Description Usage Arguments Details Value Author(s) References Examples

The function estimates the discrete and continuous regression in a single value or in a grid using associated kernels. Different associated kernels are available: extended beta, gamma, lognormal, reciprocal inverse Gaussian (for continuous data), DiracDU (for categorical data), binomial and also discrete triangular (for count data).

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`Vec` |
The explanatory variable. |

`y` |
The response variable. |

`type_data` |
The sample data type. |

`ker` |
The associated kernel: "dirDU" DiracDU,"bino" binomial, "triang" discrete triangular, etc. |

`h` |
The bandwidth or smoothing parameter. |

`x` |
The single value or the grid where the regression is computed. |

`a0` |
The left bound of the support used for extended beta kernel. Default value is 0 for beta kernel. |

`a1` |
The right bound of the support used for extended beta kernel. Default value is 0 for beta kernel. |

`a` |
The arm in Discrete Triangular kernel. The default value is 1. |

`c` |
The number of categories in DiracDU. The default value is 2. |

`...` |
Further arguments |

The associated kernel estimator *\widehat{m}_n* of *m* is defined in the above sections; see also Kokonendji and Senga Kiessé (2011). The bandwidth parameter in the function is obtained using the cross-validation technique for the seven associated kernels. For binomial kernel, the local Bayesian approach is also implemented; see Zougab et al. (2014).

Returns a list containing:

`data` |
The data sample, explanatory variable |

`y` |
The data sample, response variable |

`n` |
The size of the sample |

`kernel` |
The asociated kernel |

`h` |
The bandwidth |

`eval.points` |
The grid where the regression is computed |

`m_n` |
The estimated values |

`Coef_det` |
The coefficient of determination |

W. E. Wansouwé, S. M. Somé and C. C. Kokonendji

Kokonendji, C.C. and Senga Kiessé, T. (2011). Discrete associated kernel method and extensions,
*Statistical Methodology* **8**, 497 - 516.

Kokonendji, C.C., Senga Kiessé, T. and Demétrio, C.G.B. (2009). Appropriate kernel regression on a count explanatory variable and applications,
*Advances and Applications in Statistics* **12**, 99 - 125.

Zougab, N., Adjabi, S. and Kokonendji, C.C. (2014). Bayesian approach in nonparametric count regression with binomial kernel, * Communications in Statistics - Simulation and Computation * **43**, 1052 - 1063.

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