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The purpose of this paper is to show that multivariate t-distribution assumption provides a better description of stock return data than multivariate normality assumption.

The EM algorithm is applied to solve the statistical estimation problem almost analytically, and the asymptotic theory is provided for inference.

The authors find that the multivariate normality assumption is almost always rejected by real stock return data, while the multivariate t-distribution assumption can often be adequate. Conclusions under normality vs under t can be drastically different for estimating expected returns and Jensen’s αs, and for testing asset pricing models.

The results provide improved estimates of cost of capital and asset moment parameters that are useful for corporate project evaluation and portfolio management.

The authors proposed new procedures that makes it easy to use a multivariate t-distribution, which models well the data, as a simple and viable alternative in practice to examine the robustness of many existing results.

The purpose of this study is to propose an effective unsupervised one-class-classifier (OCC) support vector machine (SVM)-based single multivariate control chart (OCC-SVM) to simultaneously monitor “location” and “scale” shifts of a manufacturing process.

The step-by-step approach to developing, implementing and fine-tuning the intrinsic parameters of the OCC-SVM chart is demonstrated based on simulation and two real-life case examples.

A comparative study, considering varied known and unknown response distributions, indicates that the OCC-SVM is highly effective in detecting process shifts of samples with individual observations. OCC-SVM chart also shows promising results for samples with a rational subgroup of observations. In addition, the results also indicate that the performance of OCC-SVM is unaffected by the small reference sample size.

The sample responses are considered identically distributed with no significant multivariate autocorrelation between sample observations.

The proposed easy-to-implement chart shows satisfactory performance to detect an out-of-control signal with known or unknown response distributions.

Various multivariate (e.g. parametric or nonparametric) control chart(s) are recommended to monitor the mean (e.g. location) and variance (e.g. scale) of multiple correlated responses in a manufacturing process. However, real-life implementation of a parametric control chart may be complex due to its restrictive response distribution assumptions. There is no evidence of work in the open literature that demonstrates the suitability of an unsupervised OCC-SVM chart to simultaneously monitor “location” and “scale” shifts of multivariate responses. Thus, a new efficient OCC-SVM single chart approach is proposed to address this gap to monitor a multivariate manufacturing process with unknown response distributions.

The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian X‾ control chart based on predictive distribution with two types of informative and noninformative prior distributions.

The design used in this study is based on determining the control chart of the predictive distribution and then its ESD. The new proposed cost model is presented by considering the conjugate and Jeffrey's prior distribution in calculating the expected total cycle time and expected cost per cycle, and finally, the optimal design parameters and related costs are compared with the fixed ratio sampling (FRS) mode.

Numerical results show decreases in costs in this Bayesian approach with both Jeffrey's and conjugate prior distribution compared to the FRS mode. This result shows that the Bayesian approach which is based on predictive density works better than the classical approach. Also, for the Bayesian approach, however, there is no significant difference between the results of using Jeffrey's and conjugate prior distributions. Using sensitivity analysis, the effect of cost parameters and shock model parameters and deviation from the mean on the optimal values of design parameters and related costs have been investigated and discussed.

This research adds to the body of knowledge related to quality control of process monitoring systems. This paper may be of particular interest to quality system practitioners for whom the effect of the prior distribution of parameters on the quality characteristic distribution is important.

economic statistical design (ESD) of Bayesian control charts based on predictive distribution is presented for the first time.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

This chapter develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation study. The proposed approach is flexible in that it can account for common and individual-specific parameters, as well as multivariate heterogeneity associated with several covariates. The methodology is applied to study female labor force participation and home ownership in the United States. The results offer new insights at the various quantiles, which are of interest to policymakers and researchers alike.

The purpose of this paper is to develop a new easy-to-implement distribution-free integrated multivariate statistical process control (MSPC) approach with an ability to recognize out-of-control points, identify the key influential variable for the out-of-control state, and determine necessary changes to achieve the state of statistical control.

The proposed approach integrates the control chart technique, the Mahalanobis-Taguchi System concept, the Andrews function plot, and nonlinear optimization for multivariate process control. Mahalanobis distance, Taguchi’s orthogonal array, and the main effect plot concept are used to identify the key influential variable responsible for the out-of-control situation. The Andrews function plot and nonlinear optimization help to identify direction and necessary correction to regain the state of statistical control. Finally, two different real life case studies illustrate the suitability of the approach.

The case studies illustrate the potential of the proposed integrated multivariate process control approach for easy implementation in varied manufacturing and process industries. In addition, the case studies also reveal that the multivariate out-of-control state is primarily contributed by a single influential variable.

The approach is limited to the situation in which a single influential variable contributes to out-of-control situation. The number and type of cases used are also limited and thus generalization may not be debated. Further research is necessary with varied case situations to refine the approach and prove its extensive applicability.

The proposed approach does not require multivariate normality assumption and thus provides greater flexibility for the industry practitioners. The approach is also easy to implement and requires minimal programming effort. A simple application Microsoft Excel is suitable for online implementation of this approach.

The key steps of the MSPC approach are identifying the out-of-control point, diagnosing the out-of-control point, identifying the “influential” variable responsible for the out-of-control state, and determining the necessary direction and the amount of adjustment required to achieve the state of control. Most of the approaches reported in open literature are focused only until identifying influencing variable, with many restrictive assumptions. This paper addresses all key steps in a single integrated distribution-free approach, which is easy to implement in real time.

In this paper, we consider the analysis of models for univariate and multivariate ordinal outcomes in the context of the latent variable inferential framework of Albert and Chib (1993). We review several alternative modeling and identification schemes and evaluate how each aids or hampers estimation by Markov chain Monte Carlo simulation methods. For each identification scheme we also discuss the question of model comparison by marginal likelihoods and Bayes factors. In addition, we develop a simulation-based framework for analyzing covariate effects that can provide interpretability of the results despite the nonlinearities in the model and the different identification restrictions that can be implemented. The methods are employed to analyze problems in labor economics (educational attainment), political economy (voter opinions), and health economics (consumers’ reliance on alternative sources of medical information).

This paper is the main section on quantitative data analysis. It explains the concepts at a greater detail to help non-Math/Stat scholars to understand the basics easily. Proper data analysis is critical to any research. If data are not properly analyzed, then it may give results which either cannot be properly interpreted or wrongly interpreted. This section covers univariate, multivariate analysis and then, factor analysis, cluster analysis, conjoint analysis, and multidimensional scaling (MDS) techniques.