Significant research attention has been given to historical patterns of marital fertility transitions in currently industrialized countries. Specifically, studies consider the time of the onset of fertility decline and its distribution among populations or population subgroups; the distribution of pre-decline parital fertility levels; and/or the rate of marital fertility decline. Analyses of pre-decline fertility level and its rate of decline, however, depend upon the procedure used to estimate the time of fertility decline. The Princeton European Fertility Project is the most prominent historical fertility study ever conducted. The procedure employed to estimate the timing parameter in these Princeton studies is described. An alternative statistical procedure is then proposed for detecting the onset of the transition from high to low marital fertility; the method may also be used to find the termination point of decline where the sequence of fertility variables is long enough. Both methods produce maximum likelihood least squares estimates, but the form proposed in the text has conceptual advantages.

中文翻译：

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一种估算婚姻生育率下降时间及相关参数的方法

对当前工业化国家婚姻生育率转变的历史模式给予了大量研究关注。具体而言，研究考虑生育率下降的开始时间及其在人口或人口亚群中的分布；生育率下降前的分布；和/或婚姻生育率下降。然而，对生育率下降前水平及其下降率的分析取决于用于估计生育率下降时间的程序。普林斯顿欧洲生育计划是有史以来最杰出的生育研究。描述了在这些普林斯顿研究中用于估计时间参数的程序。然后提出了另一种统计程序来检测从高婚姻生育率到低婚姻生育率的转变的开始；该方法还可用于找到生育率变量序列足够长的下降终止点。两种方法都产生最大似然最小二乘估计，但文中提出的形式具有概念上的优势。