Statsmodels is a Python library that provides a wide range of statistical models and algorithms for data analysis. One area where statsmodels excels is in its support for nonparametric methods. Nonparametric methods are statistical techniques that do not rely on specific assumptions about the underlying data distribution. In this blog post, we will explore some of the popular nonparametric methods available in statsmodels and learn how to use them in Python.

Kernel Density Estimation (KDE)

Kernel Density Estimation is a nonparametric way to estimate the probability density function (PDF) of a random variable. Kernel Density Estimation can be particularly useful when data distribution is not known or when the assumption of normality is violated. Statsmodels provides a convenient implementation of KDE through its KernelDensity class.

To get started with KDE in statsmodels, you will need to import the necessary modules:

import numpy as np
import statsmodels.api as sm

Next, you can generate some random data to demonstrate KDE:

np.random.seed(0)
data = np.random.randn(1000)  # Generate 1000 random data points

Once you have your data, you can create an instance of the KernelDensity class and fit it to your data:

kde = sm.nonparametric.KDEUnivariate(data)
kde.fit()

After fitting the KDE to the data, you can estimate the probability density at any point using the evaluate method:

density_estimation = kde.evaluate(x)  # Estimate the density at point x

You can also plot the estimated density using matplotlib:

import matplotlib.pyplot as plt

x = np.linspace(-4, 4, 100)  # Generate points for x-axis
plt.plot(x, kde.evaluate(x))
plt.show()

Rank-based nonparametric tests

Nonparametric tests are statistical tests that do not assume a specific distribution for the data. Statsmodels provides several nonparametric tests, such as the Wilcoxon rank-sum test and the Kruskal-Wallis H test.

To perform the Wilcoxon rank-sum test using statsmodels, you can follow these steps:

from scipy.stats import ranksums
import statsmodels.api as sm

group1 = [2, 4, 6, 8, 10]
group2 = [1, 3, 5, 7, 9]

statistic, pvalue = ranksums(group1, group2)
print(f"Wilcoxon rank-sum test statistic: {statistic}")
print(f"p-value: {pvalue}")

To perform the Kruskal-Wallis H test to compare more than two groups:

from scipy.stats import kruskal

group1 = [2, 4, 6, 8, 10]
group2 = [1, 3, 5, 7, 9]
group3 = [0, 3, 6, 9, 12]

statistic, pvalue = kruskal(group1, group2, group3)
print(f"Kruskal-Wallis H test statistic: {statistic}")
print(f"p-value: {pvalue}")

These nonparametric tests can be helpful when you have data that does not meet the assumptions of parametric tests such as t-tests or ANOVA.

Statsmodels provides a comprehensive set of nonparametric statistical methods, allowing you to explore and analyze your data without assuming a specific distribution. Whether you need to estimate probability density using KDE or perform rank-based tests, statsmodels has you covered.