• Corpus ID: 247411390

Single-index models for extreme value index regression

  title={Single-index models for extreme value index regression},
  author={Takuma Yoshida},
Since the extreme value index (EVI) controls the tail behaviour of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent developments in the estimation of EVI along with covariates have been in the context of nonparametric regression. However, for the large dimension of covariates, the fully nonparametric estimator faces the problem of the curse of dimensionality. To avoid this, we apply the single index model to EVI regression under Pareto… 

Figures and Tables from this paper



A nonparametric estimator for the conditional tail index of Pareto-type distributions

The tail index is an important parameter in the whole of extreme value theory. In this article, we consider the estimation of the tail index in the presence of a random covariate, where the

Inference for single-index quantile regression models with profile optimization

Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a

Tail Index Regression

In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution. Under Pareto-type distributions, we employ the logarithmic function to link


For the past two decades, the single-index model, a special case of pro- jection pursuit regression, has proven to be an efficient way of coping with the high-dimensional problem in nonparametric

Extreme Quantile Estimation Based on the Tail Single-index Model

It is important to quantify and predict rare events that have huge societal effects. Existing works on analyzing such events mainly rely on either inflexible parametric models or nonparametric models


Under mild conditions, it is shown that the simple linear quantile regression offers a consistent estimate of the index parameter vector, and the resulting estimator of the quantile function performs asymptotically as efficiently as if the true value of theindex vector were known.

Nonparametric regression estimation of conditional tails: the random covariate case

We present families of nonparametric estimators for the conditional tail index of a Pareto-type distribution in the presence of random covariates. These families are constructed from locally weighted

Efficient estimation in single index models through smoothing splines

A method to compute the penalized least squares estimators (PLSEs) of the parametric and the nonparametric components given independent and identically distributed (i.i.d.) data is developed and it is proved the consistency and the rates of convergence of the estimators.

Single-index quantile regression

Semiparametric Tail Index Regression

Abstract–Understanding why extreme events occur is often of major scientific interest in many fields. The occurrence of these events naturally depends on explanatory variables, but there is a severe