Quantile-based Approach Research Articles

Stress-strength reliability: a quantile approach

In reliability modelling and analysis of systems, quantile functions play a significant role when the distribution function under consideration does not possess an analytically tractable form, though the corresponding quantile function has an explicit form. In the present paper, we propose a quantile-based approach for stress-strength reliability of a system. We also introduce the quantile versions of stress-strength reliability for residual lifetime random variables. The effect of monotone transformations and some characterizations of the proposed measures are discussed. The reliability of multi-component stress-strength systems based on quantiles is also considered.

Green bonds as hedging assets before and after COVID: A comparative study between the US and China

The COVID pandemic reveals the fragility of the global financial market during rare disasters. Conventional safe-haven assets like gold can be used to hedge against ordinary risks, but tail dependence can substantially reduce the hedging effectiveness. In contrast, green bonds focus on long-term, sustainable investments, so they become an important hedging tool against climate risks, financial risks, as well as rare disasters like COVID. The copula approach based on the TGARCH model is applied to estimate the joint distributions between green bonds and selected financial assets in both US and China. The quantile-based approach is also performed to offer a robustness check on tail dependence. The results show that all assets in the two countries have thick tails and tail dependence with time-varying features. The hedging effectiveness does decline during the COVID pandemic, but it is the hedging effectiveness against tail risks rather than against normal risks. It is argued that green bonds play a significant role in hedging against rare disasters especially in forex markets. It is also found that green bonds in the US and China converge in many aspects, suggesting a smaller cross-country difference than cross-asset difference.

Powerful and robust non-parametric association testing for microbiome data via a zero-inflated quantile approach (ZINQ)

BackgroundIdentification of bacterial taxa associated with diseases, exposures, and other variables of interest offers a more comprehensive understanding of the role of microbes in many conditions. However, despite considerable research in statistical methods for association testing with microbiome data, approaches that are generally applicable remain elusive. Classical tests often do not accommodate the realities of microbiome data, leading to power loss. Approaches tailored for microbiome data depend highly upon the normalization strategies used to handle differential read depth and other data characteristics, and they often have unacceptably high false positive rates, generally due to unsatisfied distributional assumptions. On the other hand, many non-parametric tests suffer from loss of power and may also present difficulties in adjusting for potential covariates. Most extant approaches also fail in the presence of heterogeneous effects. The field needs new non-parametric approaches that are tailored to microbiome data, robust to distributional assumptions, and powerful under heterogeneous effects, while permitting adjustment for covariates.MethodsAs an alternative to existing approaches, we propose a zero-inflated quantile approach (ZINQ), which uses a two-part quantile regression model to accommodate the zero inflation in microbiome data. For a given taxon, ZINQ consists of a valid test in logistic regression to model the zero counts, followed by a series of quantile rank-score based tests on multiple quantiles of the non-zero part with adjustment for the zero inflation. As a regression and quantile-based approach, the method is non-parametric and robust to irregular distributions, while providing an allowance for covariate adjustment. Since no distributional assumptions are made, ZINQ can be applied to data that has been processed under any normalization strategy.ResultsThorough simulations based on real data across a range of scenarios and application to real data sets show that ZINQ often has equivalent or higher power compared to existing tests even as it offers better control of false positives.ConclusionsWe present ZINQ, a quantile-based association test between microbiota and dichotomous or quantitative clinical variables, providing a powerful and robust alternative for the current microbiome differential abundance analysis.9TU_kfqMVHfUkABshrfuDQVideo

Modelling the COVID-19 Infection Trajectory: A Piecewise Linear Quantile Trend Model

AbstractWe propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by COVID-19 infection curves) and automatically delivers both point and interval forecasts with minimal assumptions. Building on a self-normalized (SN) test statistic, this paper proposes a novel segmentation algorithm for multiple change-point estimation. Theoretical guarantees such as segmentation consistency are established under mild and verifiable assumptions. Using the proposed method, we analyse the COVID-19 infection curves in 35 major countries and discover patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. A simple change-adaptive two-stage forecasting scheme is further designed to generate short-term prediction of COVID-19 cumulative new cases and is shown to deliver accurate forecast valuable to public health decision-making.

Quantile Risk Premiums

This paper studies quantile-based moment premiums. The quantile-based approach delivers robust and flexible alternatives to premiums for variance, skewness and kurtosis risk and enhances our understanding of the pricing of risks in derivatives markets. To quantify these premiums, the paper introduces a new class of synthetic derivatives contracts: quantile swaps. Such contracts mimic quantile-based moment measures from robust statistics. An empirical study of index options detects two distinct premiums for dispersion and asymmetry, but no premium for steepness. The premium for dispersion can be explained by traditional moment risk premiums, whereas the asymmetry premium is a novel premium that our approach is able to detect. This finding contrasts markedly with results obtained with traditional moment swaps, and warns us to interpret moment premiums cautiously.

