A linear regression model, when a design matrix has not full column rank and a covariance matrix is singular, is considered. The problem of testing hypotheses on mean value parameters is studied. Conditions when a hypothesis can be tested or when need not be tested are given. Explicit forms of test statistics based on residual sums of squares are presented.

Data mining has brought a new philosophy in data analysis that is primarily driven by computational efficiency and predictive performance. In this paper we attempt to show that while this new philosophy opens new horizons, these new techniques may themselves gain much when coupled with traditional statistical reasoning. For example, I recently introduced some sociologists of the University of G...

In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X1, . . . ,Xn are i.i.d. with distribution Pθ, with θ ∈ R . Let g(θ) be some real-valued parameter of interest. The null hypothesis asserts g(θ) / ∈ (a, b) versus the alternative g(θ)∈ (a, b). For example, such hypotheses occur in bioequivalence studies where one may wish to show two drug...

Suppose that one observes a process Y on the unit interval, where dY t = n1/2f t dt+dW t with an unknown function parameter f, given scale parameter n ≥ 1 (“sample size”) and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity. These tests are asymptotically optimal and adaptive in a certain sense. They ar...