Biases in Maximum Simulated Likelihood Estimation of Bivariate Models

This paper finds that the maximum simulated likelihood (MSL) estimator produces substantial biases when applied to the bivariate normal distribution. A specification of the random parameter bivariate normal model is considered, in which a direct comparison between the MSL and maximum likelihood (ML) estimators is feasible. The analysis shows that MSL produces biased results for the correlation parameter. This paper also finds that the MSL estimator is biased for the bivariate Poisson-lognormal model, developed by Munkin and Trivedi (1999. “Simulated Maximum Likelihood Estimation of Multivariate Mixed-Poisson Regression Models, with Application.” The Econometrics Journal 2: 29–48). A simulation study is conducted, which shows that MSL leads to serious inferential biases, especially large when variance parameters in the true data generating process are small. The MSL estimator produces biases in the estimated marginal effects, conditional means and probabilities of count outcomes.

Bivariate Distributions Underlying Responses to Ordinal Variables

The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to ordinal variables are generated by two underlying continuous latent variables with a bivariate normal distribution. When the underlying bivariate normality assumption is violated, the estimated polychoric correlation coefficient may be biased. In such a case, we may consider other distributions. In this paper, we aimed to provide an illustration of fitting various bivariate distributions to empirical ordinal data and examining how estimates of the polychoric correlation may vary under different distributional assumptions. Results suggested that the bivariate normal and skew-normal distributions rarely hold in the empirical datasets. In contrast, mixtures of bivariate normal distributions were often not rejected.

Robust Tests for the Mean Difference in Paired Data using Jackknife Resampling Technique

The paired sample t-test is a type of classical test statistics that is used to test the difference between two means in paired data, but it is not robust against the violation of the normality assumption. In this paper, some alternative robust tests are suggested by combining the Jackknife resampling with each of the Wilcoxon signed-rank test for small sample size and Wilcoxon signed-rank test for large sample size, using normal approximation. The Monte Carlo simulation experiments were employed to study the performance of the test statistics of each of these tests depending on the type one error rates and the power rates of the test statistics. All these tests were applied on different sample sizes generated from three distributions, represented by Bivariate normal distribution, contaminated Bivariate normal distribution, and Bivariate exponential distribution.

Sampling plans using extended EWMA statistic with and without auxiliary information

In this paper, we propose an Acceptance Sampling Plan (ASP) using the statistic suggested by Naveed et al. (2018) under the condition of known and unknown population standard deviation (SD) for the presence of with and without Auxiliary Information (AI). It is presumed that the study variable of quality trait and AI follow the bivariate normal distribution. The plan parameters of the recommended plan are discussed for all four cases under the constraint that specified producer and consumer risks are gratified. The suggested plan is compared in terms of sample size (SS) with numerous existing plans and showed that the presented plan has a smaller SS for any value of AQL, LQL. Various tables of plan parameters have been erected using various combinations of smoothing constants for industrial use. For the workable purpose, the industrial example has also been examined. At last, concluding remarks are discussed.

A new bivariate Archimedean copula with application to the evaluation of VaR

In this paper, a new generator function is proposed and based on this function a new Archimedean copula is introduced. The new Archimedean copula along with three representatives of Archimedean copula family which are Clayton, Gumbel and Frank copulas are considered as models for the dependence structure between the returns of two stocks. These copula models are used to simulate daily log-returns based on Monte Carlo (MC) method for calculating value at risk (VaR) of the financial portfolio which consists of two market indices, Ford and General Motor Company. The results are compared with the traditional MC simulation method with the bivariate normal assumption as a model of the returns. Based on the backtesting results, describing the dependence structure between the returns by the proposed Archimedean copula provides more reliable results over the considered models in calculating VaR of the studied portfolio.

PSIII-5 Comparison of Bivariate Machine Learning and Linear Model for Genomic Prediction with Different Heritability, QTL and SNP Panel Scenarios

This simulation study used actual SNP genotypes on the first chromosome of Brangus beef cattle to simulate 0.50 genetically correlated two traits with heritabilities of 0.25 and 0.50 determined either by 50, 100, 250 or 500 QTL and then aimed to compare the accuracies of genomic prediction from bivariate linear and artificial neural network with 1 to 10 neurons models based on G genomic relationship matrix. QTL effects of 50, 100, 250 and 500 SNPs from the 3361 SNPs of 719 animals were sampled from a bivariate normal distribution. In each QTL scenario, the breeding values (Σgijβj) of animal i for two traits were generated by using genotype (gij) of animal i at QTL j and the effects (βj) of QTL j from a bivariate normal distribution. Phenotypic values of animal i for traits were generated by adding residuals from a bivariate normal distribution to the breeding values of animal i. Genomic predictions for traits were carried out by bivariate Feed Forward MultiLayer Perceptron ANN-1–10 neurons and linear (GBLUP) models. Three sets of SNP panels were used for genomic prediction: only QTL genotypes (Panel1), all SNP markers, including the QTL (Panel2), and all SNP markers, excluding the QTL (Panel3). Correlations from 10-fold cross validation for traits were used to assess predictive ability of bivariate linear (GBLUP) and artificial neural network models based on 4 QTL scenarios with 3 Panels of SNP panels. Table 1 shows that the trait with high heritability (0.50) resulted in higher correlation than the trait with low heritability (0.25) in bivariate linear (GBLUP) and artificial neural network models. However, bivariate linear (GBLUP) model produced higher correlation than bivariate neural network. Panel1 performed the best correlations for all QTL scenarios, then Panel2 including QTL and SNP markers resulted in better prediction than Panel3.