| This dissertation was motivated by the wide use of the concept of conditional independence in statistics and econometrics and the absence of practical tests that do not make parametric assumptions.; There are two potential ways to deal with the issue. One is to use the empirical distribution, as do Linton and Gozalo (1997). The other is to apply nonparametric smoothing techniques. I follow the second approach and propose three tests for conditional independence, each of which explores the topic from separate, yet complementary, viewpoints.; Chapter 1 proposes a test based on the weighted Hellinger distance between the conditional density of Y given (X, Z) and that of Y given X. Under the null, the distance is identically zero whereas under the alternative it is nonzero. Due to the "curse of dimensionality", however, the test is less satisfactory when the dimension of (X, Y, Z) is large.; Chapter 2 explores the equality of two conditional characteristic functions. This new test is less severely subject to the adverse effects on power of the dimension of (X, Y, Z) than is the Hellinger metric test. At the same time it maintains the good consistency and asymptotic normality properties of the Hellinger metric test. Simulation results suggest that this new test complements the Hellinger metric test when the dimension of (X, Y, Z) is small, and it is also powerful when the dimension of ( X, Y, Z) is relatively large.; Chapter 3 is motivated by the optimality of the parametric likelihood ratio test and extends the applicability of empirical likelihood methods. I propose two tests. One is based upon conditional distribution functions, and the other explores a class of test functions that is generically comprehensively revealing (GCR) in the sense of Stinchcombe and White (1998). I show that in large samples both tests are weakly optimal in that they attain maximum average local power with respect to different spaces of functions for the local alternatives. Simulations suggest that the GCR test out-performs previous tests in small samples. Applications to economic and financial time series reveal some interesting nonlinear Granger causal relations that the traditional linear Granger causality test fails to detect. |
