Statistical control charts have found valuable applications in health care, having been largely adopted from operations research in manufacturing. However, the most common types are not best-suited ...to monitor high-yield processes (outcomes comprising true/false fractions, ‘near-zero’) and periodical processes (characterized by sequences of single populations of finite sizes), but rather to monitor variable vital signs levels and, to a lesser degree, service performance indicators. We discuss control charts that are most suitable for fraction non-conforming measurements. We focus particularly on high-yield and periodical processes, i.e. range in which out-of-control conditions are expected and should be identified. For these conditions, we discuss control charts based on the family of hypergeometric distributions, explaining and comparing their application to more traditional alternatives with two health care case studies. We demonstrate that hypergeometric-type control charts provide higher sensitivity in timely identification of changing rare event fractions and are well-suited for monitoring of periodical processes, while remaining more resistant to false alarms, versus their alternatives.
This paper is concerned with fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion. Moreover, we differentiate between a test of ...significance and an alternative test to control the type I error or both error types simultaneously. In contrast to classical (non-)randomized hypothesis testing, fuzzy hypothesis testing provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. In particular, various types of hypotheses with user-specified membership functions can be formulated. Additionally, the proposed test methods are compared via a comprehensive case study, which demonstrates the high flexibility of fuzzy hypothesis testing in practical applications.
•Comprehensive literature review of statistical and intelligent models to predict firms failure•Investigation of the discriminatory power of a Multilayer Perceptron for bankruptcy ...prediction•Consideration of numerous parameter setups and various evaluation metrics•Extensive case study including comparative analysis based on a data set of Taiwanese firms•Critical examination of methodologies and discrepancies in the results
High bankruptcy rates can lead to the collapse of economic systems. Therefore, having accurate and reliable models to predict firms in financial distress allows for proper management of the economic losses helping to prevent such crises. Since the 1930s, more than 500 studies have been published in the field of bankruptcy prediction models. In this paper, we firstly give a comprehensive literature review on the topic of statistical and intelligent models to predict firms failure. Then, we closely examine the discriminatory power of a Multilayer Perceptron (MLP) in the context of bankruptcy prediction. For this purpose, we consider different setups of optimization algorithms, activation functions, number of neurons, and number of layers. To find the parameter setup that achieves the best results, we use various evaluation metrics such as average accuracy, specificity, sensitivity, and precision. The case study is based on a data set of Taiwanese firms and includes comprehensive comparative analysis. The proposed MLPs show superior performance, and we critically examine the differences between the methodologies to explain the discrepancies in the results.
Often, the claims reserves exceed the available equity of non-life insurance companies and a change in the claims reserves by a small percentage has a large impact on the annual accounts. Therefore, ...it is of vital importance for any non-life insurer to handle claims reserving appropriately. Although claims data are time series data, the majority of the proposed (stochastic) claims reserving methods is not based on time series models. Among the time series models, state space models combined with Kalman filter learning algorithms have proven to be very advantageous as they provide high flexibility in modeling and an accurate detection of the temporal dynamics of a system. Against this backdrop, this paper aims to provide a comprehensive review of stochastic claims reserving methods that have been developed and analyzed in the context of state space representations. For this purpose, relevant articles are collected and categorized, and the contents are explained in detail and subjected to a conceptual comparison.
Machine learning applied to regression models offers powerful mathematical tools for predicting responses based on one or more predictor variables. This paper extends the concept of multiple linear ...regression by implementing a learning system and incorporating both fuzzy predictors and fuzzy responses. To estimate the unknown parameters of this soft regression model, the approach involves minimizing the absolute distance between two lines under three constraints related to the absolute error distance between observed data and their respective predicted lines. A thorough comparative analysis is conducted, showcasing the practical applicability and superiority of the proposed soft multiple linear regression model. The effectiveness of the model is demonstrated through a comprehensive examination involving simulation studies and real-life application examples.
•Developing a machine learning-based regression model with fuzzy predictors and fuzzy responses.•Providing a framework for reducing prediction errors and mitigating their impact on the predictions.•Allowing for higher flexibility in handling a wide range of data types and structures.•Enabling the incorporation of partial or incomplete information.•Investigating the practical applicability in the context of four application examples.
In stochastic claims reserving, state space models have been used for almost 40 years to forecast loss reserves and to compute their mean squared error of prediction. Although state space models and ...the associated Kalman filter learning algorithms are very powerful and flexible tools, comparatively few articles on this topic were published during this period. Most recently, several articles have been published which highlight the benefits of state space models in stochastic claims reserving and may lead to a significant increase in its popularity for applications in actuarial practice. To further emphasize the merits of these papers, this commentary highlights various additional aspects that are useful for practical applications and offer some fruitful directions for future research.
In this paper, an exponential autoregressive model for complex time series data is presented. As for estimating the parameters of this nonlinear model, a three-step procedure based on quantile ...methods is proposed. This quantile-based estimation technique has the benefit of being more robust compared to least/absolute squares. The performance of the introduced exponential autoregressive model is evaluated by means of four established goodness-of-fit criteria. The practical utility of the novel time series model is showcased through a comparative analysis involving simulation studies and real-world data illustrations.
Statistical regression analysis is a powerful and reliable method to determine the impact of one or several independent variable(s) on a dependent variable. It is the most widely used of all ...statistical methods and has broad applicability to numerous practical problems. However, various problems can arise, when for instance the sample size is too small, distributional assumptions are not fulfilled, the relationship between independent and dependent variables is vague or when there is an ambiguity of events. Moreover, the complexity of real-life problems often makes the underlying models inadequate, since information is frequently imprecise in many ways. To relax these rigidities, numerous researchers have modified and extended concepts of statistical regression analysis by means of concepts of fuzzy set theory. By now, there is a large number of papers on the topic of fuzzy regression analysis, especially concerning possibilistic, fuzzy least squares or machine learning approaches. Additionally, the variety of approaches includes probabilistic, logistic, type-2 and clusterwise fuzzy regression methods, among many others. Besides papers mainly devoted to advances in methodology, there are also several papers presenting case studies in various research fields. To structure this diversity of papers, proposals and applications we give in this paper a comprehensive systematic review and provide a bibliography on the topic of fuzzy regression analysis. Thus, the paper intends to consolidate the topic in order to aid new researchers in this area, focuses the field’s attention on key open questions, and highlights possible directions for future research.
•Comprehensive systematic review on the topic of fuzzy regression analysis.•Structuring and categorizing the diversity of papers, proposals and practical applications.•Extensive bibliography of 455 relevant articles.•Critical discussion of the presented methods and approaches.•Several directions for fruitful future research.
In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric ...kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.
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