Statistical inference on stationary random fields

Statistical methods are developed to model random processes on multidimensional Euclidean space from observed data. Statistical inference techniques are used to estimate model parameters and test hypotheses concerning stationarity, isotropy, and number of parameters. Algorithms are described for fitting parametric models and testing between alternative model structures. Stochastic partial difference equation models of multidimensional processes are discussed in detail. Computer generated data from a known model are used to directly demonstrate the statistical procedures.

[1]  A. Wald.  Tests of statistical hypotheses concerning several parameters when the number of observations is large , 1943 .

[2]  U. Grenander.  Stochastic processes and statistical inference , 1950 .

[3]  E. S. Pearson,et al.  Charts of the power function for analysis of variance tests, derived from the non-central F-distribution. , 1951, Biometrika.

[4]  P. Whittle,et al.  TESTS OF FIT IN TIME SERIES , 1952 .

[5]  P. Whittle,et al.  Hypothesis-Testing in Time Series Analysis. , 1952 .

[6]  P. Whittle.  The Analysis of Multiple Stationary Time Series , 1953 .

[7]  P. Whittle.  ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[8]  V. Heine.  MODELS FOR TWO-DIMENSIONAL STATIONARY STOCHASTIC PROCESSES , 1955 .

[9]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[10]  A. Yaglom.  Second-order Homogeneous Random Fields , 1961 .

[11]  A. Yaglom,et al.  An Introduction to the Theory of Stationary Random Functions , 1963 .

[12]  A. M. Walker.  Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series , 1964, Journal of the Australian Mathematical Society.

[13]  D. Brook.  On the distinction between the conditional probability and the joint probability approaches in the specification of nearest-neighbour systems , 1964 .

[14]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[15]  E. Wong.  Two-Dimensional Random Fields and Representation of Images , 1968 .

[16]  E. J. Hannan,et al.  Multiple time series , 1970 .

[17]  T. Anderson.  Statistical analysis of time series , 1974 .

[18]  Michael G. Strintzis,et al.  A solution to the matrix factorization problem , 1972, IEEE Trans. Inf. Theory.

[19]  John W. Woods,et al.  Two-dimensional discrete Markovian fields , 1972, IEEE Trans. Inf. Theory.

[20]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[21]  H. Akaike.  Maximum likelihood identification of Gaussian autoregressive moving average models , 1973 .

[22]  J. Shanks,et al.  Stability criterion for N -dimensional digital filters , 1973 .

[23]  H. Akaike.  A new look at the statistical model identification , 1974 .

[24]  R. Mehra,et al.  Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations , 1974 .

[25]  D. Brillinger.  Fourier analysis of stationary processes , 1974 .

[26]  Eugene Wong.  A likelihood ratio formula for two-dimensional random fields , 1974, IEEE Trans. Inf. Theory.

[27]  A. D. Cliff,et al.  Model Building and the Analysis of Spatial Pattern in Human Geography , 1975 .

[28]  N. K. Bose,et al.  New techniques and results in multidimensional problems , 1976 .

[29]  M. Ekstrom,et al.  Two-dimensional spectral factorization with applications in recursive digital filtering , 1976 .

[30]  Nonnested tests on model structure , 1977 .