  This article is due to appear in the Handbook of Statistics, Vol. 43,
Elsevier/North-Holland, Amsterdam, edited by Arni S. R. Srinivasa Rao and C. R.
Rao.
  In modern day analytics, there is ever growing need to develop statistical
models to study high dimensional data. Between dimension reduction,
asymptotics-driven methods and random projection based methods, there are
several approaches developed so far. For high dimensional parametric models,
estimation and hypothesis testing for mean and covariance matrices have been
extensively studied. However, practical implementation of these methods are
fairly limited and are primarily restricted to researchers involved in high
dimensional inference. With several applied fields such as genomics,
metagenomics and social networking, high dimensional inference is a key
component of big data analytics. In this chapter, a comprehensive overview of
high dimensional inference and its applications in data analytics is provided.
Key theoretical developments and computational tools are presented, giving
readers an in-depth understanding of challenges in big data analysis.
