Abstract
Crawford (The hidden biases in big data, Harvard Business Review, Cambridge, 2013, [2]) has recently warned about the risks of the sentence with enough data, the numbers speak for themselves. Some of the problems coming from ignoring sampling bias in big data statistical analysis have been recently reported by Cao (Inferencia estadística con datos de gran volumen, La Gaceta de la RSME 18:393–417, 2015, [1]). The problem of nonparametric statistical inference in big data under the presence of sampling bias is considered in this work. The mean estimation problem is studied in this setup, in a nonparametric framework, when the biasing weight function is known (unrealistic) as well as for unknown weight functions (realistic). Two different scenarios are considered to remedy the problem of ignoring the weight function: (i) having a small sized simple random sample of the real population and (ii) having observed a sample from a doubly biased distribution. In both cases the problem is related to nonparametric density estimation. A simulated dataset is used to illustrate the performance of the nonparametric methods proposed in this work.
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References
Cao R (2015) Inferencia estadística con datos de gran volumen. La Gaceta de la RSME 18:393–417
Crawford K (2013) The hidden biases in big data. Harvard Business Review, Cambridge. https://hbr.org/2013/04/the-hidden-biases-in-big-data
Hargittai E (2015) Is bigger always better? potential biases of big data derived from social network sites. Ann Am Acad Pol Soc Sci 659:63–76
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Acknowledgements
This research has been supported by MINECO Grants MTM2014-52876-R and MTM2017-82724-R and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and Centro Singular de Investigación de Galicia ED431G/01), all of them through the European Regional Development Fund (ERDF). The second author’s research was sponsored by the Xunta de Galicia predoctoral grant (with reference ED481A-2016/367) for the universities of the Galician University System, public research organizations in Galicia and other entities of the Galician R&D&I System, whose funding comes from the European Social Fund (ESF) in 80% and in the remaining 20% from the General Secretary of Universities, belonging to the Ministry of Culture, Education and University Management of the Xunta de Galicia.
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Cao, R., Borrajo, L. (2018). Nonparametric Mean Estimation for Big-But-Biased Data. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_5
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DOI: https://doi.org/10.1007/978-3-319-73848-2_5
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