Kernel Density Estimation for Heaped Data

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractIn self-reported data usually a phenomenon called 'heaping' occurs, i.e. survey participants round the values of their income, weight or height to some degree. Additionally, respondents may be more prone to round off or up due to social desirability. By ignoring the heaping process a severe bias in terms of spikes and bumps is introduced when applying kernel density methods naively to the rounded data. A generalized Stochastic Expectation Maximization (SEM) approach accounting for heaping with potentially asymmetric rounding behaviour in univariate kernel density estimation is presented in this work. The introduced methods are applied to survey data of the German Socio-Economic Panel and exhibit very good performance simulations.

Domain Prediction with Grouped Income Data

“…First, the proposed methodology does not adjust for the effects of heaping. This can be resolved by following the methods proposed by Groß and Rendtel (2016). Second, we also acknowledge that another type of measurement error may exist when respondents report their income in the wrong interval.…”

A new hierarchical analysis framework of building heights: Towards a more intuitive understanding of 3D urban structure

“…After the visual observation and comparison, the results generated by Silverman's Rule of Thumb method (Figures 7g1–g5) were adopted in this article because they show the most relatively distinct structure characteristics, which not only present the global trend and show local necessary differences but also contain fewer fragments. Moreover, many other scholars adopt and further propose using Silverman's Rule of Thumb method to reduce the computational burden of KDE in their studies (Bakouch et al., 2022; Groß & Rendtel, 2016).…”

“…The bandwidth parameter plays a significant role in the generation of results, which determines its synthesis degree. The determination of bandwidth in this article adopts the Silverman's Rule of Thumb method, which considers the spatial distribution discretization of the input dataset, avoids the ring around the points phenomenon that often occurs with sparse datasets and is resistant to spatial outliers, which explains why it is commonly used to determine the bandwidth parameter by scholars (Bakouch et al., 2022; Groß & Rendtel, 2016). where, SD is the standard distance.…”

Switching Between Different Non-Hierachical Administrative Areas via Simulated Geo-Coordinates: A Case Study for Student Residents in Berlin

“…Such a factor has to be computed for every spot where the kernel function is evaluated. This costs computational time, but it is not a real obstacle as it is implemented in existing software (Groß 2018).…”