Relation Between Cumulative Residual Entropy and Excess Wealth Transform with Applications to Reliability and Risk

Abstract Dynamic cumulative residual entropy is a new addition to the class of information measures. In the present paper, we study its relationship with excess wealth transform and derive some identities connecting the two using the quantile-based approach. Some theoretical results that have applications to infer ageing properties and risk measures are presented. These are used as tools to analyse real life data.

The Quantile Frailty Index: A Cutpoint-Free Approach to Biomarker-Based Health Assessment

We develop a frailty index (FI) from continuous valued biomarker measurements that does not use thresholds to binarize deficits. In this work we construct a quantile frailty index (FI-Q) directly from risk quantiles, without binarizing the deficits. FI-Q is the average risk quantile for an individual in the population with respect to the set of measured biomarkers. We show that FI-Q predicts adverse health outcomes better than either a quantile-based cutpoint approach or an FI-Lab method used in previous studies. We also address practical questions such as how to use longitudinal data. We use data from the English Longitudinal Study of Ageing (ELSA) for longitudinal analysis and data from the National Health and Nutrition Examination Survey (NHANES) and the Canadian Study of Health and Aging (CSHA) to compare predictive value of FI-QM with previous FI-Lab studies.

Assessing Systemic Risk Based on the CARE System

Expectile is a coherent and elicitable risk measure that responds to the catastrophic losses more properly than a quantile-based approach. In this paper, we extend the univariate conditional autoregressive expectile (CARE) model of Kuan et al. (2009) to a multivariate CARE system to model the systemic risk of financial institutions. We propose an estimation method and derive its asymptotic properties. In the empirical study, we model the 12-variate CARE system on the global systemically important banks' (G-SIBs') returns for the period Jan 2015 to Jun 2020. We show that the CARE system identifies the asymmetric transmissions of the banks' systemic risk, i.e., the square positive and the square negative lagged returns generate different patterns of associations in the expectile connectedness. In addition, the out-of-sample Expectile-based Value-at-Risk prediction captures the 2020 mid-March US trading curb turbulence.

FUNCTION-ON-SCALAR QUANTILE REGRESSION WITH APPLICATION TO MASS SPECTROMETRY PROTEOMICS DATA.

Mass spectrometry proteomics, characterized by spiky, spatially heterogeneous functional data, can be used to identify potential cancer biomarkers. Existing mass spectrometry analyses utilize mean regression to detect spectral regions that are differentially expressed across groups. However, given the inter-patient heterogeneity that is a key hallmark of cancer, many biomarkers are only present at aberrant levels for a subset of, not all, cancer samples. Differences in these biomarkers can easily be missed by mean regression, but might be more easily detected by quantile-based approaches. Thus, we propose a unified Bayesian framework to perform quantile regression on functional responses. Our approach utilizes an asymmetric Laplace working likelihood, represents the functional coefficients with basis representations which enable borrowing of strength from nearby locations, and places a global-local shrinkage prior on the basis coefficients to achieve adaptive regularization. Different types of basis transform and continuous shrinkage priors can be used in our framework. A scalable Gibbs sampler is developed to generate posterior samples that can be used to perform Bayesian estimation and inference while accounting for multiple testing. Our framework performs quantile regression and coefficient regularization in a unified manner, allowing them to inform each other and leading to improvement in performance over competing methods as demonstrated by simulation studies. We also introduce an adjustment procedure to the model to improve its frequentist properties of posterior inference. We apply our model to identify proteomic biomarkers of pancreatic cancer that are differentially expressed for a subset of cancer patients compared to the normal controls, which were missed by previous mean-regression based approaches. Supplementary materials for this article are available online.

A generic prediction interval estimation method for quantifying the uncertainties in ultra-short-term building cooling load prediction

Ultra-short-term building cooling load prediction is useful for optimal operations of building energy systems. The uncertainties of predicted cooling loads affect the reliability of the optimal operations significantly. This paper proposes a generic prediction interval estimation method to describe the uncertainties quantitatively. The basic idea is that the residual of a predicted cooling load would follow the same distribution as the residuals of historical predicted cooling loads of the similar operating condition. A Chebyshev distance-based agglomerative hierarchical clustering approach is proposed to gather historical prediction residuals of similar operating conditions into the same cluster. A quantile-based approach is proposed to estimate the prediction interval of a predicted cooling load using the cluster of the most similar operating condition. To evaluate the proposed method, an artificial neural network-based cooling load prediction model is trained to predict the cooling loads of a real building. The prediction intervals of the predicted cooling loads are then estimated using the proposed method. The results show that the estimated prediction intervals of the predicted cooling loads are very reliable.

