Asymptotic Expansion of the Distribution of a Studentized Test Statistic for the Slope Parameter in a Simple Linear Structural Relationship

Journal of Korean Society for Quality Management > Volume 21(1); 1993 > Article

Journal of Korean Society for Quality Management 1993;21(1): 171-.

ABSTRACT

Variables, x and y are said to have a linear relation if $y={eta}_0+{eta}_1;x$, and ${eta}_0$ and ${eta}_1$ are constants. The relationship is called a structural relationship if x has positive variance (i.e., x is not fixed) and only error-prone measurements of x and y can be obtained. This paper derives (to order $n^{+1/2}$) an approximate distribution of the Studentized test statistic for testing hypotheses about the slope parameter, ${eta}_1$ in a simple linear structural model. A simulation study suggests our approximate distribution is more accurate approximation to the exact distributions of the Studentized statistic than is the limiting distribution.