Generalized Quantile Treatment Effect: A Flexible Bayesian Approach Using Quantile Ratio Smoothing

We propose a new general approach for estimating the effect of a binary treatment on a continuous and potentially highly skewed response variable, the generalized quantile treatment effect (GQTE). The GQTE is defined as the difference between a function of the quantiles under the two treatment conditions. As such, it represents a generalization over the standard approaches typically used for estimating a treatment effect (i.e., the average treatment effect and the quantile treatment effect) because it allows the comparison of any arbitrary characteristic of the outcome's distribution under the two treatments. Following Dominici et al. (2005), we assume that a pre-specified transformation of the two quantiles is modeled as a smooth function of the percentiles. This assumption allows us to link the two quantile functions and thus to borrow information from one distribution to the other. The main theoretical contribution we provide is the analytical derivation of a closed form expression for the likelihood of the model. Exploiting this result we propose a novel Bayesian inferential methodology for the GQTE. We show some finite sample properties of our approach through a simulation study which confirms that in some cases it performs better than other nonparametric methods. As an illustration we finally apply our methodology to the 1987 National Medicare Expenditure Survey data to estimate the difference in the single hospitalization medical cost distributions between cases (i.e., subjects affected by smoking attributable diseases) and controls.Comment: Published at http://dx.doi.org/10.1214/14-BA922 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Time-Varying Quantiles

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide information on various aspects of a time series, including dispersion, asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks

Confidence regions for high quantiles of a heavy tailed distribution

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.Comment: Published at http://dx.doi.org/10.1214/009053606000000416 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org