Asymptotic Distributions of Innovation Density Estimators in Linear Processes

In this article, we demonstrate that at a fixed point, the asymptotic distribution of the innovation density estimator is normal for stationary linear process. Also, we show that the asymptotic distribution of the global measure of the deviation of the density estimator from the expectation of the kernel innovation density (based on the true innovations) is the same as that in the case when we can observe the true innovations.     

Inference under Heteroscedasticity of Unknown Form Using an Adaptive Estimator

The heteroscedasticity consistent covariance matrix estimators are commonly used for the testing of regression coefficients when error terms of regression model are heteroscedastic. These estimators are based on the residuals obtained from the method of ordinary least squares and this method yields inefficient estimators in the presence of heteroscedasticity. It is usual practice to use estimated weighted least squares method or some adaptive methods to find efficient estimates of the regression parameters when the form of heteroscedasticity is unknown. But HCCM estimators are seldom derived from such efficient estimators for testing purposes in the available literature. The current article addresses the same concern and presents the weighted versions of HCCM estimators. Our numerical work uncovers the performance of these estimators and their finite sample properties in terms of interval estimation and null rejection rate.     

Local Estimation of the Second-Order Parameter in Extreme Value Statistics and Local Unbiased Estimation of the Tail Index

We develop and study in the framework of Pareto-type distributions a class of nonparametric kernel estimators for the conditional second order tail parameter. The estimators are obtained by local estimation of the conditional second order parameter using a moving window approach. Asymptotic normality of the proposed class of kernel estimators is proven under some suitable conditions on the kernel function and the conditional tail quantile function. The nonparametric estimators for the second order parameter are subsequently used to obtain a class of bias-corrected kernel estimators for the conditional tail index. In particular it is shown how for a given kernel function one obtains a bias-corrected kernel function, and that replacing the second order parameter in the latter with a consistent estimator does not change the limiting distribution of the bias-corrected estimator for the conditional tail index. The finite sample behavior of some specific estimators is illustrated with a simulation experiment. The developed methodology is also illustrated on fire insurance claim data.     

About the Nonparametric Estimation of the Bernoulli Regression

The nonparametric estimation of the Bernoulli regression function is studied. The uniform consistency conditions are established and the limit theorems are proved for continuous functionals on C[a, 1 ? a], 0 < a < 1/2.     

Asymptotic Normality of a Kernel Conditional Quantile Estimator Under Strong Mixing Hypothesis and Left-Truncation

We consider the estimation of the conditional quantile when the interest variable is subject to left truncation. Under regularity conditions, it is shown that the kernel estimate of the conditional quantile is asymptotically normally distributed, when the data exhibit some kind of dependence. We use asymptotic normality to construct confidence bands for predictors based on the kernel estimate of the conditional median.     

PROMETHEE IV through kernel density estimation

ABSTRACT

This paper presents a new version of PROMETHEE IV, which considers the empirical distribution of the criteria through kernel density estimation to evaluate alternatives. The developed method has the ability to treat criteria according to their distribution. The classic PROMETHEE IV can produce divergent integrals, and this could be the cause for its insufficient exploration in literature. The proposed method overcomes this situation since large values have little weight compared to values near the mean.     

A Local Linear Least-Absolute-Deviations Estimator of Volatility

An important empirical characteristic of financial time series is that the unconditional distribution of the returns tends to possess heavy tails. This is the motivation for the particular local kernel volatility estimator proposed in this work. Whereas least-square-deviations (LSD) estimators are strongly affected by heavy-tailed distributions, the performance of least-absolute-deviations (LAD) estimators is not. This robustness to heavy tails is evidenced by the more flexible assumptions made on the distributional moments of the observable variable. The simulation examples also highlight the superior performances of the LAD estimator when compared to the LSD estimator under heavy tails conditions. The full nonparametric model is described and the asymptotic properties of the LAD estimator are derived. Extensive Monte Carlo studies strongly suggest that the LAD estimator is asymptotically adaptive to the unknown conditional first moment. The LAD estimator is also used to estimate the volatility of the S&P500 and the BOVESPA returns.     

Bootstrap MISE Estimators to Obtain Bandwidth for Kernel Density Estimation

Research in the area of bandwidth selection was an active topic in the 1980s and 1990s, however, recently there has been little research in the area. We re-opened this investigation and have found a new method for estimating mean integrated squared error for kernel density estimators. We provide an overview of other methods to obtain optimal bandwidths and offer a comparison of these methods via a simulation study. In certain situations, our method of estimating an optimal bandwidth yields a smaller MISE than competing methods to compute bandwidths. This procedure is illustrated by an application to two data sets.     

Youden Index and Associated Cut-Points for Three Ordinal Diagnostic Groups

Directly relating to sensitivity and specificity and providing an optimal cut-point, which maximizes overall classification effectiveness for diagnosis purpose, the Youden index has been frequently utilized in biomedical diagnosis practice. Current application of the Youden index is limited to two diagnostic groups. However, there usually exists a transitional intermediate stage in many disease processes. Early recognition of this intermediate stage is vital to open an optimal window for therapeutic intervention. In this article, we extend the Youden index to assess diagnostic accuracy when there are three ordinal diagnostic groups. Parametric and nonparametric methods are presented to estimate the optimal Youden index, the underlying optimal cut-points, and the associated confidence intervals. Extensive simulation studies covering representative distributional assumptions are reported to compare performance of the proposed methods. A real example illustrates the usefulness of the Youden index in evaluating discriminating ability of diagnostic tests.     

More efficient local polynomial regression with random-effects panel data models

We propose a modification on the local polynomial estimation procedure to account for the “within-subject” correlation presented in panel data. The proposed procedure is rather simple to compute and has a closed-form expression. We study the asymptotic bias and variance of the proposed procedure and show that it outperforms the working independence estimator uniformly up to the first order. Simulation study shows that the gains in efficiency with the proposed method in the presence of “within-subject” correlation can be significant in small samples. For illustration purposes, the procedure is applied to explore the impact of market concentration on airfare.