Thesis advisor: Zhijie Xiao / This dissertation contains three essays. It provides an application of quantile regression in Financial Economics. The first essay investigates whether tail dependence makes a difference in the estimation of systemic risk. This chapter develops a common framework based on a copula model to estimate several popular return-based systemic risk measures: Delta Conditional Value at Risk (ΔCoVaR) and its modification; and Marginal Expected Shortfall (MES) and its extension, systemic risk measure (SRISK). By eliminating the discrepancy of the marginal distribution, copula models provide the flexibility to concentrate only on the effects of dependence structure on the systemic risk measure. We estimate the systemic risk contributions of four financial industries consisting of a large number of institutions for the sample period from January 2000 to December 2010. First, we found that the linear quantile regression estimation of ΔCoVaR, proposed by Adrian and Brunnermeier (AB hereafter) (2011), is inadequate to completely capture the non-linear contagion tail effect, which tends to underestimate systemic risk in the presence of lower tail dependence. Second, ΔCoVaR originally proposed by AB (2011) is in conflict with dependence measures. By comparison, the modified version of ΔCoVaR put forward by Girardi et al. (2011) and MES, proposed by Acharya et al. (2010), are more consistent with dependence measures, which conforms with the widely held notion that stronger dependence strength results in higher systemic risk. Third, the modified ΔCoVaR is observed to have a strong correlation with tail dependence. In contrast, MES is found to have a strong empirical relationship with firms' conditional CAPM beta. SRISK, however, provides further connection with firms' level characteristics by accounting for information on market capitalization and liability. This stylized fact seems to imply that ΔCoVaR is more in line with the ``too interconnected to fail" paradigm, while SRISK is more related to the ``too big to fail" paradigm. In contrast, MES offers a compromise between these two paradigms. The second essay proposes a quantile regression approach to stock return prediction. I show that incorporating distributional information together with combining model information can produce a superior forecast for the conditional mean as well as the entire distribution of future equity premium, which significantly outperforms the forecast that utilizes either source of information alone. Meanwhile, the order of combination strategies appears to make a difference in the efficiency of pooling both distributional information and model information. It turns out that aggregating distributional information in the first step, followed by combining model information in the second step is more advantageous in return forecast than the alternative combination strategies which reverse the order of combination strategy. Furthermore, the forecast based on LASSO model selection can be significantly improved as well if the distributional information is further incorporated. In other word, aggregating distributional information via combining multiple quantiles estimators contributes to the improvement of forecasts obtained either from model combination or model selection. This paper not only investigates the forecast of conditional mean, but also studies the forecast of the whole distribution of future stock returns. The approaches of quantile combination together with either model combination or model selection turn out to deliver statistically and economically significant out-of-sample forecasts relative to a historical average benchmark. The third essay proposes a quantile-based approach to efficiently estimate the conditional beta coefficient without assuming a parametric structure on the distribution of data generating process. Multiple quantiles estimates are combined in a weighting scheme to utilize distributional information across different quantile of the distribution. Monte Carlo simulation demonstrated that combining multiple quantile estimates can substantially improve the estimation efficiency for beta risk estimates in the absence of Gaussian distribution. The robustness of quantile-based beta estimates are pronounced during financial crisis when the distribution of stock returns deviates most from normality. I also explored the performance of different beta estimators in an application of portfolio management analysis and found that beta estimates from the proposed quantile combination approaches are superior to the OLS estimates in constructing Global Minimum Variance Portfolio, which generates lower variance of portfolio but does not come at the expense of persistent lower returns. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

The goal of this thesis is to propose a new quantile regression approach to identify and estimate the quantiles of the private value conditional distribution in ascending and rst price auctions under the Independent Private Value (IPV) paradigm. The quantile regression framework provides a exible and convenient parametrization of the private value distribution, which is not a ected by the curse of dimensionality. The rst Chapter of the thesis introduces a quantile regression methodology for ascending auctions. The Chapter focuses on revenue analysis, optimal reservation price and its associated screening level. An empirical application for the USFS timber auctions suggests an optimal reservation price policy with a probability of selling the good as low as 58% for some auctions with two bidders. The second Chapter tries to address this issue by considering a risk averse seller with a CRRA utility function. A numerical exercise based on the USFS timber auctions shows that increasing the CRRA of the sellers is su cient to give more reasonable policy recommendations and a higher probability of selling the auctioned timber lot. The third Chapter develops a quantile regression methodology for rst-price auction. The estimation method combines local polynomial, quantile regression and additive sieve methods. It is shown in addition that the new quantile regression methodology is not subject to boundary issues. The choice of smoothing parameters is also discussed.

The traffic accident all causes the greatest damage and the loss of the world. There are approximate million people to die and about 10 million people to be injured every year of the traffic accident of the world, but middle develops countries have the highest ratio of accident. According to the National Highway Traffic Safety Administration a preliminary appraisal shows that number of death of drunk driving is highest for 14 years of the United States., 2006. Ruthm(1996) and Wilkinson(1987) indicate that the main reason of all age¡¦s populace is the traffic accident fatality on the United States. Phelp(1988) found that there are 5,100 people death for the serious traffic accident in 1980¡¦s of the United States. Above show drunk driving is serious and necessary of discussion. In the past, the research about drunk driving, the kinds of data are cross-section¡Btime series and panel data. The tradition econometrics data have two estimate methods¡GFirst is the Ordinary Least Square; second is the Least Absolute Deviation. The two way¡¦s common characteristic is comprehensive discussion. Therefore the study draw on Quantile Regression and that is analysis of drunk driving of the United States. By the research, we can find that in different rats of fatality must be to take the different policy measure to improve the fatality of drunk driving. Not like other research only provide the concise suggestion.

Climatic change has been observed in many locations and has been seen to have dramatic impact on a wide range of ecosystems. The traditional method to analyse trends in climatic series is regression analysis. Koenker and Bassett (1978) developed a regression-type model for estimating the functional relationship between predictor variables and any quantile in the distribution of the response variable. Quantile regression has received considerable attention in the statistical literature, but less so in the water resources literature. This study aims to apply quantile regression to problems in water resources and climate change studies. The core of the thesis is made up of three papers of which two have been published and one has been submitted. One paper presents a novel application of quantile regression to analyze the distribution of sea ice extent. Another paper investigates changes in temperature and precipitation extremes over the Canadian Prairies using quantile regression. The third paper presents a Bayesian model averaging method for variable selection adapted to quantile regression and analyzes the relationship of extreme precipitation with large-scale atmospheric variables. This last paper also develops a novel statistical downscaling model based on quantile regression. The various applications of quantile regression support the conclusion that the method is useful in climate change studies.

Climatic change has been observed in many locations and has been seen to have dramatic impact on a wide range of ecosystems. The traditional method to analyse trends in climatic series is regression analysis. Koenker and Bassett (1978) developed a regression-type model for estimating the functional relationship between predictor variables and any quantile in the distribution of the response variable. Quantile regression has received considerable attention in the statistical literature, but less so in the water resources literature. This study aims to apply quantile regression to problems in water resources and climate change studies. The core of the thesis is made up of three papers of which two have been published and one has been submitted. One paper presents a novel application of quantile regression to analyze the distribution of sea ice extent. Another paper investigates changes in temperature and precipitation extremes over the Canadian Prairies using quantile regression. The third paper presents a Bayesian model averaging method for variable selection adapted to quantile regression and analyzes the relationship of extreme precipitation with large-scale atmospheric variables. This last paper also develops a novel statistical downscaling model based on quantile regression. The various applications of quantile regression support the conclusion that the method is useful in climate change studies.

The motivation for this thesis came from the provision of a large data set from Saudi Arabia giving anthropometric measurements of children and adolescents from birth to eighteen years of age, with a requirement to construct growth charts. The construction of these growth charts revealed a number of issues particularly in the respect to statistical inference relating to quantile regression. To investigate a range of different statistical inference procedures in parametric quantile regression in particular the estimation of the confidence limits of the ?th (?? [0, 1]) quantile, a number of sets of simulated data in which various error structures are imposed including homoscedastic and heteroscedastic structures were developed. Methods from the statistical literature were then compared with a method proposed within this thesis based on the idea of Silverman's (1986) kernel smoothing. This proposed bootstrapping method requires the estimation of the conditional variance function of the fitted quantile. The performance of a variety of variance estimation methods combined within the proposed bootstrapping procedure are assessed under various data structures in order to examine the performance of the proposed bootstrapping approach. The validity of the proposed bootstrapping method is then illustrated using the Saudi Arabian anthropometric data.

