A New Kernel Estimator of Copulas Based on Beta Quantile Transformations

A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0,1). For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, which increases the difficulty of the estimation and, in practice, the bias boundary correction might not provide the desired improvement. A quantile transformation of marginals is a way to improve the classical kernel approach. This paper shows a Beta quantile transformation to be optimal and analyses a kernel estimator based on this transformation. Furthermore, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves alternative kernel estimators of copulas. We illustrate our proposal with a financial risk data analysis.

Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

Strong consistency of regression function estimator with martingale difference errors

In this paper, we consider the regression model with fixed design: Y i = g ( x i ) + ε i {Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i} , 1 ≤ i ≤ n 1\le i\le n , where { x i } \left\{{x}_{i}\right\} are the nonrandom design points, and { ε i } \left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and g g is an unknown function. Nonparametric estimator g n ( x ) {g}_{n}\left(x) of g ( x ) g\left(x) will be introduced and its strong convergence properties are established.

Strong convergence of the functional nonparametric relative error regression estimator under right censoring

In this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a functional explanatory variable, in the case of a scalar censored response, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional censored data. We establish the strong almost complete convergence rate and asymptotic normality of these estimators. A simulation study is performed to illustrate and compare the higher predictive performances of our proposed method to those obtained with standard estimators.

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

In this work, we treat a prediction problem via the conditional hazard function of a scalar response variable Y given a functional random variable X by using the local linear technique. The main purpose of this paper is to investigate the asymptotic normality of the nonparametric estimator of the conditional hazard function, under some general conditions. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our method than the standard kernel method

NONPARAMETRIC EULER EQUATION IDENTIFICATION AND ESTIMATION

We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identification analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo experiment shows a satisfactory finite sample performance for our estimators.

Characteristic-Sorted Portfolios: Estimation and Inference

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of five or ten. To illustrate the relevance of our results, we revisit the size and momentum anomalies.

A Shift-Dependent Measure of Extended Cumulative Entropy and Its Applications in Blind Image Quality Assessment

Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy (ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past version. These results contain stochastic order, upper and lower bounds, the symmetry property and some relationships with other reliability functions. We also discuss some properties of conditional weighted ECE under some assumptions. Finally, we propose a nonparametric estimator of this new measure and study its practical results in blind image quality assessment.