On Estimation of a Probability Density Function and Mode
E274132
"On Estimation of a Probability Density Function and Mode" is a seminal statistical paper by Emanuel Parzen that develops kernel-based methods for nonparametric density and mode estimation.
All labels observed (4)
| Label | Occurrences |
|---|---|
| On Estimation of a Probability Density Function and Mode canonical | 1 |
| Parzen kernel | 1 |
| Parzen window | 1 |
| Parzen window method | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2515039 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: On Estimation of a Probability Density Function and Mode Context triple: [Emanuel Parzen, hasPublication, On Estimation of a Probability Density Function and Mode]
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A.
Innovations approach to detection and estimation
"Innovations approach to detection and estimation" is a seminal work by Thomas Kailath that develops a powerful stochastic framework for solving signal detection and parameter estimation problems, particularly in control and communication systems.
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B.
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
"Extrapolation, Interpolation, and Smoothing of Stationary Time Series" is a foundational mathematical work by Norbert Wiener that developed the theory of optimal prediction and filtering for stationary stochastic processes, laying the groundwork for modern signal processing and control theory.
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C.
Statistical Decision Functions
Statistical Decision Functions is a foundational work in decision theory and statistics that systematically develops the theory of optimal decision-making under uncertainty.
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D.
Neyman–Pearson theory of hypothesis testing
The Neyman–Pearson theory of hypothesis testing is a foundational statistical framework that formalizes how to construct and evaluate tests for competing hypotheses using concepts like Type I and Type II errors and power.
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E.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: On Estimation of a Probability Density Function and Mode Target entity description: "On Estimation of a Probability Density Function and Mode" is a seminal statistical paper by Emanuel Parzen that develops kernel-based methods for nonparametric density and mode estimation.
-
A.
Innovations approach to detection and estimation
"Innovations approach to detection and estimation" is a seminal work by Thomas Kailath that develops a powerful stochastic framework for solving signal detection and parameter estimation problems, particularly in control and communication systems.
-
B.
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
"Extrapolation, Interpolation, and Smoothing of Stationary Time Series" is a foundational mathematical work by Norbert Wiener that developed the theory of optimal prediction and filtering for stationary stochastic processes, laying the groundwork for modern signal processing and control theory.
-
C.
Statistical Decision Functions
Statistical Decision Functions is a foundational work in decision theory and statistics that systematically develops the theory of optimal decision-making under uncertainty.
-
D.
Neyman–Pearson theory of hypothesis testing
The Neyman–Pearson theory of hypothesis testing is a foundational statistical framework that formalizes how to construct and evaluate tests for competing hypotheses using concepts like Type I and Type II errors and power.
-
E.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
scientific article
ⓘ
seminal work in nonparametric statistics ⓘ statistics paper ⓘ |
| author | Emanuel Parzen ⓘ |
| citedAs | Parzen (1962) kernel density estimation paper ⓘ |
| contribution |
analyzed asymptotic properties of kernel density estimators
ⓘ
developed kernel-based methods for mode estimation ⓘ formalized the concept of kernel density estimation ⓘ introduced ideas related to bandwidth selection in kernel density estimation ⓘ introduced kernel-based estimators for probability density functions ⓘ provided a framework for nonparametric mode estimation ⓘ studied bias and variance of kernel density estimators ⓘ studied consistency of kernel density estimators ⓘ |
| field |
density estimation
ⓘ
kernel methods ⓘ nonparametric statistics ⓘ statistics ⓘ |
| focusesOn |
estimation of continuous probability distributions
ⓘ
nonparametric inference without assuming a parametric family ⓘ properties of estimators as sample size tends to infinity ⓘ |
| hasConcept |
asymptotic consistency
ⓘ
bandwidth ⓘ bias-variance tradeoff in smoothing ⓘ kernel function ⓘ mean integrated squared error ⓘ mode of a distribution ⓘ pointwise convergence of estimators ⓘ smoothing parameter ⓘ window estimator ⓘ |
| influenced |
applications of kernel methods in machine learning
ⓘ
applications of kernel methods in pattern recognition ⓘ applications of kernel methods in signal processing ⓘ development of modern kernel density estimation theory ⓘ subsequent research in nonparametric statistics ⓘ |
| language | English ⓘ |
| mainTopic |
nonparametric estimation of a probability density function
ⓘ
nonparametric estimation of the mode ⓘ |
| method |
kernel density estimation
ⓘ
smoothing of empirical distributions using kernels ⓘ use of window functions for density estimation ⓘ |
| usedIn |
biostatistics
ⓘ
econometrics ⓘ machine learning ⓘ pattern recognition ⓘ signal processing ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: On Estimation of a Probability Density Function and Mode Description of subject: "On Estimation of a Probability Density Function and Mode" is a seminal statistical paper by Emanuel Parzen that develops kernel-based methods for nonparametric density and mode estimation.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: On Estimation of a Probability Density Function and Mode
linked to: On Estimation of a Probability Density Function and Mode