## A First Course on Parametric InferenceStarting with the basic concept of sufficient statistics, the approach based on minimum variance unbiased estimation is presented, in detail, in this text. |

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this book is a great source to learn parametric inference. i have tried this. this is great :D

### Contents

Introduction | 1 |

Sufficient Statistic | 11 |

Minimum Variance Unibased Estimation | 44 |

Simultaneous Estimation of Several Parameters | 72 |

Consistent Estimators | 90 |

Consistent Asymptotically Normal Estimators | 115 |

Method of Maximum Likelihood | 138 |

Tests of HypothesesI | 174 |

Tests of HypothesesII | 205 |

Interval Estimation | 239 |

263 | |

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### Common terms and phrases

assume asymptotic distribution asymptotic variance Cauchy distribution conditional distribution consider consistent estimator Cramer family critical region CRLB defined denote depend determine distribution with pdf error Example exists exponential distribution exponential with mean Fisher information Fisher information matrix fixed Hence hypotheses implies independent interval joint pdf Laplace large sample level a test likelihood equation log L(x M-optimal method of moments minimal sufficient statistic MP test multinomial distribution MVUE N-P lemma normal Note null hypothesis observed obtain order statistic parameter exponential family Pareto distribution pdf belonging pdf f(x percentile pivotal quantity Poisson Poisson distribution power function problem random sample Rao-Blackwell regularity conditions reject H0 SELCI solution test is given testing H0 Theorem transformation type I error UMP level unbiased estimator variance covariance matrix zero otherwise