Parametric and nonparametric estimation techniques are two approaches used in estimating statistical models.
Parametric estimation is an approach that assumes a particular distributional form for the population, and the estimation process involves estimating the parameters of that distribution. Parametric models are typically more restrictive than nonparametric models, but they require fewer data points to estimate, and as a result, they often provide more accurate estimates when the underlying assumptions are satisfied. Examples of parametric models include linear regression, logistic regression, and normal distribution.
On the other hand, nonparametric estimation makes no assumptions about the underlying distribution of the population. Instead, the estimation process involves using the data to construct the estimator. Nonparametric models are often more flexible than parametric models, but they require more data points to estimate accurately. Examples of nonparametric models include kernel density estimation, spline regression, and decision trees.
In terms of when to use each approach, parametric models should be used when the underlying distributional assumptions are well understood and accurate, and when there is enough data to estimate the parameters of the model reliably. For example, if we know that the population follows a normal distribution and we have enough data, then a parametric model such as linear regression would be appropriate.
Nonparametric estimation should be used when there is not enough information about the population distribution, or when the underlying distribution assumptions are violated. Nonparametric models are also preferred when the data is of low dimensional or there is no exact probabilistic data descriptions. For example, kernel density estimation can be used to estimate the probability density function of a random variable, even when the underlying distribution is unknown and/or the sample size is small.
In summary, the choice between parametric and nonparametric estimation depends on the circumstances of the problem at hand. Understanding the strengths and limitations of each approach is important for selecting the most appropriate tool for a given project.