As a technical supplement to Zhu and Zhang (2004), we give detailed information on how to establish asymptotic theory for both maximum likelihood estimate and maximum modified likelihood estimate in mixture regression models. Under specific and reasonable conditions, we show that the optimal convergence rate of n− 1 4 for estimating the mixing distribution is achievable for both the maximum lik...

When using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a chi2 distribution with degrees of freedom equal to the number of parameters te...

in this research, an iterative approach is employed to recognize and classify control chart patterns. to do this, by taking new observations on the quality characteristic under consideration, the maximum likelihood estimator of pattern parameters is first obtained and then the probability of each pattern is determined. then using bayes’ rule, probabilities are updated recursively. finally, when...

in order to assess the satellite data for soil investigation, aster digital data 20 june 2006, field study and phisiochemical properties of soil, were analyzed. all landcover classes including soils are classified based onmorphological and physico-chemical characteristics. images were geocorrected and photomorphic units were selected based upon visual interpretation and sampling in study area. ...

We propose likelihood and restricted likelihood ratio tests for goodness-of-fit of nonlinear regression. The first order Taylor approximation around the MLE of the regression parameters is used to approximate the null hypothesis and the alternative is modeled nonparametrically using penalized splines. The exact finite sample distribution of the test statistics is obtained for the linear model a...

In many causal inference problems, one is interested in the direct causal effect of an exposure on an outcome of interest that is not mediated by certain intermediate variables. Robins and Greenland (1992) and Pearl (2001) formalized the definition of two types of direct effects (natural and controlled) under the counterfactual framework. The efficient scores (under a nonparametric model) for t...

Matched case-control study designs are commonly implemented in the field of public health. While matching is intended to eliminate confounding, the main potential benefit of matching in case-control studies is a gain in efficiency. Methods for analyzing matched case-control studies have focused on utilizing conditional logistic regression models that provide conditional and not causal estimates...