# Biased cross-validation (BCV) bandwidth matrix selector for bivariate data

### Description

BCV bandwidth matrix for bivariate data.

### Usage

1 2 |

### Arguments

`x` |
matrix of data values |

`whichbcv` |
1 = BCV1, 2 = BCV2. See details below. |

`Hstart` |
initial bandwidth matrix, used in numerical optimisation |

`binned` |
flag for binned kernel estimation. Default is FALSE. |

`amise` |
flag to return the minimal BCV value. Default is FALSE. |

`verbose` |
flag to print out progress information. Default is FALSE. |

### Details

Use `Hbcv`

for full bandwidth matrices and `Hbcv.diag`

for diagonal bandwidth matrices. These selectors are only
available for bivariate data. Two types of BCV criteria are
considered here. They are known as BCV1 and BCV2, from Sain, Baggerly
& Scott (1994) and only differ slightly. These BCV
surfaces can have multiple minima and so it can be quite difficult to
locate the most appropriate minimum. Some times, there can be no local minimum at all so there
may be no finite BCV selector.

For details about the advanced options for `binned`

, `Hstart`

, see `Hpi`

.

### Value

BCV bandwidth matrix. If `amise=TRUE`

then the minimal BCV value is returned too.

### References

Sain, S.R, Baggerly, K.A. & Scott, D.W. (1994)
Cross-validation of multivariate densities. *Journal of the
American Statistical Association*. **82**, 1131-1146.

### See Also

`Hlscv`

, `Hpi`

, `Hscv`

### Examples

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