In this paper, we apply the empirical likelihood approach to discriminant analysis of non-Gaussian vector stationary processes. We propose a classification statistic based on the empirical likelihood ratio function, and develop the discriminant procedure without assuming that the true spectral density matrix is known. Even if the true structure of the process is unknown, it is shown that the empirical likelihood classification criterion is consistent in the sense that the misclassification probabilities converge to 0 as sample size tends to infinity. A noteworthy point of the procedure is that the asymptotics of the empirical likelihood discriminant statistic for scalar processes are always independent of non-Gaussianity of the process under contiguous conditions.

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In this paper, we improve Komori-Shirai’s result about the boundedness of the fractional integral operators on weighted Morrey spaces.

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The present paper proposes a new model to discuss the efficiency of optimal business hours for retailers. The model can be applied generally for any retailer and especially exercised within the newsvendor problem framework. Under the proposed model, the customers’ residences are uniformly distributed over the Hotelling unit interval and each individual customer departs from her residence for the store at a finite velocity. Customers purchase a single product only if they arrive at the retailer’s store during business hours. Under these circumstances, this study explores efficiency of the model to obtain optimal business hours for retailers. Numerical examples are also provided to illustrate the theoretical underpinnings of the proposed model formulation.

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