scholarly journals Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression

2014 ◽  
Author(s):  
Alice X.D. Dong ◽  
Jennifer S.K. Chan ◽  
Gareth William Peters
Keyword(s):  
Quantile Regression ◽  
Quantile Function ◽  
Bayesian Quantile Regression ◽  
Risk Margin ◽  
Non Parametric

RISK MARGIN QUANTILE FUNCTION VIA PARAMETRIC AND NON-PARAMETRIC BAYESIAN APPROACHES

2015 ◽  
Vol 45 (3) ◽  
pp. 503-550 ◽  
Author(s):  
Alice X.D. Dong ◽  
Jennifer S.K. Chan ◽  
Gareth W. Peters
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Loss Function ◽  
Regression Models ◽  
Quantile Function ◽  
Parametric Model ◽  
Parametric Models ◽  
Risk Margin ◽  
Quantile Functions ◽  
Non Parametric

AbstractWe develop quantile functions from regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modeling frameworks are considered based around parametric and non-parametric regression models which we develop specifically in this insurance setting. In the parametric framework, quantile functions are derived using several distributions including the flexible generalized beta (GB2) distribution family, asymmetric Laplace (AL) distribution and power-Pareto (PP) distribution. In these parametric model based quantile regressions, we detail two basic formulations. The first involves embedding the quantile regression loss function from the nonparameteric setting into the argument of the kernel of a parametric data likelihood model, this is well known to naturally lead to the AL parametric model case. The second formulation we utilize in the parametric setting adopts an alternative quantile regression formulation in which we assume a structural expression for the regression trend and volatility functions which act to modify a base quantile function in order to produce the conditional data quantile function. This second approach allows a range of flexible parametric models to be considered with different tail behaviors. We demonstrate how to perform estimation of the resulting parametric models under a Bayesian regression framework. To achieve this, we design Markov chain Monte Carlo (MCMC) sampling strategies for the resulting Bayesian posterior quantile regression models. In the non-parametric framework, we construct quantile functions by minimizing an asymmetrically weighted loss function and estimate the parameters under the AL proxy distribution to resemble the minimization process. This quantile regression model is contrasted to the parametric AL mean regression model and both are expressed as a scale mixture of uniform distributions to facilitate efficient implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.

scholarly journals Probabilistic Prediction of Separation Buffer to Compensate for the Closing Effect on Final Approach

Aerospace ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 29
Author(s):  
Stanley Förster ◽  
Michael Schultz ◽  
Hartmut Fricke
Keyword(s):  
Quantile Regression ◽  
Prediction Interval ◽  
Quantile Function ◽  
Air Traffic ◽  
Point Estimate ◽  
Probabilistic Prediction ◽  
Traffic System ◽  
Final Approach ◽  
Model Training ◽  
Prediction Approach

The air traffic is mainly divided into en-route flight segments, arrival and departure segments inside the terminal maneuvering area, and ground operations at the airport. To support utilizing available capacity more efficiently, in our contribution we focus on the prediction of arrival procedures, in particular, the time-to-fly from the turn onto the final approach course to the threshold. The predictions are then used to determine advice for the controller regarding time-to-lose or time-to-gain for optimizing the separation within a sequence of aircraft. Most prediction methods developed so far provide only a point estimate for the time-to-fly. Complementary, we see the need to further account for the uncertain nature of aircraft movement based on a probabilistic prediction approach. This becomes very important in cases where the air traffic system is operated at its limits to prevent safety-critical incidents, e.g., separation infringements due to very tight separation. Our approach is based on the Quantile Regression Forest technique that can provide a measure of uncertainty of the prediction not only in form of a prediction interval but also by generating a probability distribution over the dependent variable. While the data preparation, model training, and tuning steps are identical to classic Random Forest methods, in the prediction phase, Quantile Regression Forests provide a quantile function to express the uncertainty of the prediction. After developing the model, we further investigate the interpretation of the results and provide a way for deriving advice to the controller from it. With this contribution, there is now a tool available that allows a more sophisticated prediction of time-to-fly, depending on the specific needs of the use case and which helps to separate arriving aircraft more efficiently.

scholarly journals Projection of Long-Term Care Costs in China, 2020–2050: Based on the Bayesian Quantile Regression Method

2019 ◽  
Vol 11 (13) ◽  
pp. 3530 ◽  
Author(s):  
Xiaocang Xu ◽  
Linhong Chen
Keyword(s):  
Quantile Regression ◽  
Long Term Care ◽  
Financial Burden ◽  
Severe Disabilities ◽  
Term Care ◽  
Bayesian Quantile Regression ◽  
The Future ◽  
The Government ◽  
Quantile Regression Method

