Parametric Methods:

  1. Definition: Parametric methods involve assuming a specific form for the underlying probability distribution of the data (e.g., normal distribution). They estimate parameters (like mean and variance) of this distribution.

  2. Assumptions: These methods rely on strong assumptions about the data distribution (e.g., data follows a normal distribution).

  3. Efficiency: When the assumptions hold true, parametric methods are efficient and provide precise estimates with smaller sample sizes.

  4. Examples: Linear regression, t-tests, ANOVA.

  5. Limitations: If the assumptions about the distribution are incorrect, the model’s performance can be significantly degraded.

Non-Parametric Methods:

  1. Definition: Non-parametric methods do not assume a specific form for the underlying distribution. Instead, they rely on the data itself to estimate relationships and patterns.

  2. Assumptions: These methods make fewer assumptions, making them more flexible and robust to different data distributions.

  3. Efficiency: They may require larger sample sizes to achieve the same level of accuracy as parametric methods, especially in complex datasets.

  4. Examples: K-nearest neighbors, decision trees, kernel density estimation.

  5. Limitations: Non-parametric methods can be computationally intensive and may struggle with high-dimensional data. They may also lack interpretability compared to parametric methods.

In summary, parametric methods assume specific distributions for data, while non-parametric methods are more flexible but may require larger datasets and more computational resources.