### 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 language | English (US) |
---|---|

Pages (from-to) | 3217-3245 |

Number of pages | 29 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 25 |

Issue number | 12 |

State | Published - 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Boundary kernel
- Categorical data
- Density estimation
- Smoothing

### ASJC Scopus subject areas

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

### Cite this

**A minimum variance kernel estimator and a discrete frequency polygon estimator for ordinal contingency tables.** / Dong, Jianping; Ye, Qian K.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 25, no. 12, pp. 3217-3245.

}

TY - JOUR

T1 - A minimum variance kernel estimator and a discrete frequency polygon estimator for ordinal contingency tables

AU - Dong, Jianping

AU - Ye, Qian K.

PY - 1996

Y1 - 1996

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=0041938198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041938198&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041938198

VL - 25

SP - 3217

EP - 3245

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 12

ER -