), pp. 593-603.
D.R. Brillinger and J.P. Segundo, "Empirical examination of the
threshold model of neuron firing," Bio. Cybernetics, Vol. 35 (1979),
"Confidence intervals for the cross-covariance function," Selecta
Statistica Canadiana, Vol. V (1979), pp. 1-16.
W.H.K. Lee and D.R. Brillinger, "On Chinese earthquake history - an
attempt to model an incomplete data set by point process analysis," Pure
and Applied Geophysics, Vol. 117 (1979), pp. 1229-1257.
D.R. Brillinger, A. Udias and B.A. Bolt, "A probability model
for regional focal mechanism solutions," Bul. Seismol. Soc. Amer. Vol.
70 (1980), pp. 149-170.
Vremenne Ryad: Oraotka Dannh e. Teoreya. Mir Publisher,
Moscow, Translation of first edition of #70 (1980).
D.R. Brillinger, J. Guckenheimer, P. Guttorp and G. Oster,
"Empirical modelling of population time series data: The case of
age and density dependent vital rates," Lectures on Mathematics
in the Life Sciences, Vol. 13 (1980), American Mathematical Society,
Providence, pp. 65-90.
"Analysis of variance problems under time series models,"
Handbook of Statistics, Vol. 1 (ed. P.R. Krishnaiah), North-Holland
A. Udias, E. Buforn, D.R. Brillinger and B.A. Bolt, "A
numerical method for individual and regional fault plane
determinations," Publ. Inst. Geophys. Pol. Acad. Sc. A-10 (1980), pp.
"The comparison of least squares and third-order
periodogram procedures in the estimation of bifrequency," J. Time
Series Analysis, Vol. I (1980), pp. 95-102.
Time Series: Data Analysis and Theory (Expanded Edition) Holden-Day
Inc., San Francisco (1981).
"Some aspects of the analysis of evoked response experiments,"
in Statistics and Related Topics (eds., M. Csorgo, D. Dawson, J. Rao and
A. Saleh), Amsterdam, North-Holland, (1981), pp. 155-168.
"Some aspects of modern population mathematics," Canadian J.
Statistics, Vol. 9, (1981), pp. 173-194.
"The key role of tapering in spectrum estimation," IEEE
Trans. Acoust., Speech, Signal Processing, Vol. ASSP-29 (1981), pp.
1075-1076. Reprinted in Coherence and Time Delay Estimation
(Ed. G.C. Carter) IEEE Press, New York (1993), pp. 37-38.
"The general linear model in the design and analysis of
evoked response experiments," J. Theoret. Neurobiol. Vol. 1 (1981) pp.
Problem 6372. Amer. Math. Monthly, Vol. 88, (1981), 769.
"Asymptotic normality of finite Fourier transforms of
stationary generalized processes," J. Mult. Analysis, Vol. 12 (1982),
"Seismic risk assessment: some statistical aspects," Earthquake
Prediction Research, Vol. 1 (1982), pp. 183-195.
A Udias, E. Buforn, D.R. Brillinger and B.A. Bolt, "Joint
statistical determination of fault plane parameters," Physics of Earth
and Planetary Interiors, Vol. 30 (1982), pp. 178-184.
"A generalized linear model with `Gaussian' regressor
variables," Lehmann Festschrift, Wadsworth (1982), pp. 97-114.
"Some bounds for seismic risk," Bull. Seismol. Soc. Amer. Vol.
72 (1982), pp. 1403-1410.
examples of the time and frequency domain approaches to time
series analysis," Time Series Methods in Hydrosciences, (eds.
and S.R. Esterby), Elsevier, Amsterdam (1982), pp. 1-15.
J.A. Comis, E. Marg, D.R. Brillinger, D.P. Rudiak, E.L. Keller,
of means and medians in the reduction of visual evoked
potential data," Proc.
Fifteenth Hawaii International Conference on System Sciences,
Vol. 2 (1982), pp. 242-253.
"Statistics in Fertility Research: Value and Limitations,"
Report No. 19, Committee
on Population and Demography, National Research Council,
"Jump process," Encyclopedia of Statistical Sciences, Vol. 4, J.
Wiley, New York
(1983), pp. 336-338.
D.R. Brillinger and H.K. Preisler, "Maximum likelihood
estimation in a latent
variable problem," Studies in Econometrics, Time Series and
(eds. S. Karlin, T. Amemiya and L.A. Goodman), Academic
Press, New York
(1983), pp. 31-65.
"The finite Fourier transform of a stationary process, "
Handbook of Statistics, Vol.
3 (eds. D.R. Brillinger and P.R. Krishnaiah), Elsevier,
Amsterdam, (1983), pp. 21-37.
"Statistical inference for random processes," Proceedings
1982 International Congress of Mathematicians, Warsaw, (1984) pp.
"Statistical inference for irregularly observed
processes," Proceedings of the Symposium on Time Series Analysis
of Irregularly Observed Data, (ed. E. Parzen), Lecture Notes
in Statistics, Springer-Verlag, (1984), pp. 38-57.
89. D.R. Brillinger and H.K. Preisler, "An exploratory analysis of the
Joyner-Boore attenuation data," Bull. Seismol. Soc. America, Vol. 74
(1984), pp. 1441-1450.
