Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

In this paper, we propose parametric and nonparametric locally andasymptotically optimal tests for regression models with superdiagonal bilinear time series errors in short panel data (large n, small T). We establish a local asymptotic normality property– with respect to intercept μ, regression coefficient β, the scale parameter σ of the error, and the parameter b of panel superdiagonal bilinear model (which is the parameter of interest)– for a given density f1 of the error terms. Rank-based versions of optimal parametric tests are provided. This result, which allows, by Hájek’s representation theorem, the construction of locally asymptotically optimal rank-based tests for the null hypothesis b = 0 (absence of panel superdiagonal bilinear model). These tests –at specified innovation densities f1– are optimal (most stringent), but remain valid under any actual underlying density. From contiguity, we obtain the limiting distribution of our test statistics under the null and local sequences of alternatives. The asymptotic relative efficiencies, with respect to the pseudo-Gaussian parametric tests, are derived. A Monte Carlo study confirms the good performance of the proposed tests.

Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes

Seasonal fluctuations are often found in many time series. In addition, non-linearity and the relationship with other time series are prominent behaviors of several, of such series. In this paper, we consider the modeling of multiplicative seasonal threshold autoregressive processes with exogenous input (TSARX), which explicitly and simultaneously incorporate multiplicative seasonality and threshold nonlinearity. Seasonality is modeled to be stochastic and regime dependent. The proposed model is a special case of a threshold autoregressive process with exogenous input (TARX). We develop a procedure based on Bayesian methods to identify the model, estimate parameters, validate the model and calculate forecasts. In the identification stage of the model, we present a statistical test of regime dependent multiplicative seasonality. The proposed methodology is illustrated with a simulated example and applied to economic empirical data.

PLS Generalized Linear Regression and Kernel Multilogit Algorithm (KMA) for Microarray Data Classification Problem

This study involves the implentation of the extensions of the partial least squares generalized linear regression (PLSGLR) by combining it with logistic regression and linear discriminant analysis, to get a partial least squares generalized linear regression-logistic regression model (PLSGLR-log), and a partial least squares generalized linear regression-linear discriminant analysis model (PLSGLRDA). A comparative study of the obtained classifiers with the classical methodologies like the k-nearest neighbours (KNN), linear discriminant analysis (LDA), partial least squares discriminant analysis (PLSDA), ridge partial least squares (RPLS), and support vector machines(SVM) is then carried out. Furthermore, a new methodology known as kernel multilogit algorithm (KMA) is also implemented and its performance compared with those of the other classifiers. The KMA emerged as the best classifier based on the lowest classification error rates compared to the others when applied to the types of data are considered; the un- preprocessed and preprocessed.

On Predictive Distribution of K-Inflated Poisson Models with and Without Additional Information

This paper addresses different approaches in finding the Bayesian predictive distribution of a random variable from a Poisson model that can handle count data with an inflated value of K ∈ N, known as the KIP model. We explore how we can use other source of additional information to find such an estimator. More specifically, we find a Bayesian estimator of future density of random variable Y1 , based on observable X1 from the K1 IP(p1 , λ1 ) model, with and without assuming that there exists another random variable X2 , from the K2 IP(p2 , λ2 ) model, independent of X1 , provided λ1 ≥ λ2 , and compare their performance using simulation method.

Corrigendum to ``Descriptive Measures of Poisson-Lomax Distribution''

This corrigendum focuses on the correction of numerical results derived from Poisson-Lomax Distribution (PLD) originally proposed by Al-Zahrani & Sagor (2014). Though the mathematical properties and derivations by Al-Zahrani & Sagor (2014) were immaculate but during the execution ofthe R codes using Monte Carlo simulation some anomalies occurred in the calculation of the mean values. The same anomalies are addressed in thepresent corrigendum. The outcome of the corrigendum will provide basic guidelines for the academia and reviewers of various journals to match thenumerical results with the shape of the probability distribution under study. The results will also emphasize the fact that code writing is a cumbersome process and due diligence be exercised in executing the codes using any programming language. Relevant R codes are appended in Appendix 'A'.

An Optimal Design Criterion for Within-Individual Covariance Matrices Discrimination and Parameter Estimation in Nonlinear Mixed Effects Models

In this paper, we consider the problem of nding optimal populationdesigns for within-individual covariance matrices discrimination andparameter estimation in nonlinear mixed eects models. A compound optimality criterion is provided, which combines an estimation criterion and a discrimination criterion. We used the D-optimality criterion for parameter estimation, which maximizes the determinant of the Fisher information matrix. For discrimination, we propose a generalization of the T-optimality criterion for xed-eects models. Equivalence theorems are provided for these criteria. We illustrated the application of compound criteria with an example in a pharmacokinetic experiment.

Convergence Theorems in Multinomial Saturated and Logistic Models

In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demonstrated. Furthermore, properties are identified and, based on an asymptotic theory, convergence theorems are tested for score vectors and information matrices of both models. Finally, an application of this theory is presented and assessed using data from the R statistical program.

On the Alpha Power Kumaraswamy Distribution: Properties, Simulation and Application

Adding new parameters to classical distributions becomes one of the most important methods for increasing distributions flexibility, especially, in simulation studies and real data sets. In this paper, alpha power transformation (APT) is used and applied to the Kumaraswamy (K) distribution and a proposed distribution, so called the alpha power Kumaraswamy (AK) distribution, is presented. Some important mathematical properties are derived, parameters estimation of the AK distribution using maximum likelihood method is considered. A simulation study and a real data set are used to illustrate the flexibility of the AK distribution compared with other distributions.

Method to Obtain a Vector of Hyperparameters: Application in Bernoulli Trials

The main difficulties when using the Bayesian approach are obtaining information from the specialist and obtaining hyperparameters values of the assumed probability distribution as representative of knowledge external to the data. In addition to the fact that a large part of the literature on this subject is characterized by considering prior conjugated distributions for the parameter of interest. An method is proposed to find the hyperparameters of a nonconjugated prior distribution. The following scenarios were considered for Bernoulli trials: four prior distributions (Beta, Kumaraswamy, Truncated Gamma and Truncated Weibull) and four scenarios for the generating process. Two necessary, but not sufficient conditions were identified to ensure the existence of a vector of values for the hyperparameter. The Truncated Weibull prior distribution performed the worst. The methodology was used to estimate the prevalence of two transmitted sexually infections in an Colombian indigenous community.