Semiparametric Sample Selection Models with Applications in Biostatistics, Economics and Environmetrics

样本选择偏差（SSB）的问题出现在许多实际数据应用中，其中观察样本的子集由于特定属性而被系统地排除。这种排除可能导致结果失真，因为用于统计分析的样本不能代表人口水平上的所有统计单位。让我们考虑这样一个例子：在考虑了经验和年龄等其他变量的情况下，研究人员有兴趣估计女性样本中教育程度对工资的影响。在这里，零工资的个体通常被排除在样本之外，因为这些个体的许多特征可能与那些有正工资的个体不同，仅基于正工资个体的统计分析将产生有偏差的估计。具体来说，在不考虑社会福利的情况下，教育每增加一个单位，工资就会增加1.2个单位。如果我们考虑到SSB，则后者的值增加到2.1。修正后的估计对政策规划和决策至关重要，因为与偏差较小的估计相比，它可能导致对教育和技能的投资增加或减少。另外的问题是，教育（以及经验和年龄）的影响可以表现出复杂的模式，并且这些变量可以对(i)个人工资不同于零的概率产生不同的影响，以及（ii）工资大于零的个人的工资值的大小。在当前的例子中，例如，人们相信，教育对工资的影响在一定程度上是积极的（比如15年），之后这种影响趋于平稳或可能下降，经验和年龄对(i)和（ii）有不同的影响。这一信息也至关重要，因为可以设计针对特定类别个人的政策，从而最大限度地利用经济资源。人们认识到，目前的方法不能令人满意地解决上述问题。该项目的目的是为半参数样本选择建模提供统计理论，数值方法和软件，其中这些问题可以同时和全面地处理。

The issue of sample selection bias (SSB) arises in many real data applications where a subset of a sample of observations is systematically excluded due to a particular attribute. This exclusion can lead to distorted results because the sample used for statistical analysis would not be representative of all statistical units at population level. Let us consider the example in which the researcher is interested in estimating the effect of education on wage in a sample of women, accounting for other variables such as experience and age. Here individuals with zero wage are typically excluded from the sample, and because many features of these individuals are likely to differ from those with positive wage, statistical analysis based only on the positive wage individuals will yield biased estimates. Specifically, when not accounting for SSB, as education increases by say 1 unit, wage increases by 1.2 units. If we account for SSB, then the latter value increases to 2.1. The corrected estimate is crucial for policy planning and decision-making in that it can lead, for instance, to larger or smaller investments in education and skills as compared to the case of a biased smaller estimate. Additional issues are that the effect of education (as well as experience and age) can exhibit complicated patterns, and that these variables can have a different effect on (i) the probability that the individual has wage different from zero, and on (ii) the magnitude of the wage value for individuals whose wage is greater than zero. In the current example, it is believed, for example, that the effect of education on wage is positive up to a certain level (say 15 years) after which the effect tends to plateau or perhaps decline, and that experience and age have different impacts on (i) and (ii). This piece of information is also crucial in that policies targeting specific categories of individuals can be designed, hence maximising the use of economic resources. It is recognized that current methods do not address the issues mentioned above satisfactorily. The aim of this project is to provide the statistical theory, a numerical method and software for semiparametric sample selection modelling, where these issues can be simultaneously and fully dealt with.