### Abstract

In this paper, we consider the estimation problem of f(0), the value of density f at the left endpoint 0. Nonparametric estimation of f(0) is rather formidable due to boundary effects that occur in nonparametric curve estimation. It is well known that the usual kernel density estimates require modifications when estimating the density near endpoints of the support. Here we investigate the local polynomial smoothing technique as a possible alternative method for the problem. It is observed that our density estimator also possesses desirable properties such as automatic adaptability for boundary effects near endpoints. We also obtain an 'optimal kernel' in order to estimate the density at endpoints as a solution of a variational problem. Two bandwidth variation schemes are discussed and investigated in a Monte Carlo study.

Original language | English (US) |
---|---|

Pages (from-to) | 301-316 |

Number of pages | 16 |

Journal | Journal of Statistical Planning and Inference |

Volume | 70 |

Issue number | 2 |

DOIs | |

State | Published - Jul 15 1998 |

### Fingerprint

### Keywords

- Bandwidth variation
- Boundary effects
- Density estimation
- Local polynomial smoothers
- Optimal kernel
- Primary 62G07
- Secondary 62C20, 62J20

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

*Journal of Statistical Planning and Inference*,

*70*(2), 301-316. https://doi.org/10.1016/S0378-3758(97)00187-0

**On kernel density estimation near endpoints.** / Zhang, Shunpu; Karunamuni, Rohana J.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 70, no. 2, pp. 301-316. https://doi.org/10.1016/S0378-3758(97)00187-0

}

TY - JOUR

T1 - On kernel density estimation near endpoints

AU - Zhang, Shunpu

AU - Karunamuni, Rohana J.

PY - 1998/7/15

Y1 - 1998/7/15

N2 - In this paper, we consider the estimation problem of f(0), the value of density f at the left endpoint 0. Nonparametric estimation of f(0) is rather formidable due to boundary effects that occur in nonparametric curve estimation. It is well known that the usual kernel density estimates require modifications when estimating the density near endpoints of the support. Here we investigate the local polynomial smoothing technique as a possible alternative method for the problem. It is observed that our density estimator also possesses desirable properties such as automatic adaptability for boundary effects near endpoints. We also obtain an 'optimal kernel' in order to estimate the density at endpoints as a solution of a variational problem. Two bandwidth variation schemes are discussed and investigated in a Monte Carlo study.

AB - In this paper, we consider the estimation problem of f(0), the value of density f at the left endpoint 0. Nonparametric estimation of f(0) is rather formidable due to boundary effects that occur in nonparametric curve estimation. It is well known that the usual kernel density estimates require modifications when estimating the density near endpoints of the support. Here we investigate the local polynomial smoothing technique as a possible alternative method for the problem. It is observed that our density estimator also possesses desirable properties such as automatic adaptability for boundary effects near endpoints. We also obtain an 'optimal kernel' in order to estimate the density at endpoints as a solution of a variational problem. Two bandwidth variation schemes are discussed and investigated in a Monte Carlo study.

KW - Bandwidth variation

KW - Boundary effects

KW - Density estimation

KW - Local polynomial smoothers

KW - Optimal kernel

KW - Primary 62G07

KW - Secondary 62C20, 62J20

UR - http://www.scopus.com/inward/record.url?scp=0032527297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032527297&partnerID=8YFLogxK

U2 - 10.1016/S0378-3758(97)00187-0

DO - 10.1016/S0378-3758(97)00187-0

M3 - Article

AN - SCOPUS:0032527297

VL - 70

SP - 301

EP - 316

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 2

ER -