"Tukey's work on time series analysis," The Collected Works of J.W.
Tukey, Vol. 1, (ed. D.R. Brillinger) Wadsworth (1984), pp. xliii-lxv.
D.R. Brillinger and H.K. Preisler, "Further analysis of
the Joyner-Boore attenuation data," Bull. Seismol. Soc. America, Vol. 75
(1985), pp. 611-614.
D.R. Brillinger and J.W. Tukey, "Spectrum analysis in the presence
of noise: some issues and examples," The Collected Works of J.W. Tukey,
Vol. 2, (ed. D.R. Brillinger) Wadsworth (1985), pp. 1001-1141.
"A maximum likelihood approach to frequency-wavenumber
analysis," IEEE Trans. Acoustics, Speech, Signal Processing, Vol. ASSP-33
(1985), pp. 1076-1085.
"Fourier inference: some methods for the analysis of array
and nongaussian series data," Water Resources Bulletin, Vol. 21
(1985), pp. 743-756.
"Statistics," New Canadian Encyclopedia, Hurtig (1985), p. 1754.
"Some statistical aspects of NMR spectroscopy" Actas del Segundo
Congresso Latinoamericano de Probabilidad y Estatistica
Mathematica, Caracas (1985), pp. 9-17.
96a. Lehmann, E. L., Brillinger, D.R. and Singer, I.M. "Jack Carl Kiefer, Statis
tics and Mathematics: Berkeley".
In Memorian, University of California, Berkeley
Pp. 215-216 (1985).
"Regression for randomly sampled spatial series: the trigonometric
case," Essays in Time Series and Allied Processes, Applied Probability
Trust, Sheffield (1986), pp. 275-289.
"What do seismology and neurophysiology have in common? -
Statistics." C.R. Math. Rep. Acad. Sci. Canada, Vol. 8 (1986), pp, 1-11.
D.R. Brillinger and H.K. Preisler, "Two examples of quantal
data analysis: a) multivariate point process b)
pure death process in an experimental design," Proc. XIII
International Biometric Conference, Seattle (1986), pp. 94-113.
"The natural variability of vital rates and associated statistics
Biometrics, Vol. 42 (1986), pp. 693-712. (with discussion).
"Fitting cosines : some procedures and some physical examples,"
Applied Probability, Stochastic Processes, and Sampling Theory,
(eds. I.B. MacNeill and G.J. Umphrey) D. Reidel, Boston (1987),
"Analysing interacting nerve cell spike trains to assess causal
connections," Advanced Methods of Physiological System Modelling,
Vol. 1 (1987) (ed. V.Z. Marmarelis), pp. 29-40.
"Statistiques," L'encyclopedie du Canada, Hurtig (1987), p.1871.
(Translation of 95.)
"The maximum likelihood approach to the identification of neuronal
firing systems," Annals of Biomedical Engineering, Vol. 16 (1988), pp. 3-16.
The 1983 Wald Memorial Lectures : "Some statistical methods for
random process data from seismology and neurophysiology," Annals of
Statistics, Vol. 16 (1988), pp. 1-54.
P. Bloomfield, D.R. Brillinger, D.W. Nychka and R.S. Stolarski,
"Statistical issues", Report of the International Ozone Trends
Panel, World Meteorological Organization Report 18 (1988).
"Maximum likelihood analysis of spike trains of interacting
nerve cells," Biological Cybernetics, Vol. 59 (1988), pp. 189-200.
"An elementary trend analysis of Rio Negro levels at Manaus,
1903-1985," Revista Brasileira de Probabilidade e Estatistica,
Vol. 2 (1988), pp. 63-79.
"Estimating the chances of large earthquakes by radiocarbon dating
and statistical modelling," pp. 249-260 in Statistics : a Guide to
the Unknown, (eds. J.M. Tanur et al.), third edition. Pacific
Grove, Wadsworth (1989).
K. Sieh, M. Stuiver and D.R. Brillinger, "A more precise chronology
of earthquakes produced by the San Andreas Fault in Southern
California," J. Geophysical Research, Vol. 94 (1989), pp. 603-623.
Reprinted in Engineering Geology Practice in Southern California
(Eds. B. Pipkin and R.J. Proctor). Star, Belmont (1992).
"Consistent detection of a montonic trend superposed on a
stationary time series," Biometrika, Vol. 76, (1989) pp. 23-30.
D.R. Brillinger, K.H. Downing and R.M. Glaeser,
"Combining noisy images of small crystalline domains in high
resolution electron microscopy," J. Applied Statistics, Vol. 16
(1989), pp. 53-61.
J.R. Rosenberg, A.M. Amjad, P. Breeze, D.R. Brillinger and
D.M. Halliday, "The Fourier approach to the identification of
functional coupling between neuronal spike trains," Progress in
Biophysics and Molecular Biology, Vol. 53 (1989), pp. 1-31.
"Parameter estimation for nonGaussian processes via second and third
order spectra with an application to some endocrine data," pp. 53-61 in
Advanced Methods of Physiological System Modelling, (ed. V.Z. Marmarelis)
New York, Plenum (1989).
"Some examples of the statistical analysis of seismological
data," pp. 266-278 in Observatory Seismology (Ed. J.L. Litehiser) Univ.
Calif. Press, Berkeley (1989).