We develop several new composite models based on the Weibull distribution for heavy tailed insurance loss data. The composite model assumes different weighted distributions for the head and tail of the distribution and several such models have been introduced in the literature for modeling insurance loss data. For each model proposed in this paper, we specify two parameters as a function of the remaining parameters. These models are fitted to two real insurance loss data sets and their goodness-of-fit is tested. We also present an application to risk measurements and compare the suitability of the models to empirical results.
With the advancement of technology, analysis of large-scale data of gene expression is feasible and has become very popular in the era of machine learning. This paper develops an improved ridge approach for the genome regression modeling. When multicollinearity exists in the data set with outliers, we consider a robust ridge estimator, namely the rank ridge regression estimator, for parameter estimation and prediction. On the other hand, the efficiency of the rank ridge regression estimator is highly dependent on the ridge parameter. In general, it is difficult to provide a satisfactory answer about the selection for the ridge parameter. Because of the good properties of generalized cross validation (GCV) and its simplicity, we use it to choose the optimum value of the ridge parameter. The GCV function creates a balance between the precision of the estimators and the bias caused by the ridge estimation. It behaves like an improved estimator of risk and can be used when the number of explanatory variables is larger than the sample size in high-dimensional problems. Finally, some numerical illustrations are given to support our findings.
This article aims at testing real interest parity (RIP) by using nonlinear unit root tests. The results from Kapetanios et al. (2003) demonstrated that the adjustment of ASEAN-5 real interest rates towards real interest rates in Japan and the US follows a nonlinear (stationary) process. Overall, the evidence is in favour of RIP.
Abstract. Generally, the classical Schwarz information criterion ( ) used for model selection has been computed based on the least squares ( ) method, which minimizes the sum of squared residuals; is sensitive to outlier observations. A robust version of this estimator is produced by replacing the squared residuals by a function , of residuals. In this article, an approach based on high breakdown point estimators has been considered. The performance of this criterion has also been compared with the classical non-robust and the existing , based on -estimators and the influence of outliers on is also discussed. Our finding showed that the high breakdown estimators are capable of selecting the appropriate models in presence of outliers.
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