arXiv subjects

Tobias Niebuhr

Publications and source records attributed to Tobias Niebuhr.

2 recordsLinked to original sources

arXiv2018

Profiting from correlations: Adjusted estimators for categorical data

To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the estimation. Studying contingency tables, estimators for marginal distributions are proposed under the assumption that another marginal is known. It is shown that the weighted estimators have a strictly smaller asymptotic variance whenever the two marginals are correlated. The finite sample performance is illustrated in a simulation study. As an application to traffic accident data the method allows for correcting a well-known bias in the observed injury severity distribution.

stat.ME↗

arXiv2016

Specification testing in nonparametric AR-ARCH models

In this paper an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. A test for the model assumption of independence of innovations from past time series values is suggested. The test is based on an weighted $L^2$-distance of empirical characteristic functions. The asymptotic distribution under the null hypothesis of independence is derived and consistency against fixed alternatives is shown. A smooth autoregressive residual bootstrap procedure is suggested and its performance is shown in a simulation study.

math.ST↗