Asymptotic Tests of Composite Hypotheses

Composite Hypotheses and Generalized Likelihood Ratio Tests

In many real world problems, it is difficult to precisely specify probability distributions. Our models for data may involve unknown parameters or other characteristics. Here are a few motivating examples. Example: Unknown amplitudes/delays in wireless communications. We don't always know how many relays a signal will go through, how strong the signal will be at each receiver, the distance betw...

Bayesian tests for composite alternative hypotheses in cross-tabulated data

Multistage Tests ofMultiple Hypotheses

Conventional multiple hypothesis tests use step-up, step-down, or closed testing methods to control the overall error rates. We will discuss marrying these methods with adaptive multistage sampling rules and stopping rules to perform efficient multiple hypothesis testing in sequential experimental designs. The result is a multistage step-down procedure that adaptively tests multiple hypotheses ...

Expectations Hypotheses Tests

We investigate the expectations hypotheses of the term structure of interest rates and of the foreign exchange market using vector autoregressive methods for U.S. dollar, Deutsche mark, and British pound interest rates and exchange rates. We examine Wald, Lagrange multiplier, and distance metric tests by iterating on approximate solutions that require only matrix inversions. Bias-corrected, con...

On Bootstrap Tests of Hypotheses

The size of the bootstrap test of hypotheses is studied for the normal and exponential one and two-sample problems. It is found that the size depends not only on the problem, but on the choice of test statistic and the nominal level. In some special cases, the bootstrap test is UMP, but in other cases, it can be totally useless, such as being completely randomized or rejecting the null hypothes...