Spatio-temporal patterns of larval fish settlement in the northwestern Mediterranean Sea

Most coastal fish species spend their early life stages in the pelagic environment, before settling in coastal habitats. The variability in the arrival of larvae to coastal habitats provides information on the species’ biology and recruitment potential. To explore the dynamics of larval fish supply to coastal habitats in the NW Mediterranean Sea, 13 sites were monitored using light-traps, from July 2012 to December 2015. Most variation in catches per unit effort (CPUE) among topographic basins and species were statistically significant for high (quantile 75%) and very high (quantile 90%) catches only. At the yearly scale, CPUE displayed strong seasonality, and 3 main species assemblages were detected in late spring-early summer, summer and late autumn-early winter. At the monthly scale, CPUE were higher around the new moon for all quantiles and temporally autocorrelated at a lag of ~28 d. Larval supply also varied spatially with site-specific associations and with riverine influence. Altogether, these results confirm that the previously described patterns of larval supply observed in tropical and subtropical environments (e.g. the high variability at all spatial and temporal scales and the strong influence of the moon) also apply to Mediterranean fish assemblages. Our quantile-based approach demonstrated that the larval supply in the NW Mediterranean Sea is a solid candidate for monitoring the state of the marine ecosystems, highlighting the need to continue such time series.

A Multifidelity Quantile-Based Approach for Confidence Sets of Random Excursion Sets with Application to Ice-Sheet Dynamics

In this paper, we address uncertainty quantification of physics-based computational models when the quantity of interest concerns geometrical characteristics of their spatial response. Within the p...

A Quantile-Based Approach for Transmission Expansion Planning

Transmission expansion planning is an integral part of power system planning and consists of generating and selecting transmission proposals for maintaining sufficient transmission capacity to satisfy the electric load. Specifically, the desire to increase the use of renewable energy has exposed the limitations of transmission networks and has elevated the importance of transmission expansion planning. However, considering the random nature of renewable sources in conjunction with the power outages makes the planning process very challenging. We present a new procedure for selecting the best transmission enhancement proposal from a set of finite proposals under uncertainty. The selection is based on the quantile value of the cost of each proposal. The procedure uses a combination of simulation and optimization and considers randomness of uncertain parameters of the network. Wind energy and network contingencies are among the considered random parameters. The procedure is suitable for evaluating investor-initiated enhancement proposals by the planner and statistically guarantees satisfaction of the planner's prespecified probability of correct selection since simulation is involved. Two IEEE test networks are used for demonstrating the implementation of the new procedure. For these two test networks, solutions obtained using quantiles are compared with those when the expected value or a weighted combination of the expected value and the conditional-value-at-risk are used as selection criteria. The comparison shows that similar to the use of conditional-value-at-risk, the selection is sensitive to the choice of the quantile.

Oil market conditions and sovereign risk in MENA oil exporters and importers

We analyze for the first time how various levels of oil returns and oil volatility changes affect sovereign risk in static and time-varying settings. Empirical analyses involve daily data from February 14, 2011 to November 23, 2018 covering a sample of MENA oil-exporters and importers. The results from a quantile-based approach show that the sovereign risk of MENA oil-exporters and importers is directionally predicted by shocks in oil prices and oil volatility, especially during the oil crash of 2014–2016. Overall, the impact of oil returns and volatility changes occur in a very short time span, that is within one day lag, and the quantile specific reactions of sovereign risk spreads are time varying. The impact of oil returns is asymmetric across quantiles. The results hold when we control for stock market returns. The findings have implications for investors in terms of portfolio and risk management. Importantly, the findings are useful to policymakers for sovereign risk management decisions, the cost of sovereign borrowing, and the market timing of debt issuance. Finally, the findings matter to bankers given that central and domestic banks hold large amounts of sovereign debt, which makes banking systems particularly exposed to their own sovereign stress.

A global record of annual urban dynamics (1992–2013) from nighttime lights

The nighttime light (NTL) observations from Defense Meteorological Satellite Program/Operational Linescane System (DMSP/OLS) offer great potentials to study urban dynamics from regional to global scales, for more than two decades. In this paper, we presented a new approach to develop spatially and temporally consistent global urban maps from 1992 to 2013, using the DMSP/OLS NTL observations. First, potential urban clusters were delineated using the NTL data and a segmentation method. Then, a quantile-based approach was used to remove rural and suburban areas sequentially in the potential urban clusters. Finally, the derived series of urban extents in the entire study period (1992–2013) were improved for temporal consistency. We found the percentage of global urban areas relative to the world's land surface area increased from 0.23% in 1992 to 0.53% in 2013. Asia is the continent with the most significant urban growth, worldwide. The time series of global urban maps were evaluated for the spatial agreement and temporal consistency using a variety of widely used independent land-cover products. This evaluation indicates that the proposed approach is robust and performs well in deriving global urban dynamics across different spatial scales, i.e., cluster, province (or state), country, and region. Moreover, this quantile-based approach is advantageous, compared with other methods used in previous studies, because it does not require additional data for enhancement or calibration. The new time series of urban maps from this study offer a new dataset for studying global urbanization during the past decades and unique information to explore potential future trajectories of urban development, which appears to be distinct for different nations/regions, globally. Such information is pre-requisite for achieving the sustainable development goals, and associated targets, during ensuing decades.

