Multivariate geometric expectiles

Quantiles, Expectiles and Splines

A time-varying quantile can be …tted by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modi…ed state space signal extraction algorithm. It is shown that such quantiles satisfy the de…ning property of …xed quantiles in having the appropriate number of observations above and below. Like quantiles, time-varying expectiles can be estima...

Multivariate Statistical Analysis: a Geometric Perspective

Multivariate normal approximation in geometric probability

x ξxδx where the sum is over points x of a Poisson point process of intensity λ on a bounded region in d-space, and ξx is a functional determined by the Poisson points near to x, i.e. satisfying an exponential stabilization condition, along with a moments condition (examples include statistics for proximity graphs, germ-grain models and random sequential deposition models). A known general resu...

Relating quantiles and expectiles under weighted-symmetry

Recently, quantiles and expectiles of a regression function have been investigated by several authors. In this work, we give a suu-cient condition under which a quantile and an expectile coincide. We extend some classical results known for mean, median and symmetry to expectiles, quantiles and weighted-symmetry. We also study split-models and sample estimators of expectiles.

Expectiles for subordinated Gaussian processes with applications

In this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process. These estimators are based on sample expectiles of discrete variations of a sample path of the fBm process. In order to derive the statistical properties of the proposed estimators, we establish asymptotic results for sample expectiles of subordinated stationary Gaussian ...