Journal of Statistical Modelling: Theory and Applications
https://jsm.yazd.ac.ir/
Journal of Statistical Modelling: Theory and Applicationsendaily1Sat, 01 Jul 2023 00:00:00 +0430Sat, 01 Jul 2023 00:00:00 +0430Detection of outliers and influential observations in linear mixed measurement error models with Liu estimation
https://jsm.yazd.ac.ir/article_3422.html
In this paper, the case deletion approach and mean shift outlier model are developed to identify influential and outlier observations using the Liu corrected likelihood estimator in linear mixed measurement error models when multicollinearity is present. We derive a corrected score test statistic for outlier detection based on mean shift outlier models. Furthermore, according to the Liu corrected likelihood estimator, several Cook&rsquo;s distance is constructed for influence diagnostics. A parametric bootstrap procedure is used to obtain empirical distribution of the test statistic and a simulation study is conducted to demonstrate the performance of the diagnostic criteria. Finally, a real example is provided to illustrate the performance of the test statistics.Least square regression in intuitionistic fuzzy environment with crisp coefficients with the ability to determine the decision level
https://jsm.yazd.ac.ir/article_3425.html
In practical problems where imprecise components are an inseparable part of them, using fuzzy sets to check their features and measure their eﬀiciency solves some of the current limitations. In this article, we examine the problem of linear regression in an intuitionistic fuzzy environment. Here, we consider the input and output data as intuitionistic fuzzy numbers and assume that the coeﬀicients of the model are crisp numbers. Since to correctly determine the coeﬀicients, we need to calculate the distance between the output of the model and the output data, we present a new parametric distance to calculate the distance between intuitionistic fuzzy numbers. The salient point in this article is that the researcher can estimate the parameter values of the model based on different decision-making levels. To show the eﬀiciency and test the proposed method, several examples are presented at the end of the article. The results are calculated and compared based on the values of different levels of decision-making.Mixtures of the normal mean-variance of Lindley factor analysis model with missing data
https://jsm.yazd.ac.ir/article_3428.html
For a heterogeneous community comprised of multiple sub-communities&lrm;, &lrm;the model-based clustering method stands out as a suitable recommendation&lrm;. &lrm;Moreover&lrm;, &lrm;incomplete data collection and information loss may occur due to a variety of causes&lrm;. &lrm;In this paper&lrm;, &lrm;our focus is on investigating the mixture of factor analysis model in the presence of missing data&lrm;. &lrm;Here&lrm;, &lrm;the latent factors and errors within each sub-cluster exhibit non-normal characteristics and adhere to the normal mean-variance mixture of Lindley distribution&lrm;. &lrm;This model is termed the mixture of normal mean-variance mixture of Lindley factor analysis&lrm;. &lrm;To estimate model parameters and generate a single imputation of potential missing values under the missing with random mechanism&lrm;, &lrm;we introduce a generalized expectation-maximization algorithm&lrm;. &lrm;The number of factors and mixture components are determined by the evaluation criteria of the model&lrm;. &lrm;The proposed model's advantage is validated through a real dataset and simulation studies&lrm;, &lrm;demonstrating its superior performance compared to existing models.The impact of reinsurance strategies on the ruin probability in the context of dependent and heavy-tailed losse
https://jsm.yazd.ac.ir/article_3448.html
The frequency and severity of extreme events have increased in recent years in many areas&lrm;. &lrm;In the context of risk management for insurance companies&lrm;, &lrm;reinsurance provides a safe&lrm; &lrm;solution as it offers coverage for large claims&lrm;. &lrm;This paper investigates the impact of&lrm; &lrm;dependent extreme losses on ruin probabilities under four types of reinsurance&lrm;: &lrm;excess of loss&lrm;, &lrm;quota share&lrm;, &lrm;largest claims&lrm;, &lrm;and ecomor&lrm;. &lrm;To achieve this&lrm;, &lrm;we use the dynamic GARCH-extreme value theory-copula&lrm; &lrm;combined model to fit the specific features of claim data and provide more accurate estimates&lrm; &lrm;than classical models&lrm;. &lrm;We derive the surplus processes and asymptotic ruin probabilities &lrm;under the Cramer-Lundberg risk process&lrm;. &lrm;Using a numerical example with real-life data&lrm;, &lrm;we illustrate the effects of dependence and the behavior of reinsurance strategies&lrm; &lrm;for both insurers and reinsurers&lrm;. &lrm;This comparison includes risk premiums&lrm;, &lrm;surplus processes&lrm;, &lrm;risk measures&lrm;, &lrm;and ruin probabilities&lrm;. &lrm;The findings show that the GARCH-extreme value theory-copula model mitigates the over&lrm;- &lrm;and under-estimation&lrm; &lrm;of risk associated with extremes and lowers the ruin probability for heavy-tailed distributions&lrm;.