596 research outputs found
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
A mixture transition distribution modeling for higher-order circular Markov processes
The stationary higher-order Markov process for circular data is considered.
We employ the mixture transition distribution (MTD) model to express the
transition density of the process on the circle. The underlying circular
transition distribution is based on Wehrly and Johnson's bivariate joint
circular models. The structures of the circular autocorrelation function
together with the circular partial autocorrelation function are found to be
similar to those of the autocorrelation and partial autocorrelation functions
of the real-valued autoregressive process when the underlying binding density
has zero sine moments. The validity of the model is assessed by applying it to
some Monte Carlo simulations and real directional data
Circular Data in Political Science and How to Handle It
There has been no attention to circular (purely cyclical) data in political science research. We show that such data exist and are mishandled by models that do not take into account the inherently recycling nature of some phenomenon. Clock and calendar effects are the obvious cases, but directional data are observed as well. We describe a standard maximum likelihood regression modeling framework based on the von Mises distribution, then develop a general Bayesian regression procedure for the first time, providing an easy-to-use Metropolis-Hastings sampler for this approach. Applications include a chronographic analysis of U.S. domestic terrorism and directional party preferences in a two-dimensional ideological space for German Bundestag elections. The results demonstrate the importance of circular models to handle periodic and directional data in political scienc
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