Copulas are full measures of dependence among components of random vectors. Unlike the marginal and the joint distributions, which are directly observable, a copula is a hidden dependence structure that couples a joint distribution with its marginals. This makes the task of proposing a parametric copula model non-trivial and is where a nonparametric estimator can play a significant role. In thi...

In this paper, we propose an adaptation of the Parzen Rosenblatt cumulative distribution function estimator that uses maxitive kernels. The result of this estimator, on every point of the domain of F , the cumulative distribution to be estimated, is interval valued instead of punctual valued. We prove the consistency of our approach with the classical Parzen Rosenblatt estimator, since, accordi...

For the problem of estimation of Money demand model of Pakistan, money supply (M1) shows heteroscedasticity of the unknown form. For estimation of such model we compare two adaptive estimators with ordinary least squares estimator and show the attractive performance of the adaptive estimators, namely, nonparametric kernel estimator and nearest neighbour regression estimator. These comparisons a...

The paper evaluates the properties of nonparametric estimators of the expected shortfall, an increasingly popular risk measure in financial risk management. It is found that the existing kernel estimator based on a single bandwidth does not offer variance reduction, which is surprising considering that kernel smoothing reduces the variance of estimators for the value at risk and the distributio...

This paper investigates nonparametric estimation of density on [0,1]. The kernel estimator of density on [0,1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive ...

in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

Gaussian kernel regularization is widely used in the machine learning literature and has proved successful in many empirical experiments. The periodic version of Gaussian kernel regularization has been shown to be minimax rate optimal in estimating functions in any finite order Sobolev space. However, for a data set with n points, the computation complexity of the Gaussian kernel regularization...

Abs t rac t . To estimate the quantile density function (the derivative of the quantile function) by kernel means, there are two alternative approaches. One is the derivative of the kernel quantile estimator, the other is essentially the reciprocal of the kernel density estimator. We give ways in which the former method has certain advantages over the latter. Various closely related smoothing i...

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimat...