On a Vector-Valued Measure of Multivariate Skewness

The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-based clustering, and multivariate normality testing. This paper investigates some properties of the canonical skewness vector with respect to representations, transformations, and norm. In particular, the paper shows its connections with tensor contraction, scalar measures of multivariate kurtosis and Mardia’s skewness, the best-known scalar measure of multivariate skewness. A simulation study empirically compares the powers of tests for multivariate normality based on the squared norm of the canonical skewness vector and on Mardia’s skewness. An example with financial data illustrates the statistical applications of the canonical skewness vector.

Pemodelan Generalized Additive Model For Location, Scale, and Shape (Gamlss) Dengan Pemulusan Locally Estimated Scatterplot Smoothing (Loess) pada Kasus Hiv/Aids Di Jawa Timur

HIV / AIDS is a contagious disease that can attack all age groups of the population and is a health challenge in almost all over the world including Indonesia. Therefore, it is necessary to model HIV / AIDS cases for the factors that are suspected to influence them. One suitable method for estimating factors that influence HIV / AIDS is the Generalized Additive Model for Location, Scale, and Shape (GAMLSS). The GAMLSS method is flexible because it includes expansion of a good exponential family distribution to handle overdispersion data, continuous data, and discrete data. This research will apply GAMLSS semiparametric modeling with LOESS smoothing to find out the characteristics and models of HIV / AIDS cases in East Java in 2017. Based on the analysis, it was found that the variables that significantly affected were the number of homeless people, number of victims of drug abuse, population poor, and the number of fertile age couples using condom contraception with AIC value of 437,404, degree = 1 and span = 0.3, and the distribution used is Negative Binomial I.

Bayesian Semiparametric Double Autoregressive Modeling

This paper proposes a Bayesian semiparametric modeling approach for the return distribution in double autoregressive models. Monte Carlo investigation of finite sample properties and an empirical application are presented. The results indicate that the semiparametric model developed in this paper is valuable and competitive.