Entropy 2019, 21(4), 348; https://doi.org/10.3390/e21040348
Robust Inference after Random Projections via Hellinger Distance for Location-Scale Family
1
Department of Statistics, George Mason University, Fairfax, VA 22030, USA
2
Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada
*
Author to whom correspondence should be addressed.
Received: 6 February 2019 / Revised: 23 March 2019 / Accepted: 24 March 2019 / Published: 29 March 2019
(This article belongs to the Special Issue New Developments in Statistical Information Theory Based on Entropy and Divergence Measures)
Abstract
Big data and streaming data are encountered in a variety of contemporary applications in business and industry. In such cases, it is common to use random projections to reduce the dimension of the data yielding compressed data. These data however possess various anomalies such as heterogeneity, outliers, and round-off errors which are hard to detect due to volume and processing challenges. This paper describes a new robust and efficient methodology, using Hellinger distance, to analyze the compressed data. Using large sample methods and numerical experiments, it is demonstrated that a routine use of robust estimation procedure is feasible. The role of double limits in understanding the efficiency and robustness is brought out, which is of independent interest. View Full-TextKeywords:
compressed data; Hellinger distance; representation formula; iterated limits; influence function; consistency; asymptotic normality; location-scale family
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Li, L.; Vidyashankar, A.N.; Diao, G.; Ahmed, E. Robust Inference after Random Projections via Hellinger Distance for Location-Scale Family. Entropy 2019, 21, 348.
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