Confidence Intervals for a New Characteristic of Central Tendency of Distributions

The t-mean is a new characteristic of the central tendency of continuous distributions. In this article, we introduce a t-difference in the sample space, which is used for a construction of confidence intervals for the t-mean.     

Properties and Inference on the Skew-Curved-Symmetric Family of Distributions

In this article, we study some results related to a specific class of distributions, called skew-curved-symmetric family of distributions that depends on a parameter controlling the skewness and kurtosis at the same time. Special elements of this family which are studied include symmetric and well-known asymmetric distributions. General results are given for the score function and the observed information matrix. It is shown that the observed information matrix is always singular for some special cases. We illustrate the flexibility of this class of distributions with an application to a real dataset on characteristics of Australian athletes.     

Testing stability in a spatial unilateral autoregressive model

ABSTRACT

Least squares estimator of the stability parameter ? ? |α| + |β| for a spatial unilateral autoregressive process X_{k, ?} = αX_{k ? 1, ?} + βX_{k, ? ? 1} + ?_{k, ?} is investigated and asymptotic normality with a scaling factor n^5/4 is shown in the unstable case ? = 1. The result is in contrast to the unit root case of the AR(p) model X_k = α₁X_{k ? 1} + ??? + α_pX_{k ? p} + ?_k, where the limiting distribution of the least squares estimator of the unit root parameter ? ? α₁ + ??? + α_p is not normal.     

Readouts for echo-state networks built using locally regularized orthogonal forward regression

Echo state network (ESN) is viewed as a temporal expansion which naturally give rise to regressors of various relevance to a teacher output. We illustrate that often only a certain amount of the generated echo-regressors effectively explain the teacher output and we propose to determine the importance of the echo-regressors by a joint calculation of the individual variance contributions and Bayesian relevance using the locally regularized orthogonal forward regression (LROFR). This information can be advantageously used in a variety of ways for an analysis of an ESN structure. We present a locally regularized linear readout built using LROFR. The readout may have a smaller dimensionality than the ESN model itself, and improves robustness and accuracy of an ESN. Its main advantage is ability to determine what type of an additional readout is suitable for a task at hand. Comparison with PCA is provided too. We also propose a radial basis function (RBF) readout built using LROFR, since flexibility of the linear readout has limitations and might be insufficient for complex tasks. Its excellent generalization abilities make it a viable alternative to feed-forward neural networks or relevance-vector-machines. For cases where more temporal capacity is required we propose well studied delay&sum readout.     

On the performance of the Jackknifed Liu-type estimator in linear regression model

In this paper, we are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the Liu-type estimator (LTE) and the jackknifed Liu-type estimator (JLTE). We will also present the necessary and sufficient conditions for superiority of the MJLTE over the LTE and JLTE, in terms of mean square error matrix criterion. Finally, a real data example and a Monte Carlo simulation are also given to illustrate theoretical results.     

Bayesian Additive Regression Trees using Bayesian model averaging

Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However, for datasets where the number of variables p is large the algorithm can become inefficient and computationally expensive. Another method which is popular for high-dimensional data is random forests, a machine learning algorithm which grows trees using a greedy search for the best split points. However, its default implementation does not produce probabilistic estimates or predictions. We propose an alternative fitting algorithm for BART called BART-BMA, which uses Bayesian model averaging and a greedy search algorithm to obtain a posterior distribution more efficiently than BART for datasets with large p. BART-BMA incorporates elements of both BART and random forests to offer a model-based algorithm which can deal with high-dimensional data. We have found that BART-BMA can be run in a reasonable time on a standard laptop for the “small n large p” scenario which is common in many areas of bioinformatics. We showcase this method using simulated data and data from two real proteomic experiments, one to distinguish between patients with cardiovascular disease and controls and another to classify aggressive from non-aggressive prostate cancer. We compare our results to their main competitors. Open source code written in R and Rcpp to run BART-BMA can be found at: https://github.com/BelindaHernandez/BART-BMA.git.     

The power piecewise exponential model

In this paper an extension of the piecewise exponential distribution based on the distribution of the maximum of a random sample is considered. Properties of its density and hazard function are investigated. Maximum likelihood inference is discussed and the Fisher information matrix is identified. Results of two real data applications are reported, where model fitting is implemented by using maximum likelihood. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models.     

A novel weighted likelihood estimation with empirical Bayes flavor

We propose a novel approach to estimation, where a set of estimators of a parameter is combined into a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood evaluated at the estimators. We investigate the method for a set of estimators obtained by using the maximum likelihood principle applied to each individual observation. The method can be viewed as a Bayesian approach with a data-driven prior distribution. We provide several examples illustrating the new method and argue for its consistency, asymptotic normality, and efficiency. We also conduct simulation studies to assess the performance of the estimators. This straightforward methodology produces consistent estimators comparable with those obtained by the maximum likelihood method. The method also approximates the distribution of the estimator through the “posterior” distribution.     

Increasing offensive or defensive efficiency? An analysis of Italian and Spanish football

This paper analyses technical efficiency of Italian and Spanish football during three recent seasons, to shed light on the sport performance of professional football clubs. To achieve this we have used mathematical optimisation methods, particularly DEA models, which enable the calculation of the frontiers of efficient production. Some of the most interesting results are the following. Firstly, the Spanish league is clearly more homogeneous and competitive than the Italian league. Secondly, to obtain a better classification in the Italian league, it is much more important to improve defensive, rather than offensive, efficiency. The popular maxim holds in Italy: the best attack begins with a good defence. Third, in Spain our analysis supports the idea that to improve the ranking in the league, the best-rewarded strategy consists in improving offensive efficiency playing at home ground, followed by increasing offensive efficiency when playing away from home.