The aging population in China highlights the significance of elderly long-term care (LTC) services. The number of people aged 65 and above increased from 96 million in 2003 to 150 million in 2016, some of whom were disabled due to chronic diseases or the natural effects of aging on bodily functions. Therefore, the measurement of future LTC costs is of crucial value. Following the basic framework but using different empirical methods from those presented in previous literature, this paper attempts to use the Bayesian quantile regression (BQR) method, which has many advantages over traditional linear regression. Another innovation consists of setting and measuring the high, middle, and low levels of LTC cost prediction for each disability state among the elderly in 2020–2050. Our projections suggest that by 2020, LTC costs will increase to median values of 39.46, 8.98, and 20.25 billion dollars for mild, moderate, and severe disabilities, respectively; these numbers will reach 141.7, 32.28, and 72.78 billion dollars by 2050. The median level of daily life care for mild, moderate, and severe disabilities will increase to 26.23, 6.36, and 27 billion dollars. Our results showed that future LTC cost increases will be enormous, and therefore, the establishment of a reasonable individual-social-government payment mechanism is necessary for the LTC system. The future design of an LTCI system must take into account a variety of factors, including the future elderly population, different care conditions, the financial burden of the government, etc., in order to maintain the sustainable development of the LTC system.

scholarly journals Is Carbon Dioxide (CO2) Emission an Important Factor Affecting Healthcare Expenditure? Evidence from China, 2005–2016

2019 ◽  
Vol 16 (20) ◽  
pp. 3995 ◽  
Author(s):  
Chen ◽  
Zhuo ◽  
Xu ◽  
Xu ◽  
Gao
Keyword(s):  
Carbon Dioxide ◽  
Air Pollution ◽  
Quantile Regression ◽  
Co2 Emission ◽  
Healthcare Expenditure ◽  
Carbon Dioxide Emission ◽  
Ordinary Least Squares ◽  
Bayesian Quantile Regression ◽  
Carbon Dioxide Co2 ◽  
The Relationship

As a result of China’s economic growth, air pollution, including carbon dioxide (CO2) emission, has caused serious health problems and accompanying heavy economic burdens on healthcare. Therefore, the effect of carbon dioxide emission on healthcare expenditure (HCE) has attracted the interest of many researchers, most of which have adopted traditional empirical methods, such as ordinary least squares (OLS) or quantile regression (QR), to analyze the issue. This paper, however, attempts to introduce Bayesian quantile regression (BQR) to discuss the relationship between carbon dioxide emission and HCE, based on the longitudinal data of 30 provinces in China (2005–2016). It was found that carbon dioxide emission is, indeed, an important factor affecting healthcare expenditure in China, although its influence is not as great as the income variable. It was also revealed that the effect of carbon dioxide emission on HCE at a higher quantile was much smaller, which indicates that most people are not paying sufficient attention to the correlation between air pollution and healthcare. This study also proves the applicability of Bayesian quantile regression and its ability to offer more valuable information, as compared to traditional empirical tools, thus expanding and deepening research capabilities on the topic.

scholarly journals Friction Characteristics of Post-Tensioned Tendons of Full-Scale Structures Based on Site Tests

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Haoyun Yuan ◽  
Yuan Li ◽  
Bin Zhou ◽  
Shuanhai He ◽  
Peizhi Wang
Keyword(s):  
Friction Coefficient ◽  
Quantile Regression ◽  
Least Square Method ◽  
Regression Method ◽  
Full Scale ◽  
Least Square ◽  
Friction Characteristics ◽  
Bayesian Quantile Regression ◽  
Prestressing Force ◽  
Quantile Regression Method

In the design of prestressing concrete structures, the friction characteristics between strands and channels have an important influence on the distribution of prestressing force, which can be considered comprehensively by curvature and swing friction coefficients. However, the proposed friction coefficient varies widely and may lead to an inaccurate prestress estimation. In this study, four full-scale field specimens were established to measure the friction loss of prestressing tendons with electromagnetic sensors and anchor cable dynamometers to evaluate the friction coefficient. The least square method and Bayesian quantile regression method were adopted to calculate the friction coefficient, and the results were compared with that in the specifications. Field test results showed that Bayesian quantile regression method was more effective and significant in the estimation of the friction coefficient.

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