According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-par...

Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with known functional form and some unknown parameters. In this paper, studied several parametric tests based on statistics are symmetric functions of m-step disjoint spacings. Asymptotic properties these been investigated under the simple null hypothesis sequence local alternatives conv...

For some variants of regression models, including partial, measurement error or error-in-variables, latent effects, semi-parametric and otherwise corrupted linear models, the classical parametric tests generally do not perform well. Various modifications and generalizations considered extensively in the literature rests on stringent regularity assumptions which are not likely to be tenable in m...

In the context of testing the speci cation of a nonlinear parametric regression function, we study the power of speci cation tests using the minimax approach. We determine the maximum rate at which a set of smooth local alternatives can approach the parametric model while ensuring consistency of a test uniformly against any alternative in this set. We show that a smooth nonparametric testing pr...