Confidence Intervals for the Slope in a Linear Errors-in-Variables Regression Model

Abstract

The linear errors-in-variables model treated in this paper is the following. Independent observations (x _i , y _i ), i = 1, 2, ..., N, are obtained, where

$$ \begin{gathered} \left( {\begin{array}{*{20}c} {x_i } \\ {y_i } \\ \end{array} } \right) = \left( {\begin{array}{*{20}c} {u_i } \\ {a + bu_i } \\ \end{array} } \right) + \left( {\begin{array}{*{20}c} {e_i } \\ {f_i } \\ \end{array} } \right),i = 1,2, \ldots ,N, \hfill \\ \left( {\begin{array}{*{20}c} {e_i } \\ {f_i } \\ \end{array} } \right), \ldots ,\left( {\begin{array}{*{20}c} {e_n } \\ {f_N } \\ \end{array} } \right),conditional\;on\;u_1 , \ldots ,u_N \;are i.i.d. N\left( {\left( {\begin{array}{*{20}c} 0 \\ 0 \\ \end{array} } \right),\sum } \right) \hfill \\ \end{gathered} $$

((1.1))