Nonparametric Functional Smoothing Techniques

一套人口测量数据的相对频率分布模型，称为概率密度函数，描述了落在不同间隔内的观测数据的比例，并回答了诸如“加拿大人中有多少百分比低于贫困线？或者“在装配线上生产的产品中有多少百分比低于规定的质量阈值？“这是一条数学曲线，比如钟形高斯曲线，然后用来计算人口的各种其他特征，比如平均值、中位数和平均值。通常，标准模型（称为参数模型，仅依赖于少数常数，例如高斯模型中的平均值和标准差）在计算总体测量的复杂函数时很有用。例如，在钟形曲线上，我们估计95%的观测值将落在平均值的两个标准差之内。如果模型不合适，则基于模型的推断将无效。

A model for the relative frequency distribution of a set of measurements on a population, known as a probability density function, describes the proportion of observations falling in various intervals, and answers such questions as "what percentage of Canadians are below the poverty line?" or "what percentage of items produced on an assembly line will be found below the prescribed quality threshold?" This is a mathematical curve, such as the bell-shaped Gaussian curve, that is then used to compute various other characteristics of the population such the average, median and percentiles. Often the standard models, known as the parametric models that depend only on a few constants, such as the mean and standard deviation in the case of the Gaussian model, are useful in computing complex functions of the population measurements. For example, on a bell curve, we estimate that 95% of the observations will fall within two standard deviations from the mean. If the model is not appropriate, such model based inferences will be invalid.