In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distribution under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce...

In this study, we propose a Rao's score (RS) statistic (Lagrange multiplier (LM) statistic) to test for endogeneity of the spatial weights matrix in a spatial autoregressive model. To achieve this, we start with a spatial autoregressive model with an acceptable form for the generating process...

The delta method that consists of a Taylor approximation can be used to determine the asymptotic variance and distribution of test statistics. In an alternative approach, the test statistic can be combined with some estimating equations in the M-estimation framework for the purpose of deriving...

In the presence of heteroskedasticity, conventional test statistics based on the ordinary least square estimator lead to incorrect inference results for the linear regression model. Given that heteroskedasticity is common in cross-sectional data, the test statistics based on various forms of...

Rao's (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao's score (RS) test loses its optimality. A model could be misspecified in a...

In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally...

We consider a spatial econometric model containing a spatial lag in the dependent variable and the disturbance term with an unknown form of heteroskedasticity in innovations. We first prove that the maximum likelihood (ML) estimator for spatial autoregressive models is generally inconsistent...

This contribution presents an overview of sensitivity analysis of simulation models, including the estimation of gradients. It covers classic designs and their corresponding (meta)models; namely, resolution-III designs including fractional-factorial two-level designs for first-order polynomial...

We derive new statistical tests for leave-one-out cross-validation of Kriging models. Graphically, we present these tests as scatterplots augmented with confidence intervals. We may wish to avoid extrapolation, which we define as prediction of the output for a point that is a vertex of the...

Classic linear regression models and their concomitant statistical designs assume a univariate response and white noise. By definition, white noise is normally, independently, and identically distributed with zero mean. This survey tries to answer the following questions: (i) How realistic are...