Nonparametric Functional Smoothing Techniques

人口中一组测量数据的相对频率分布模型称为概率密度函数，它描述了在不同间隔内观察到的数据的比例，并回答了这样的问题：“加拿大人中有多少人生活在贫困线以下？”或者“装配线上生产的产品有多大比例低于规定的质量门槛？”这是一条数学曲线，如钟形高斯曲线，然后用于计算人口的各种其他特征，如平均值、中位数和百分位数。通常，被称为参数模型的标准模型在计算人口测量的复杂函数时是有用的，这些模型仅依赖于几个常量，例如在高斯模型的情况下的平均值和标准差。例如，在钟形曲线上，我们估计95%的观测值将落在与平均值的两个标准差以内。如果模型不合适，这种基于模型的推理将是无效的。

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.