## Adaptive RegressionLinear regression is an important area of statistics, theoretical or applied. There have been a large number of estimation methods proposed and developed for linear regression. Each has its own competitive edge but none is good for all purposes. This manuscript focuses on construction of an adaptive combination of two estimation methods. The purpose of such adaptive methods is to help users make an objective choice and to combine desirable properties of two estimators. |

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### Contents

II | 1 |

III | 6 |

IV | 8 |

V | 11 |

VII | 12 |

VIII | 17 |

IX | 19 |

X | 21 |

XXXII | 91 |

XXXIII | 94 |

XXXIV | 97 |

XXXV | 99 |

XXXVII | 100 |

XXXVIII | 102 |

XXXIX | 107 |

XL | 109 |

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### Common terms and phrases

a-trimmed LS absolutely continuous adaptive combination adaptive procedures assume asymptotic distribution asymptotic representation asymptotic variance asymptotically normally distributed based on regression Boscovich Brownian bridge calculate Chapter choice combination of LAD component computed consistent estimator convex combination corresponding data set decision procedure defined denote density f design matrix diagonal elements Dodge and Jurecková equations errors F-test finite fixed Gutenbrunner hence Koenker and Bassett kurtosis L1-norm LAD and LS LAD estimator LAD+TLS least absolute deviations least squares estimator leverage linear model linear regression model Ln(a location model LS-TLS M-test mean squared error median-type test minimization normal distribution obtain off-diagonal elements Op(n optimal order statistics parameter problem proposed regression coefficients regression quantile regression rank scores residuals resulting estimator S-PLUS sample satisfying Sn(Y solution studentized M-estimators studentized residuals symmetric TABLE Theorem trimmed least squares trimmed LS estimator trimmed mean trimming proportion vector

### Popular passages

Page 162 - Dodge, Y. (1984). Robust estimation of regression coefficients by minimizing a convex combination of least squares and least absolute deviations. Computational Statistics Quarterly, vol. 1, pp. 139-153. Field, CA, and EM Ronchetti (1991). An overview of small sample asymptotic«.