Statistics, as a critical component in transportation research, has been widely used to analyze driver safety, travel time, traffic flow and numerous other problems. Many of these popular topics can be interpreted as to establish the statistical models for the latent structure of data. Over the past several years, the interest in latent class models has continuously increased due to their great potential in solving practical problems. In this dissertation, I developed several latent class models to quantitatively analyze the hidden structure of transportation data and addressed related application issues. The first model is focused on the uncertainty of travel time, which is critical for assessing the reliability of transportation systems. Travel time is random in nature, and contains substantial variability, especially under congested traffic conditions. A Bayesian mixture model, with the ability to incorporate the influence from covariates such as traffic volume, has been proposed. This model advances the previous multi-state travel time reliability model in which the relationship between response and predictors was lacking. The Bayesian mixture travel time model, however, lack the power to accurately predict the future travel time. The analysis indicates that the independence assumption, which is difficult to justify in real data, could be a potential issue. Therefore, I proposed a Hidden Markov model to accommodate dependency structure, and the modeling results were significantly improved. The second and third parts of the dissertation focus on the driver safety identification. Given the demographic information and crash history, the number of crashes, as a type of count data, is commonly modeled by Poisson regression. However, the over-dispersion issue within the data implies that a single Poisson distribution is insufficient to depict the substantial variability. Poisson mixture model is proposed and applied to identify risky and safe drivers. The lower bound of the estimated misclassification rate is evaluated using the concept of overlap probability. Several theoretical results have been discussed regarding the overlap probability. I also introduced quantile regression based on discrete data to specifically model the high-risk drivers. In summary, the major objective of my research is to develop latent class methods and explore the hidden structure within the transportation data, and the approaches I employed can also be implemented for similar research questions in other areas. / Ph. D.

Buried pipelines are vulnerable to the threat of corrosion. Hence, they are normally coated with a protective coating to isolate the metal substrate from the surrounding environment with the addition of CP current being applied to the pipeline surface to halt any corrosion activity that might be taking place. With time, this barrier will deteriorate which could potentially lead to corrosion of the pipe. The External Corrosion Direct Assessment (ECDA) methodology was developed with the intention of upholding the structural integrity of pipelines. Above ground indirect inspection techniques such as the DCVG which is an essential part of an ECDA, is commonly used to determine coating defect locations and measure the defect's severity. This is followed by excavation of the identified location for further examination on the extent of pipeline damage. Any coating or corrosion defect found at this stage is repaired and remediated. The location of such excavations is determined by the measurements obtained from the DCVG examination in the form of %IR and subjective inputs from experts which bases their justification on the environment and the physical characteristics of the pipeline. Whilst this seems to be a straight forward process, the factors that comes into play which gave rise to the initial %IR is not fully understood. The lack of understanding with the additional subjective inputs from the assessors has led to unnecessary excavations being conducted which has put tremendous financial strain on pipeline operators. Additionally, the threat of undiscovered defects due to the erroneous nature of the current method has the potential to severely compromise the pipeline's safe continual operation. Accurately predicting the coating defect size (TCDA) and interpretation of the indication signal (%IR) from an ECDA is important for pipeline operators to promote safety while keeping operating cost at a minimum. Furthermore, with better estimates, the uncertainty from the DCVG indication is reduced and the decisions made on the locations of excavation is better informed. However, ensuring the accuracy of these estimates does not come without challenges. These challenges include (1) the need of proper methods for large data analysis from indirect assessment and (2) uncertainty about the probability distribution of quantities. Standard mean regression models e.g. the OLS, were used but fail to take the skewness of the distributions involved into account. The aim of this thesis is thus, to come up with statistical models to better predict TCDA and to interpret the %IR from the indirect assessment of an ECDA more precisely. The pipeline data used for the analyses is based on a recent ECDA project conducted by TWI Ltd. for the Middle Eastern Oil Company (MEOC). To address the challenges highlighted above, Quantile Regression (QR) was used to comprehensively characterise the underlying distribution of the dependent variable. This can be effective for example, when determining the different effect of contributing variables towards different sizes of TCDA (different quantiles). Another useful advantage is that the technique is robust to outliers due to its reliance on absolute errors. With the traditional mean regression, the effect of contributing variables towards other quantiles of the dependent variable is ignored. Furthermore, the OLS involves the squaring of errors which makes it less robust to outliers. Other forms of QR such as the Bayesian Quantile Regression (BQR) which has the advantage of supplementing future inspection projects with prior data and the Logistic Quantile Regression (LQR) which ensures the prediction of the dependent variable is within its specified bounds was applied to the MEOC dataset. The novelty of research lies in the approaches (methods) taken by the author in producing the models highlighted above. The summary of such novelty includes: * The use of non-linear Quantile Regression (QR) with interacting variables for TCDA prediction. * The application of a regularisation procedure (LASSO) for the generalisation of the TCDA prediction model.* The usage of the Bayesian Quantile Regression (BQR) technique to estimate the %IR and TCDA. * The use of Logistic Regression as a guideline towards the probability of excavation * And finally, the use of Logistic Quantile Regression (LQR) in ensuring the predicted values are within bounds for the prediction of the %IR and POPD. Novel findings from this thesis includes: * Some degree of relationship between the DCVG technique (%IR readings) and corrosion dimension. The results of the relationship between TCDA and POPD highlights a negative trend which further supports the idea that %IR has some relation to corrosion. * Based on the findings from Chapter 4, 5 and 6 suggests that corrosion activity rate is more prominent than the growth of TCDA at its median depth. It is therefore suggested that for this set of pipelines (those belonging to MEOC) repair of coating defects should be done before the coating defect has reached its median size. To the best of the Author's knowledge, the process of employing such approaches has never been applied before towards any ECDA data. The findings from this thesis also shed some light into the stochastic nature of the evolution of corrosion pits. This was not known before and is only made possible by the usage of the approaches highlighted above. The resulting models are also of novelty since no previous model has ever been developed based on the said methods. The contribution to knowledge from this research is therefore the greater understanding of relationship between variables stated above (TCDA, %IR and POPD). With this new knowledge, one has the potential to better prioritise location of excavation and better interpret DCVG indications. With the availability of ECDA data, it is also possible to predict the magnitude of corrosion activity by using the models developed in this thesis. Furthermore, the knowledge gained here has the potential to translate into cost saving measures for pipeline operators while ensuring safety is properly addressed.

