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Everything about Kernel density estimation

Concept in statistics

In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Kernel density estimationA 5-minute orientation
  2. Skim a recent paper: Incipient Fault Detection in a Hydraulic System Using Canonical Variable Analysis Combined with Adaptive Kernel Density EstimationInfluential work since 2022
  3. Pick up a classic book: The Elements of Statistical LearningThe most-reprinted book on the subject
  4. Read the landmark paper: Variable Kernel Density EstimationCited 699 times
  5. Go sideways: Multivariate kernel density estimationA closely related topic
  6. Go sideways: Kernel regressionA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Definition
  2. Example
  3. Bandwidth selection
  4. Relation to the characteristic function density estimator
  5. Geometric and topological features
  6. Statistical implementation

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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