This paper describes a method for estimating a confidence value (CV) by which we can express the potential correctness of handwritten Kanji character recognition candidates. An accumulated confidence value (ACV), calculated as the sum of CVs, is also applied to reduce the number of candidates. Such reduction is vital to increasing the speed of such applications as Kanji address recognition, and it also reduces the probability of misreadings in linguistic postprocessing. Sorted sets of character candidates, ranked in increasing order of each candidates distance value, are used as feature vectors. A CV is defined as the a posteriori probability with respect to each rank. To obtain good quality approximations of probability density functions (PDFs), we introduce a subspace within which correct data can easily be separated from erroneous data and then estimate PDF parameters over this subspace. Next, we use an ACV as a measure for expressing a threshold for candidate acceptance in Kanji character recognition. The efficiency of the proposed method is evaluated in an experiment using IPTP CD-ROM2 Japanese address images, and a comparison with the results for a conventional method shows that a roughly 35% reduction in the number of candidates is obtained without reducing the number of correct candidates.