Multiariate Wavelet-based sahpe preserving estimation for dependant observation

We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations.Conditional quantile; time series; shape preserving wavelet estimation; B-splines; multivariate process

VAR for VaR: measuring systemic risk using multivariate regression quantiles.

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market returns data to analyse spillovers in the values at risk (VaR) of different financial institutions. We construct impulse-response functions for the quantile processes of a sample of 230 financial institutions around the world and study how financial institution-specific and system-wide shocks are absorbed by the system.Quantile impulse-responses; spillover; codependence; CAViaR

Quantile contours and allometric modelling for risk classification of abnormal ratios with an application to asymmetric growth-restriction in preterm infants

We develop an approach to risk classification based on quantile contours and allometric modelling of multivariate anthropometric measurements. We propose the definition of allometric direction tangent to the directional quantile envelope, which divides ratios of measurements into half-spaces. This in turn provides an operational definition of directional quantile that can be used as cutoff for risk assessment. We show the application of the proposed approach using a large dataset from the Vermont Oxford Network containing observations of birthweight (BW) and head circumference (HC) for more than 150,000 preterm infants. Our analysis suggests that disproportionately growth-restricted infants with a larger HC-to-BW ratio are at increased mortality risk as compared to proportionately growth-restricted infants. The role of maternal hypertension is also investigated.Comment: 31 pages, 3 figures, 8 table

Extreme Value Theory Approach to Simultaneous Monitoring and Thresholding of Multiple Risk Indicators

Risk assessments often encounter extreme settings with very few or no occurrences in reality.Inferences about risk indicators in such settings face the problem of insufficient data.Extreme value theory is particularly well suited for handling this type of problems.This paper uses a multivariate extreme value theory approach to establish thresholds for signaling levels of risk in the context of simultaneous monitoring of multiple risk indicators.The proposed threshold system is well justified in terms of extreme multivariate quantiles, and its sample estimator is shown to be consistent.As an illustration, the proposed approach is applied to developing a threshold system for monitoring airline performance measures.This threshold system assigns different risk levels to observed airline performance measures.In particular, it divides the sample space into regions with increasing levels of risk.Moreover, in the univariate case, such a thresholding technique can be used to determine a suitable cut-off point on a runway for holding short of landing aircrafts.This cut-off point is chosen to ensure a certain required level of safety when allowing simultaneous operations on two intersecting runways in order to ease air traffic congestion.Extreme value theory;extreme quantile;multiple risk indicators;multivariate quantile;rare event;statistics of extremes;threshold system

An Ordinal Approach to Risk Measurement

In this short note, we aim at a qualitative framework for modeling multivariate risk. To this extent, we consider completely distributive lattices as underlying universes, and make use of lattice functions to formalize the notion of risk measure. Several properties of risk measures are translated into this general setting, and used to provide axiomatic characterizations. Moreover, a notion of quantile of a lattice-valued random variable is proposed, which shown to retain several desirable properties of its real-valued counterpart.lattice; risk measure; Sugeno integral; quantile.