Bandwidth selection for nonparametric kernel testing
نویسندگان
چکیده
We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed–form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.
منابع مشابه
Discrimination of time series based on kernel method
Classical methods in discrimination such as linear and quadratic do not have good efficiency in the case of nongaussian or nonlinear time series data. In nonparametric kernel discrimination in which the kernel estimators of likelihood functions are used instead of their real values has been shown to have good performance. The misclassification rate of kernel discrimination is usually less than ...
متن کاملBandwidth Selection in Nonparametric Kernel Testing
We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power ...
متن کاملTesting lack of fit of regression models under heteroscedasticity
A test is proposed for assessing the lack of fit of heteroscedastic nonlinear regression models that is based on comparison of nonparametric kernel and parametric fits. A data-driven method is proposed for bandwidth selection using the parametric null model asymptotically optimal bandwidth which leads to a test that has a limiting normal distribution under the null hypothesis and is consistent ...
متن کاملNonparametric Specification Testing for Nonlinear Time Series with Nonstationarity
This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for testing whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time seri...
متن کاملNonparametric Estimation of Expected Shortfall
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...
متن کامل