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Mac problem with supersync 6.23/11/2023 An iterative least asymmetrically weighted squares algorithm is developed for computation. The principal component functions are modeled as splines and are estimated by minimizing a penalized asymmetric loss measure. Our approach assumes that the generalized regression quantiles share some common features that can be summarized by a small number of principal component functions. We develop a functional data analysis approach to jointly estimate a family of generalized regression quantiles. Generalized regression quantiles, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. Guo, Mengmeng Zhou, Lan Huang, Jianhua Z. Quantile regression can provide evidence for a statistical relationship between two variables even.įunctional data analysis of generalized regression quantiles Quantile regression can therefore detect whether the partial effect of a regressor on the conditional quantiles is the same for all quantiles or differs across quantiles. While the latter only focuses on one aspect of the conditional distribution of the dependent variable, the mean, quantile regression provides more detailed insights. ![]() Quantile regression is emerging as a popular statistical approach, which complements the estimation of conditional mean models. This is followed by briefly sketching the underlying statistical model for linear quantile regression based. We provide a short informal introduction into the principle of quantile regression which includes an illustrative application from empirical labor market research. Then the theory is applied to a time series of returns of a stock in. Moreover, it is shown that many well-known time series models satisfy our conditions. Consistent estimators of the asymptotic variance are introduced, which render possible the construction of asymptotic confidence intervals for the extreme quantiles. The asymptotic normality of a class of estimators for extreme quantiles is established under mild structural conditions on the observed stationary eta-mixing time series. Here, it turns out that we obtain learning rates which are optimal in a min-max sense under some standard assumptions on the regularity of the conditional quantile functionĮxtreme quantile estimation for dependent data with applications to finance To illustrate the use of the established inequalities, we then use them to establish an oracle inequality for support vector machines that use the pinball loss. These inequalities, which hold under mild assumptions on the data-generating distribution, are then used to establish so-called variance bounds which recently turned out to play an important role in the statistical analysis of (modified) empirical risk minimization approaches. The goal of this work is to fill this gap by establishing inequalities that describe how close approximate pinball risk minimizers are to the corresponding conditional quantile. So far, however, only little work has been done to quantify the efficiency of this tool for non-parametric (modified) empirical risk minimization approaches. Using the so-called pinball loss for estimating conditional quantiles is a well-known tool in both statistics and machine learning. International Nuclear Information System (INIS) the capabilities of the elaborated neural network are also given.Įstimating conditional quantiles with the help of the pinball loss The task of estimating conditional quantiles is related to Bayes point estimation whereby a broad range of applications within engineering, economics and management can be suggested. ![]() for the design of a variety of different neural networks, some of which are considered in detail. The constructed structure constitutes a basis. A basic structure is developed using the methodology of kernel estimation, and a theory guaranteeing con-sistency on a mild set of assumptions is provided. The problem of estimating conditional quantiles using neural networks is investigated here. Estimation of Conditional Quantile using Neural Networks
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