Quantile Regression, as introduced by Koenker, R. and Bassett, G. (1978), provides a complete picture of the relationship between the response variable and covariates by estimating a family of conditional quantile functions. Also, it offers a natural solution to challenges such as; homoscedasticity and sometimes unrealistic normality assumption in the usual conditional mean regression. Most of the results for quantile regression are based on simple random sampling (SRS). In this thesis, we study the quantile regression with rank-based sampling methods. Rank-based sampling methods have a wide range of applications in medical, ecological and environmental research, and have been shown to perform better than SRS in estimating several population parameters. We propose a new objective function which takes into account the ranking information to estimate the unknown model parameters based on the maxima or minima nomination sampling designs. We compare the mean squared error of the proposed quantile regression estimates using maxima (or minima) nomination sampling design and observe that it provides higher relative e ciency when compared with its counterparts under SRS design for analyzing the upper (or lower) tails of the distribution of the response variable. We also evaluate the performance of our proposed methods when ranking is done with error. / February 2017

Thesis advisor: Zhijie Xiao / My dissertation research examines empirical issues in financial economics with a special focus on the application of quantile regression. This dissertation is composed by two self-contained papers, which center around: (1) robust estimation of conditional idiosyncratic volatility of asset returns to offer better understanding of market microstructure and asset pricing anomalies; (2) implementation of coherent risk measures in portfolio selection and financial risk management. The first chapter analyzes the roles of idiosyncratic risk and firm-level conditional skewness in determining cross-sectional returns. It is shown that the traditional EGARCH estimates of conditional idiosyncratic volatility may bring significant finite sample estimation errors in the presence of non-Gaussianity, casting strong doubt on the positive intertemporal idiosyncratic volatility effect reported in the literature. We propose an alternative estimator for conditional idiosyncratic volatility for GARCH-type models. The proposed estimation method does not require error distribution assumptions and is robust non-Gaussian innovations. Monte Carlo evidence indicates that the proposed estimator has much improved sampling performance over the EGARCH MLE in the presence of heavy-tail or skewed innovations. Our cross-section portfolio analysis demonstrates that the idiosyncratic volatility puzzle documented by Ang, Hodrick, Xiang and Zhang (2006) exists intertemporally, i.e., stocks with high conditional idiosyncratic volatility earn abnormally low returns. We solve the major piece of this puzzle by pointing out that previous empirical studies have failed to consider both idiosyncratic variance and individual conditional skewness in determining cross-sectional returns. We introduce a new concept - the "expected windfall" - as an alternative measure of conditional return skewness. After controlling for these two additional factors, cross-sectional regression tests identify a positive relationship between conditional idiosyncratic volatility and expected returns for over 99% of the total market capitalization of the NYSE, NASDAQ, and AMEX stock exchanges. The second chapter examines portfolio allocation decision for investors with general pessimistic preferences (GPP) regarding downside risk aversion and out-performing benchmark returns. I show that the expected utility of pessimistic investors can be robustly estimated within a quantile regression framework without assuming asset return distributions. The asymptotic properties of the optimal portfolio weights are derived. Empirically, this method is introduced to construct the optimal fund of CSFB/Tremont hedge-fund indices. Both the in-sample and out-of-sample backtesting results confirm that the optimal mean-GPP portfolio outperforms the mean-variance and mean-conditional VaR portfolios. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.