Quantile-based methods for prediction, risk measurement and inference

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The focus of this thesis is on the employment of theoretical and practical quantile methods in addressing prediction, risk measurement and inference problems. From a prediction perspective, a problem of creating model-free prediction intervals for a future unobserved value of a random variable drawn from a sample distribution is considered. With the objective of reducing prediction coverage error, two common distribution transformation methods based on the normal and exponential distributions are presented and they are theoretically demonstrated to attain exact and error-free prediction intervals respectively. The second problem studied is that of estimation of expected shortfall via kernel smoothing. The goal here is to introduce methods that will reduce the estimation bias of expected shortfall. To this end, several one-step bias correction expected shortfall estimators are presented and investigated via simulation studies and compared with one-step estimators. The third problem is that of constructing simultaneous confidence bands for quantile regression functions when the predictor variables are constrained within a region is considered. In this context, a method is introduced that makes use of the asymmetric Laplace errors in conjunction with a simulation based algorithm to create confidence bands for quantile and interquantile regression functions. Furthermore, the simulation approach is extended to an ordinary least square framework to build simultaneous bands for quantiles functions of the classical regression model when the model errors are normally distributed and when this assumption is not fulfilled. Finally, attention is directed towards the construction of prediction intervals for realised volatility exploiting an alternative volatility estimator based on the difference of two extreme quantiles. The proposed approach makes use of AR-GARCH procedure in order to model time series of intraday quantiles and forecast intraday returns predictive distribution. Moreover, two simple adaptations of an existing model are also presented

Quantile-based methods for prediction, risk measurement and inference

The focus of this thesis is on the employment of theoretical and practical quantile methods in addressing prediction, risk measurement and inference problems. From a prediction perspective, a problem of creating model-free prediction intervals for a future unobserved value of a random variable drawn from a sample distribution is considered. With the objective of reducing prediction coverage error, two common distribution transformation methods based on the normal and exponential distributions are presented and they are theoretically demonstrated to attain exact and error-free prediction intervals respectively. The second problem studied is that of estimation of expected shortfall via kernel smoothing. The goal here is to introduce methods that will reduce the estimation bias of expected shortfall. To this end, several one-step bias correction expected shortfall estimators are presented and investigated via simulation studies and compared with one-step estimators. The third problem is that of constructing simultaneous confidence bands for quantile regression functions when the predictor variables are constrained within a region is considered. In this context, a method is introduced that makes use of the asymmetric Laplace errors in conjunction with a simulation based algorithm to create confidence bands for quantile and interquantile regression functions. Furthermore, the simulation approach is extended to an ordinary least square framework to build simultaneous bands for quantiles functions of the classical regression model when the model errors are normally distributed and when this assumption is not fulfilled. Finally, attention is directed towards the construction of prediction intervals for realised volatility exploiting an alternative volatility estimator based on the difference of two extreme quantiles. The proposed approach makes use of AR-GARCH procedure in order to model time series of intraday quantiles and forecast intraday returns predictive distribution. Moreover, two simple adaptations of an existing model are also presented.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Quantile-based methods for prediction, risk measurement and inference

The focus of this thesis is on the employment of theoretical and practical quantile methods in addressing prediction, risk measurement and inference problems. From a prediction perspective, a problem of creating model-free prediction intervals for a future unobserved value of a random variable drawn from a sample distribution is considered. With the objective of reducing prediction coverage error, two common distribution transformation methods based on the normal and exponential distributions are presented and they are theoretically demonstrated to attain exact and error-free prediction intervals respectively. The second problem studied is that of estimation of expected shortfall via kernel smoothing. The goal here is to introduce methods that will reduce the estimation bias of expected shortfall. To this end, several one-step bias correction expected shortfall estimators are presented and investigated via simulation studies and compared with one-step estimators. The third problem is that of constructing simultaneous confidence bands for quantile regression functions when the predictor variables are constrained within a region is considered. In this context, a method is introduced that makes use of the asymmetric Laplace errors in conjunction with a simulation based algorithm to create confidence bands for quantile and interquantile regression functions. Furthermore, the simulation approach is extended to an ordinary least square framework to build simultaneous bands for quantiles functions of the classical regression model when the model errors are normally distributed and when this assumption is not fulfilled. Finally, attention is directed towards the construction of prediction intervals for realised volatility exploiting an alternative volatility estimator based on the difference of two extreme quantiles. The proposed approach makes use of AR-GARCH procedure in order to model time series of intraday quantiles and forecast intraday returns predictive distribution. Moreover, two simple adaptations of an existing model are also presented.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A new approach to measuring drinking cultures in Britain

First paragraph: When governments propose changes to alcohol policies, the announcement is often followed by public debate on the potential for the policy to change the country’s drinking culture. However, specifying what the drinking culture is, what is problematic about it, what it should be changed to, what interventions might trigger such a change and whether success has been achieved have all been problematic topics in alcohol policy discourse and the research literature

Estimated Effects of Different Alcohol Taxation and Price Policies on Health Inequalities: A Mathematical Modelling Study

