Purpose The purpose of the present work is to design robust estimators for speech enhancement by incorporation of calculation rank-order statistics and locally-adaptive neighborhoods. The proposed estimators are able to increase the speech quality of a noisy signal, to preserve better speech intelligibility, and to introduce less artifacts comparing with known speech enhancement estimators. Design/methodology/approach We design a novel speech enhancement algorithm based on rank-order statistics and local adaptive signal processing to improve the accuracy of existing speech enhancement estimators, in terms of speech quality, intelligibility, and introduction of artificial artifacts. Findings We found that by using the proposed estimators for speech enhancement we obtain a better adaptation to nonstationary characteristics of speech and noise processes comparing with that of known speech enhancement estimators. The proposed algorithm increases speech quality, preserves better speech intelligibility, and introduces less artifacts comparing with known speech enhancement estimators. Research limitations/implications The proposed approach for speech enhancement is a locally-adaptive signal processing performed for each element of a noisy speech signal. Thus, the main limitation of the proposed approach is an increase of computational complexity compared with that of nonadaptive conventional techniques. Practical implications In order to perform real-time speech enhancement with the proposed approach, it is recommended to use a digital system with a fast processor. Another option is by using a parallel architecture such as a FPGA. Originality/value We propose a novel local-adaptive algorithm for robust speech enhancement by incorporation of calculation of rank-order statistics and local-adaptive neighborhoods. The proposed algorithm is able to adjust itself in response to changes in the statistical properties of ambience noise.