The rapid development of astronomical observation has led to many large sky surveys such as SDSS (Sloan digital sky survey) and LAMOST (large sky area multi-object spectroscopic telescope). Since these surveys have produced very large numbers of spectra, automated spectral analysis becomes desirable and necessary. The present paper studies the spectral classification method based on Bayes decision theory, which divides spectra into three types: star, galaxy and quasar. Firstly, principal component analysis (PCA) is used in feature extraction, and spectra are projected into the 3D PCA feature space; secondly, the class conditional probability density functions are estimated using the non-parametric density estimation technique, Parzen window approach; finally, the minimum error Bayes decision rule is used for classification. In Parzen window approach, the kernel width affects the density estimation, and then affects the classification effect. Extensive experiments have been performed to analyze the relationship between the kernel widths and the correct classification rates. The authors found that the correct rate increases with the kernel width being close to some threshold, while it decreases with the kernel width being less than this threshold.