On tests of independence among multiple random vectors of arbitrary dimensions/ Angshuman Roy

Thesis (Ph.D.) - Indian Statistical Institute, 2020

Includes bibliography

Introduction -- Tests of Independence among Continuous Random Variables -- Test of Independence among Random Variables with Arbitrary Probability Distributions -- Test of Independence among Randoms Vectors: Methods Based on One- dimensional Projections -- Test of Independence among Random Vectors: Methods Based on Ranks of Nearest Neighbors

Guided by Prof. Anil K. Ghosh

In this thesis, we deal with this problem of testing independence among several random
vectors. This is a well-known problem in statistics and machine leaning literature, and
several methods of are available for it. But most of these existing methods deal with two
random vectors (or random variables) only. Moreover, instead of testing for independence,
many of them only test for uncorrelatedness between two vectors. Now a days, we often
deal with data sets having dimension larger than sample size. Many existing tests cannot be
used in such situations. Keeping all these in mind, in this thesis, we propose and investigate some methods that can be used for testing independence among several random vectors of arbitrary dimensions. Later we shall see that these proposed tests can also be used for testing independence among several random functions or random elements taking values in infinite dimensional Banach or Hilbert spaces.