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Bayes Estimation of Two-Phase Linear Regression Model

机译：两相线性回归模型的贝叶斯估计

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摘要

Let the regression model be Y_i = β_1X_i + ε_i, where ε_i, are i. i. d. N (0, σ~2) random errors with variance σ~2 > 0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after X_m by change in slope, regression parameter β_2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β_1,β_2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.
机译：令回归模型为Y_i =β_1X_i+ε_i，其中ε_i为i。一世。 d。 N（0，σ〜2）个随机误差，方差σ〜2> 0，但后来发现系统在某个时间点m发生了变化，并通过斜率的变化反映在X_m之后的序列中，回归参数β_2。研究的问题是这种变化何时何地开始发生。这称为更改点推断问题。 m，β_1，β_2的估计值是根据非对称损失函数（即Linex损失和General Entropy损失函数）导出的。研究正确和错误的先验信息对贝叶斯估计的影响。

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    Mayuri Pandya; Krishnam Bhatt; Paresh Andharia;

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    Department of Statistics, Bhavnagar University, University Campus, Near Gymkhana, Bhavnagar 364002, India;

    Department of Statistics, Bhavnagar University, University Campus, Near Gymkhana, Bhavnagar 364002, India;

    Department of Mathematics, Bhavnagar University, University Campus, Near Gymkhana, Bhavnagar 364002, India;

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