Asymptotic expansion for the distribution of the discriminant function in the first order autoregressive processes
This paper is concerned with the problem of classifying a series of T observations coming from one of two first order autoregressive Gaussian processes. The processes are determined by the stochastic equations \(y_ t=\alpha_ jy_{t-1}+u_ t\) \((t=...-1,0,1,...)\) where \(\alpha_ j\) \((| \alpha_ j| <1)\) is known, and \(u_ t's\) are independent identically distributed as \(N(0,\sigma^ 2_ j)\) with known variance \(\sigma^ 2_ j\) \((j=1,2)\). We consider the discriminant function based on the Bayes method, which is a quadratic function of observations. We derive an asymptotic expansion of the distributions of the discriminant function and give an approximation for the probabilities of misclassifications.
first order autoregressive Gaussian processes
scientific article; zbMATH DE number 3996902