Zonoid depth,as a well-known ordering tool,is well-defined and has been widely used in multivariate analysis.However,its depth value vanishes outside the convex hull of the data cloud,namely,outside problem,and its computation is hard to achieve,which consequently hinders its practical applications,e.g.,classification.In this paper,we propose a new class of Lq-norm zonoid depths in order to overcome the outside problem.Since the new zonoid depth in this paper satisfies all basic requirements for the axiomatic definition of general depth functions,it is a desirable statistical depth function,which can be utilized to order multivariate observations and construct other statistical methods.The new depth does not have the outside problem and is easy to be computed,which is expected to have its potential usage and worthy of further consideration.
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