2,285 research outputs found
Analyzing imputed financial data: a new approach to cluster analysis
The authors introduce a novel statistical modeling technique to cluster analysis and apply it to financial data. Their two main goals are to handle missing data and to find homogeneous groups within the data. Their approach is flexible and handles large and complex data structures with missing observations and with quantitative and qualitative measurements. The authors achieve this result by mapping the data to a new structure that is free of distributional assumptions in choosing homogeneous groups of observations. Their new method also provides insight into the number of different categories needed for classifying the data. The authors use this approach to partition a matched sample of stocks. One group offers dividend reinvestment plans, and the other does not. Their method partitions this sample with almost 97 percent accuracy even when using only easily available financial variables. One interpretation of their result is that the misclassified companies are the best candidates either to adopt a dividend reinvestment plan (if they have none) or to abandon one (if they currently offer one). The authors offer other suggestions for applications in the field of finance.
EMMIXcskew: an R Package for the Fitting of a Mixture of Canonical Fundamental Skew t-Distributions
This paper presents an R package EMMIXcskew for the fitting of the canonical
fundamental skew t-distribution (CFUST) and finite mixtures of this
distribution (FM-CFUST) via maximum likelihood (ML). The CFUST distribution
provides a flexible family of models to handle non-normal data, with parameters
for capturing skewness and heavy-tails in the data. It formally encompasses the
normal, t, and skew-normal distributions as special and/or limiting cases. A
few other versions of the skew t-distributions are also nested within the CFUST
distribution. In this paper, an Expectation-Maximization (EM) algorithm is
described for computing the ML estimates of the parameters of the FM-CFUST
model, and different strategies for initializing the algorithm are discussed
and illustrated. The methodology is implemented in the EMMIXcskew package, and
examples are presented using two real datasets. The EMMIXcskew package contains
functions to fit the FM-CFUST model, including procedures for generating
different initial values. Additional features include random sample generation
and contour visualization in 2D and 3D
Multiple Resolution Nonparametric Classifiers
Bayesian discriminant functions provide optimal classification decision boundaries in the sense of minimizing the average error rate. An operational assumption is that the probability density functions for the individual classes are either known a priori or can be estimated from the data through the use of estimating techniques. The use of Parzen- windows is a popular and theoretically sound choice for such estimation. However, while the minimal average error rate can be achieved when combining Bayes Rule with Parzen-window density estimation, the latter is computationally costly to the point where it may lead to unacceptable run-time performance. We present the Multiple Resolution Nonparametric (MRN) classifier as a new approach for significantly reducing the computational cost of using Parzen-window density estimates without sacrificing the virtues of Bayesian discriminant functions. Performance is evaluated against a standard Parzen-window classifier on several common datasets
Statistical Mechanics of Learning: A Variational Approach for Real Data
Using a variational technique, we generalize the statistical physics approach
of learning from random examples to make it applicable to real data. We
demonstrate the validity and relevance of our method by computing approximate
estimators for generalization errors that are based on training data alone.Comment: 4 pages, 2 figure
Bayesian Deep Net GLM and GLMM
Deep feedforward neural networks (DFNNs) are a powerful tool for functional
approximation. We describe flexible versions of generalized linear and
generalized linear mixed models incorporating basis functions formed by a DFNN.
The consideration of neural networks with random effects is not widely used in
the literature, perhaps because of the computational challenges of
incorporating subject specific parameters into already complex models.
Efficient computational methods for high-dimensional Bayesian inference are
developed using Gaussian variational approximation, with a parsimonious but
flexible factor parametrization of the covariance matrix. We implement natural
gradient methods for the optimization, exploiting the factor structure of the
variational covariance matrix in computation of the natural gradient. Our
flexible DFNN models and Bayesian inference approach lead to a regression and
classification method that has a high prediction accuracy, and is able to
quantify the prediction uncertainty in a principled and convenient way. We also
describe how to perform variable selection in our deep learning method. The
proposed methods are illustrated in a wide range of simulated and real-data
examples, and the results compare favourably to a state of the art flexible
regression and classification method in the statistical literature, the
Bayesian additive regression trees (BART) method. User-friendly software
packages in Matlab, R and Python implementing the proposed methods are
available at https://github.com/VBayesLabComment: 35 pages, 7 figure, 10 table
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