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Sparse data problems are prominent in applications of offline signature verification. By using a small number of training samples, the class statistics estimation errors may be significant, resulting in worsened verification performance. In this paper, we propose two methods to improve the statistics estimation. The first approach employs an elastic distortion model to artificially generate additional training samples for pairs of genuine signatures. These additional samples, together with original genuine samples, are used to compute statistic parameters for a Mahalanobis distance threshold classifier. The other approach is to adopt regularization techniques to overcome the problem of inverting an ill-conditioned sample covariance matrix due to insufficient training samples. A ridge-like estimator is modeled to add some constant values for diagonal elements of the sample covariance matrix. Experimental results showed that both methods were able to improve verification accuracy when they were incorporated with a set of peripheral features. Effectiveness of the methods was validated by quantity analysis.