Shapiro and Wilk (1965) proposed a highly intuitive goodness-offit test of normality with nuisance location and scale parameters. The test has received a considerable attention in the literature; its asymptotic null distribution is covered by the results of de Wet and Wenter (1973), and was recently studied by Sen (2002). We extend the Shapiro-Wilk test to the situation with nuisance regression...

In this article, we investigate a robust version of local linear regression smoothers for stationary and censored stochastic processes by using M-type local polynomial techniques and transformations. Under some regularity conditions, we establish the weak and strong consistency as well as the asymptotic normality of proposed estimators. We propose an easily implemented bandwidth selection crite...

a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

The validity and significance of normal range neurocognition in schizophrenia remain unclear and controversial. We assessed whether normal range patients and controls demonstrate evidence of decline relative to premorbid ability and differ in performance profiles across measures, including those external to the normality criterion. In addition, we compared below normal range healthy control par...

In nonlinear regression problems, the assumption is usually made that parameter estimates will be approximately normally distributed. The accuracy of the approximation depends on the sample size and also on the intrinsic and parameter-eeects curvatures. Based on these curvatures, criteria are deened here that indicate whether or not an experiment will lead to estimates with distributions well a...

To obtain consistency and asymptotic normality, a generalized method of moments (GMM) estimator typically is defined to be an approximate global minimizer of a GMM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. In consequence, practitioners usually ignore the problem and take the GMM estimator to be the result of a...

This paper proposes a formal model selection test for choosing between two competing structural econometric models. The procedure is based on a novel lack-oft criterion, namely, the simulated mean squared error of predictions (SMSEP), taking into account the complexity of structural econometric models. It is asymptotically valid for any xed number of simulations, and allows for any estimator wh...

Cryptographic Boolean functions must be complex to satisfy Shannon’s principle of confusion. But the cryptographic viewpoint on complexity is not the same as in circuit complexity. The two main criteria evaluating the cryptographic complexity of Boolean functions on F n 2 are the nonlinearity (and more generally the r-th order nonlinearity, for every positive r < n) and the algebraic degree. Tw...