Statistical inference with applications

近年来，基于似然的高阶渐近方法得到了广泛的研究，以准确地近似检验感兴趣的标量参数的p值。这些方法的一个问题是要获得的约束最大似然估计为一个给定的值的参数的兴趣。 在某些情况下，标准软件可能会报告一个最佳值，但实际上，不是实际的最佳值，或者方法完全无法收敛。Goffe等人（1994）表明，模拟退火算法可以发现传统软件错过的最优解。 第一个项目的目的是将模拟退火技术应用到R中，以获得无约束和有约束的最大似然估计。 因此，对于任何给定的参数模型，感兴趣的标量参数的p值可以被精确地近似。 所提出的方法可以应用于可靠性，生存数据分析，时间序列分析，和计量经济学的参数可能没有一个封闭的形式。

In recent year, likelihood-based higher order asymptotic methods have been extensively studied to accurately approximate the p-value for testing a scalar parameter of interest. One problem of these methods is to obtain the constrained maximum likelihood estimate for a given value of the parameter of interest. In some cases, standard software may either report an optimal value, but in fact, is not the actual optimum, or the methods completely failed to converge. Goffe et al. (1994) showed that the simulated annealing algorithm could uncover optima missed by traditional software. The aim of the first project is to implement the simulated annealing technique into R to obtain both the unconstrained and the constrained maximum likelihood estimates. Hence, the p-value of a scalar parameter of interest for any given parametric model can be accurately approximated. The proposed method can be applied to reliability, survival data analysis, time series analysis, and econometrics where the parameter of interest may not have a closed form.