Monetary Policy Reaction Functions of the TICKs: A Quantile Regression Approach

ABSTRACTThis study investigates how Taiwan, India, China, and Korea (TICKs) set interest rates in the context of policy reaction functions using a quantile-based approach. Our results indicate the tendency of a milder response to inflation at low interest rates and greater response at higher quantiles of interest rates, where inflation is presumably higher than desired for China and South Korea. While the response to inflation over the quantiles is significant for India, yet the Taylor principle is less likely to hold. For Taiwan, the results imply that another instrument is employed to deal with its official managed floating currency.

An On-Line Planner for POMDPs with Large Discrete Action Space: A Quantile-Based Approach

Making principled decisions in the presence of uncertainty is often facilitated by Partially Observable Markov Decision Processes (POMDPs). Despite tremendous advances in POMDP solvers, finding good policies with large action spaces remains difficult. To alleviate this difficulty, this paper presents an on-line approximate solver, called Quantile-Based Action Selector (QBASE). It uses quantile-statistics to adaptively evaluate a small subset of the action space without sacrificing the quality of the generated decision strategies by much. Experiments on four different robotics tasks with up to 10,000 actions indicate that QBASE can generate substantially better strategies than a state-of-the-art method.

Quantile and mean value measures of search process complexity

Performance measures of metaheuristic algorithms assess the quality of a search process by statistically analysing its performance. Such criteria serve two purposes: they provide the verdict on which algorithm is better for what task, and they help applying an algorithm on a given task in the most effective way. The latter goal may be achieved by an appropriate restart strategy of the search process. Furthermore, these criteria are traditionally based on analysis of the search step mean value. Our aim is to elaborate the mean value analysis as well, but via a novel and more general quantile-based analytic approach, which can be used to define new measures. We prove and demonstrate this purpose on three quantile-based performance measures.

Using variant databases for variant prioritization and to detect erroneous genotype-phenotype associations

BackgroundIn the search for novel causal mutations, public and/or private variant databases are nearly always used to facilitate the search as they result in a massive reduction of putative variants in one step. Practically, variant filtering is often done by either using all variants from the variant database (called the absence-approach, i.e. it is assumed that disease-causing variants do not reside in variant databases) or by using the subset of variants with an allelic frequency > 1% (called the 1%-approach). We investigate the validity of these two approaches in terms of false negatives (the true disease-causing variant does not pass all filters) and false positives (a harmless mutation passes all filters and is erroneously retained in the list of putative disease-causing variants) and compare it with an novel approach which we named the quantile-based approach. This approach applies variable instead of static frequency thresholds and the calculation of these thresholds is based on prior knowledge of disease prevalence, inheritance models, database size and database characteristics.ResultsBased on real-life data, we demonstrate that the quantile-based approach outperforms the absence-approach in terms of false negatives. At the same time, this quantile-based approach deals more appropriately with the variable allele frequencies of disease-causing alleles in variant databases relative to the 1%-approach and as such allows a better control of the number of false positives.We also introduce an alternative application for variant database usage and the quantile-based approach. If disease-causing variants in variant databases deviate substantially from theoretical expectancies calculated with the quantile-based approach, their association between genotype and phenotype had to be reconsidered in 12 out of 13 cases.ConclusionsWe developed a novel method and demonstrated that this so-called quantile-based approach is a highly suitable method for variant filtering. In addition, the quantile-based approach can also be used for variant flagging. For user friendliness, lookup tables and easy-to-use R calculators are provided.

A quantile-based Tsallis-[formula omitted] divergence

In the present paper, we propose a quantile version of Tsallis-α divergence and study its various properties. Examples are given in support of the importance of proposed quantile-based approach over traditional distribution-based approach. We consider quantile-based Tsallis-α divergence when random variables are truncated from both ends. Properties including bounds and inequalities are studied. Characterizations are obtained. The effects of transformations are discussed. Further, as a special case of the quantile-based doubly truncated Tsallis-α divergence, we provide a brief discussion on quantile-based residual and past Tsallis-α divergence.