混合位置分布中分量参数的统计推断

Statistical inference on component parameters in mixture location distribution

对混合位置分布族,当混合比已知时,提出了关于分量参数的假设检验和区间估计方法,所提出的方法基于广义枢轴模型.在一定的条件下,检验的实际水平等于名义水平,且各置信域的实际覆盖率等于名义覆盖率.在更一般的场合,检验是相合的,并且各置信域的实际覆盖率趋于名义覆盖率.模拟显示所给的方法是令人满意的.

The interval estimation and hypothesis testing of component parameters in mixture location distributions are discussed when mixing proportion is known. A method based on generalized pivotal model is proposed. For the situation in which the nuisance parameters are known, the true levels of the tests given in this paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds are equal to nominal ones. In other situations, the tests are consistent, and the interval estimation or confidence bounds have asymptotic coverage equal to nominal coverage. Meanwhile, some simulations are given to show that these methods are satisfactory.