Hyperspectral sensors are envisioned to acquire hundreds of images within narrow contiguous bands to characterize materials on the Earth. Many unknown materials are uncovered by the very high spectral resolution data. The virtual dimensionality (VD), originally developed by Chein-I Chang (2004), estimates the number of spectrally distinct materials in the sensed data. Subsequently, several approaches have been proposed wherein the VD is estimated by the Neyman-Pearson detection theory based eigen thresholding method. However, the methods are subjected to inflated Type I error as binary hypothesis tests are carried out separately on each band image (without controlling the overall Type I error). It may lead to false identification of the VD. In this paper, we propose a multiple-hypothesis based statistical approach while modifying p-values for the number of hypothesis tests carried out in order to overcome this issue. We propose to apply Ben-jamini and Hochberg procedure to control the false discovery rate (overall Type I error rate) and hence improve the VD estimation. It is a sequential Bonferroni type procedure which controls the expected proportion of falsely rejected null hypotheses or the false discovery rate. We evaluate the performance of the proposed approach by experimenting on synthetic hyperspectral data at different noise levels and on three real benchmark data sets. © 2019 IEEE.