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In the present paper, we define a new measure of divergence between two probability distribution functions $$F_{1}$$ F1 and $$F_{2}$$ F2 based on Jensen inequality and Gini mean difference. The proposed measure, which we call it Jensen–Gini measure of divergence (JG), is symmetric and its square root is a metric. We show that the JG can be represented as a mixture of Cramér’s distance (CD) between...
This study establishes a new approach for the analysis of variance (ANOVA) of time series. ANOVA has been sufficiently tailored for cases with independent observations, but there has recently been substantial demand across many fields for ANOVA in cases with dependent observations. For example, ANOVA for dependent observations is important to analyze differences among industry averages within financial...
The use of p values in null hypothesis statistical tests (NHST) is controversial in the history of applied statistics, owing to a number of problems. They are: arbitrary levels of Type I error, failure to trade off Type I and Type II error, misunderstanding of p values, failure to report effect sizes, and overlooking better means of reporting estimates of policy impacts, such as effect sizes, interpreted...
This paper presents the estimation procedures for a bivariate cointegration model when the errors are generated by a constant conditional correlation model. In particular, the method of maximum likelihood is discussed when the errors follow Generalised Autoregressive Conditional Hetroskedastic (GARCH) models with Gaussian and some non Gaussian innovations. The method of estimation is illustrated using...
This paper deals with linear models for a time-dependent response and explanatory variables in a high-dimensional setting. We account for the time dependency in the data by explicitly adding autoregressive terms to the response variable in the model together with an autoregressive process for the residuals. We present a penalized likelihood approach for parameter estimation and discuss its theoretical...
Whenever the computation of data distribution is unfeasible or inconvenient, the classical predictive procedures prove not to be useful. These rely, after all, on the conditional distribution of the future random variable, which is also unavailable. This paper considers a notion of composite likelihood for specifying composite predictive distributions, viewed as surrogates for true unknown predictive...
This paper studies the “truncated extended skew elliptically contoured” (TESEC) distributions and their related properties, which have never been discussed in the literature. In particular, we show that the exact distributions of order statistics arising from a doubly truncated bivariate elliptical distribution can be formulated as a mixture of six TESEC distributions. The explicit formulae for computing...
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