Journal ArticleDOI
Elliptically Symmetric Distributions: A Review and Bibliography
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In this article, a bibliography complete with discussion relates to the different areas in which elliptically symmetric distributions are considered, which range from inference to stochastic processes, and discuss different areas of interest.Abstract:
Summary This bibliography complete with discussion relates to the different areas in which elliptically symmetric distributions are considered. These areas range from inference to stochastic processes.read more
Citations
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Journal ArticleDOI
Robust Statistical Modeling Using the t Distribution
TL;DR: In this paper, an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate non-linear regression.
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Some contributions to efficient statistics in structural models: Specification and estimation of moment structures.
TL;DR: In this article, it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary, and some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed.
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Normal Variance-Mean Mixtures and z Distributions
TL;DR: A survey of general properties of normal variance-mean mixtures, including various new results, is given in this article, where it is shown that the class of self-reciprocal normal variance mixtures is rather wide, and some Tauberian results are established from which relations between the tail behaviour of a normal variance -mean mixture and its mixing distribution may be deduced.
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An optimality property of the integer least-squares estimator
TL;DR: In this article, a probabilistic justification for using the integer least squares estimator is given for global positioning system ambiguity resolution, which implies that the success rate of any other integer estimator of the carrier phase ambiguities will be smaller than or at the most equal to the ambiguity success rate.
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A Family of Distributions for Modelling Non-Elliptically Symmetric Multivariate Data
R. Dennis Cook,Mark E. Johnson +1 more
TL;DR: In this paper, the authors present a family of distributions for describing data which are not elliptically symmetric, including the Pareto, Burr and Logistic distributions, and compare the fit to a data set on uranium exploration with that obtained using the usual bivariate normal distribution.
References
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Journal ArticleDOI
Multi-Factor Experimental Designs for Exploring Response Surfaces
George E. P. Box,J. S. Hunter +1 more
TL;DR: In this paper, the concept of the variance function for an experimental design is introduced, and the problem of selecting practically useful designs is discussed, and in this connection, the notion of variance function is introduced.
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Robust $M$-Estimators of Multivariate Location and Scatter
TL;DR: In this article, the robust estimation of the location vector and scatter matrix by means of "$M$-estimators," defined as solutions of the system: √ √ u_1(d_i)(\math{x}_i - \mathbf{t}) = \mathBF{0}$ and $n^{-1]-sum_i u_2(d-i^2)
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Robust bayesian estimation for the linear model and robustifying the Kalman filter
C. Masreliez,R. Martin +1 more
TL;DR: In this article, robust Bayesian estimates of the vector x are constructed for the following two distinct situations: (1) the state x is Gaussian and the observation error v is (heavy-tailed) non-Gaussian and (2) the states x and v are Gaussian.
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Bayesian and Non-Bayesian Analysis of the Regression Model with Multivariate Student- t Error Terms
TL;DR: In this paper, the error vector has a multivariate Student-t distribution with zero location vector and scalar dispersion matrix; the multivariate Cauchy and normal distributions are special cases; the usual least squares coefficient estimate is the maximum likelihood estimate and the mean of the posterior distribution under a diffuse prior distribution.
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A representation theorem and its applications to spherically-invariant random processes
TL;DR: The form of the unit threshold likelihood ratio receiver in the detection of a known deterministic signal in additive sirp noise is shown to be a correlation receiver or a matched filter.