A minimum variance kernel estimator and a discrete frequency polygon estimator for ordinal contingency tables

Jianping Dong, Qian K. Ye

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper introduces two estimators, a boundary corrected minimum variance kernel estimator based on a uniform kernel and a discrete frequency polygon estimator, for the cell probabilities of ordinal contingency tables. Simulation results show that the minimum variance boundary kernel estimator has a smaller average sum of squared error than the existing boundary kernel estimators. The discrete frequency polygon estimator is simple and easy to interpret, and it is competitive with the minimum variance boundary kernel estimator. It is proved that both estimators have an optimal rate of convergence in terms of mean sum of squared error. The estimators are also defined for high-dimensional tables.

Original languageEnglish (US)
Pages (from-to)3217-3245
Number of pages29
JournalCommunications in Statistics - Theory and Methods
Volume25
Issue number12
StatePublished - 1996
Externally publishedYes

Fingerprint

Minimum Variance
Variance Estimator
Kernel Estimator
Contingency Table
Polygon
Estimator
Optimal Rate of Convergence
Tables
High-dimensional
kernel
Cell
Simulation

Keywords

  • Boundary kernel
  • Categorical data
  • Density estimation
  • Smoothing

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Statistics and Probability

Cite this

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AB - This paper introduces two estimators, a boundary corrected minimum variance kernel estimator based on a uniform kernel and a discrete frequency polygon estimator, for the cell probabilities of ordinal contingency tables. Simulation results show that the minimum variance boundary kernel estimator has a smaller average sum of squared error than the existing boundary kernel estimators. The discrete frequency polygon estimator is simple and easy to interpret, and it is competitive with the minimum variance boundary kernel estimator. It is proved that both estimators have an optimal rate of convergence in terms of mean sum of squared error. The estimators are also defined for high-dimensional tables.

KW - Boundary kernel

KW - Categorical data

KW - Density estimation

KW - Smoothing

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