We develop a generally applicable framework for constructing e¢ cient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a …xed number of quantiles, we derive an explicit upper bound on the di...

In many engineering applications, data samples are expensive to get and limited in number. In such a difficult context, this paper shows how classification based on Reproducing Kernel Hilbert Space (RKHS) can be used in conjunction with Extreme Value Theory (EVT) to estimate extreme multivariate quantiles and small probabilities of failure. For estimating extreme multivariate quantiles, RKHS on...

Managing telecommunication networks involves collecting and analyzing large amounts of statistical data. The standard approach to estimating quantiles involves capturing all the relevant data (what may require significant storage/processing capacities), and performing an off-line analysis (what may delay management actions). It is often essential to estimate quantiles as the data are collected,...

Designs for 0tting a generalized linear model depend on the unknown parameters of the model. The use of any design optimality criterion would therefore require some prior knowledge of the parameters. In this article, a graphical technique is proposed for comparing and evaluating designs for a logistic regression model. Quantiles of the scaled mean-squared error of prediction are obtained on con...

In data warehousing applications, numerous OLAP queries involve the processing of holistic operations such as computing the "top N", median, etc. Efficient implementations of these operations are hard to come by. Several algorithms have been proposed in the literature that estimate various quantiles of disk-resident data. Two such recent algorithms are based on sampling. In this paper we presen...

The need to summarize data has been around since the earliest days of data processing. Large volumes of raw, unstructured data easily overwhelm human ability to comprehend or digest, and tools that help identify the major underlying trends or patterns in data have enormous value. Quantiles characterize distributions of real world data sets in ways that are less sensitive to outliers than simple...

[1] A theory for quantile based hydrologic model selection and model structure deficiency assessment is presented. The paper demonstrates that the degree to which a model selection problem is constrained by the model structure (measured by the Lagrange multipliers of the constraints) quantifies structural deficiency. This leads to a formal definition of model structure deficiency (or rigidity)....