We derive an exact p-value for testing a global null hypothesis in a general adaptive regression setting. Our approach uses the Kac-Rice formula (as described in Adler & Taylor 2007) applied to the problem of maximizing a Gaussian process. The resulting test statistic has a known distribution in finite samples, assuming Gaussian errors. We examine this test statistic in the case of the lasso, g...

A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p → ∞, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square d...

This paper introduces an automatic robust nonlinear identification algorithm using the leave-one-out test score also known as the PRESS (Predicted REsidual Sums of Squares) statistic and regularised orthogonal least squares. The proposed algorithm aims to achieve maximised model robustness via two effective and complementary approaches, parameter regularisation via ridge regression and model op...

In this paper, we propose that bounded rationality of another agent be modeled as errors the agent is making while deciding on its action. We are motivated by the work on quantal response equilibria in behavioral game theory which uses Nash equilibria as the solution concept. In contrast, we use decision-theoretic maximization of expected utility. Quantal response assumes that a decision maker ...

Though the common default maximum likelihood estimator used in structural equation modeling is predicated on the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to utilize distribution-free estimation methods. Fortunately, promising alternatives are being integrated into popular softwa...

We propose a test for shape constraints which can be expressed by transformations of the coordinates of multivariate regression functions. The method is motivated by the constraint of symmetry with respect to some unknown hyperplane but can easily be generalized to other shape constraints of this type or other semi-parametric settings. In a first step, the unknown parameters are estimated and i...

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Our contribution is a new test statistic for the two-sample test of means that integrates a random projection with the classical Hotelling T 2 statistic. Working within a high-di...

Many statistical models arising in applications contain non- and weakly-identified parameters. Due to identifiability concerns, tests concerning the parameters of interest may not be able to use conventional theories and it may not be clear how to assess statistical significance. This paper extends the literature by developing a testing procedure that can be used to evaluate hypotheses under no...

We derive a complex form of the unconstrained and constrained Cramér-Rao lower bound (CRB) of composite real parameters formed by stacking the real and imaginary part of the complex parameters. The derived complex constrained and unconstrained CRB is easy to calculate and possesses similar structure as in the real parameter case but with the real covariance, Jacobian and the Fisher information ...

Complex disorders are typically characterized by multiple phenotypes. Analyzing these phenotypes jointly is expected to be more powerful than dealing with one of them at a time. A recent approach (O'Reilly et al. 2012) is to regress the genotype at a SNP marker on multiple phenotypes and apply the proportional odds model. In the current research, we introduce an explicit expression for the scor...