A theory of overparameterized structural models is presented. In such a model some "redundant" parameters are involved; the parameter vector is not identified, and the information matrix is not nonsingular. The minimum discrepancy function (MDF) test statistic is shown to have an asymptotic chi-squared distribution almost everywhere for a wide class of discrepancy functions. Asymptotic distribu...

In this paper we derive general formulae suitable for Monte Carlo computation of conditional expectations of functions of a random vector given a sufficient statistic. The problem of direct sampling from the conditional distribution is considered in particular. It is shown that this can be done by a simple parameter adjustment of the original statistical model, provided the model has a certain ...

Synopsis In order to reduce the type I and II errors and obtain more accurate brain activation map, fMR images were statistically analyzed with uncorrected ttest, false discovery rate(FDR) and family-wise error rate(FWE) in the general linear model (GLM) through statistic parameter mapping software(SPM). This study compared and evaluated the power of thresholding correction methods with uncorre...

The authors derive the joint distributions of a studentized deleted residual and various regression quantities, calculated with all the data or with one case deleted. They show that the correlation between the studentized deleted residual and the deleted test statistic has an interesting interpretation in terms of well-known regression quantities. These results allow them to examine the effect ...

For generalized linear models with multivariate response and natural link functions, likelihood ratio test of one-sided hypothesis on the regression parameter is considered under rather general conditions. The null-asymptotic distribution of the test statistic turns out to be chi-bar squared. The extension of the above results to include quasi-likellihood ratio test to incorporate over-dispersi...

A “spurious regression” is one in which the time-series variables are non-stationary and independent. It is well-known that in this context the OLS parameter estimates and the R converge to functionals of Brownian motions; the “t-ratios” diverge in distribution; and the Durbin-Watson statistic converges in probability to zero. We derive corresponding results for some common tests for the Normal...

Relations are derived that can be used to infer parameters in situations where theoretical predictions can be compared to experimental data only indirectly via Monte Carlo simulation. We consider least square and likelihood ratio fits. Parameter changes in the fitting procedures are performed by reweighting Monte Carlo events. Formulas for goodness-of-fit tests based on the w2 and the likelihoo...