Parametric Statistical Methods start off with an assumption for the shape of f. As a result, when training the model, parametric methods simplify the process of finding f by reducing the entire problem to just figuring out the parameters of an equation (i.e., $\beta_0$, $\beta_1$, $\beta_2$, etc). Compared to non-parametric approaches, it does not need as many observations, but because it starts off with an assumption, it may not fit the actual f.

Parametric Statistical Methods

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Parametric Method and Nonparametric Method

Parametric Statistical Methods have Datasets that match the following Criteria:
-Dependent variable data are continuous, not categorical 
-Data are (more or less) normally distributed 
-Variance (R^2) are similar/homogenous within each predictor group
-Data samples are randomly selected without bias 
-Sample size is adequately large (n>25) 

If these criteria are not met, then a non-parametric statistical test should be applied 

Assumption Criteria for Parametric v. Non-Parametric Method Selection

Nonparametric models are highly flexible statistical descriptions that do not rely on strong, simplifying assumptions about the underlying data generation process. A defining common theme of nonparametric approaches is that their level of complexity grows as the amount of available training data increases. While parametric models are necessary when data is scarce to prevent overfitting, the abundance of data in modern machine learning allows for the use of fully nonparametric models that can better fit complex realities.

Nonparametric Models

- Parametric statistical methods
- Non-parametric statistical methods

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Statistical learning involves using supervised tools, unsupervised tools, time series learning, and semi-supervised tools and methods to analyze data to understand the data, extract knowledge, and infer insights.

Statistical learning

Parametric and non-parametric statistical methods

- Supervised statistical learning
- Unsupervised statistical learning
- Time series learning
- Semi-Supervised learning

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