introduction air pollution is one of the critical challenges in metropolitans around the world. according to world health organization (who), three millions people die from air pollution annually. in some studies mortality costs by air pollution was estimated. social cost of air pollution was estimated 28990 billions rials in tehran city. the mortality cost by air pollution was estimated about ...

For model selection with nested classes, we propose to minimize Rissanen's stochastic complexity with a constraint on expected computational cost. The proposed solution uses the Wald statistic and dynamic programming for order selection, such that maximum likelihood estimates of only a small subset of hypothesized models needs to be computed. Simulation results are presented to compare computat...

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n−1/2, n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all fo...

The R statistic, when used in a regression or ANOVA context, is appealing because it summarizes how well the model explains the data in an easy-tounderstand way. R statistics are also useful to gauge the effect of changing a model. Generalizing R to mixed models is not obvious when there are correlated errors, as might occur if data are georeferenced or result from a designed experiment with bl...

The issue of the non-invariance of the Wald test under nonlinear reparametrisations of the restrictions under test is studied from a differential geometric viewpoint. Quantities that can be defined in purely geometrical terms are by construction invariant under reparametrisation, and various attempts are made to construct a Wald test out of such invariant quantities only. Despite the existence ...

We consider the problem of calculating power and sample size for tests based on generalized estimating equations (GEE), that arise in studies involving clustered or correlated data (e.g., longitudinal studies and sibling studies). Previous approaches approximate the power of such tests using the asymptotic behavior of the test statistics under fixed alternatives. We develop a more accurate appr...

We consider two relations between Fisher's information matrix of a stationary ARMA (autoregressive moving average) process and Sylvester's resultant matrix. One is based on the Wald test statistic for testing common roots of the AR and MA polynomials of an ARMA process, and the other one is established by using the structure of Fisher's information matrix. It turns out that the latter is also a...