INTRODUCTION: While evidence that alcohol pricing policies reduce alcohol-related health harm is robust, and alcohol taxation increases are a WHO "best buy" intervention, there is a lack of research comparing the scale and distribution across society of health impacts arising from alternative tax and price policy options. The aim of this study is to test whether four common alcohol taxation and pricing strategies differ in their impact on health inequalities. METHODS AND FINDINGS: An econometric epidemiological model was built with England 2014/2015 as the setting. Four pricing strategies implemented on top of the current tax were equalised to give the same 4.3% population-wide reduction in total alcohol-related mortality: current tax increase, a 13.4% all-product duty increase under the current UK system; a value-based tax, a 4.0% ad valorem tax based on product price; a strength-based tax, a volumetric tax of £0.22 per UK alcohol unit (= 8 g of ethanol); and minimum unit pricing, a minimum price threshold of £0.50 per unit, below which alcohol cannot be sold. Model inputs were calculated by combining data from representative household surveys on alcohol purchasing and consumption, administrative and healthcare data on 43 alcohol-attributable diseases, and published price elasticities and relative risk functions. Outcomes were annual per capita consumption, consumer spending, and alcohol-related deaths. Uncertainty was assessed via partial probabilistic sensitivity analysis (PSA) and scenario analysis. The pricing strategies differ as to how effects are distributed across the population, and, from a public health perspective, heavy drinkers in routine/manual occupations are a key group as they are at greatest risk of health harm from their drinking. Strength-based taxation and minimum unit pricing would have greater effects on mortality among drinkers in routine/manual occupations (particularly for heavy drinkers, where the estimated policy effects on mortality rates are as follows: current tax increase, -3.2%; value-based tax, -2.9%; strength-based tax, -6.1%; minimum unit pricing, -7.8%) and lesser impacts among drinkers in professional/managerial occupations (for heavy drinkers: current tax increase, -1.3%; value-based tax, -1.4%; strength-based tax, +0.2%; minimum unit pricing, +0.8%). Results from the PSA give slightly greater mean effects for both the routine/manual (current tax increase, -3.6% [95% uncertainty interval (UI) -6.1%, -0.6%]; value-based tax, -3.3% [UI -5.1%, -1.7%]; strength-based tax, -7.5% [UI -13.7%, -3.9%]; minimum unit pricing, -10.3% [UI -10.3%, -7.0%]) and professional/managerial occupation groups (current tax increase, -1.8% [UI -4.7%, +1.6%]; value-based tax, -1.9% [UI -3.6%, +0.4%]; strength-based tax, -0.8% [UI -6.9%, +4.0%]; minimum unit pricing, -0.7% [UI -5.6%, +3.6%]). Impacts of price changes on moderate drinkers were small regardless of income or socioeconomic group. Analysis of uncertainty shows that the relative effectiveness of the four policies is fairly stable, although uncertainty in the absolute scale of effects exists. Volumetric taxation and minimum unit pricing consistently outperform increasing the current tax or adding an ad valorem tax in terms of reducing mortality among the heaviest drinkers and reducing alcohol-related health inequalities (e.g., in the routine/manual occupation group, volumetric taxation reduces deaths more than increasing the current tax in 26 out of 30 probabilistic runs, minimum unit pricing reduces deaths more than volumetric tax in 21 out of 30 runs, and minimum unit pricing reduces deaths more than increasing the current tax in 30 out of 30 runs). Study limitations include reducing model complexity by not considering a largely ineffective ban on below-tax alcohol sales, special duty rates covering only small shares of the market, and the impact of tax fraud or retailer non-compliance with minimum unit prices. CONCLUSIONS: Our model estimates that, compared to tax increases under the current system or introducing taxation based on product value, alcohol-content-based taxation or minimum unit pricing would lead to larger reductions in health inequalities across income groups. We also estimate that alcohol-content-based taxation and minimum unit pricing would have the largest impact on harmful drinking, with minimal effects on those drinking in moderation

Annual full effects of policies on alcohol-related deaths, by drinking level and socioeconomic group.

<p>Annual full effects of policies on alcohol-related deaths, by drinking level and socioeconomic group.</p

UK alcohol unit content of popular drinks (1 unit = 8 g [10 ml] of pure alcohol).

<p>UK alcohol unit content of popular drinks (1 unit = 8 g [10 ml] of pure alcohol).</p

Distribution of alcohol purchasing by income.

<p>This figure shows the average number of units purchased per moderate drinker per year for alcohol across price bands, stratified by income. Moderate drinkers (a) purchase little alcohol overall and show a preference for middle and higher price bands, even when having lower incomes. Increasing risk drinkers (b) purchase alcohol across all price bands, but there is a clear gradient whereby poorer drinkers purchase more of the cheapest alcohol. Heavy drinkers (c)—across income quintiles, but especially poorer heavy drinkers—show a very clear preference for cheaper alcohol. Price bands are deciles of the price distribution of all alcohol sold in England. Income groups are defined by equivalised income quintiles.</p

Equity gap in the alcohol-related death rates between those in routine/manual and professional/managerial occupations: heavy drinkers.

<p>This figure shows the effect of alcohol pricing policies on the gap between alcohol-related death rates for heavy drinkers in the highest and lowest socioeconomic occupation groups. All policies reduce this gap, but volumetric tax and minimum unit pricing (“Minimum Price”) have larger effects on the gap than ad valorem tax (“Sales Tax”) or increasing the UK’s current tax (“Current Tax”).</p