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This paper, presents a novel identification approach using fuzzy neural networks. It focuses on structure and parameters uncertainties which have been widely explored in the literatures. The main contribution of this paper is that an integrated analytic framework is proposed for automated structure selection and parameter identification. A kernel smoothing technique is used to generate a model structure automatically in a fixed time interval. To cope with structural change, a hysteresis strategy is proposed to guarantee finite times switching and desired performance.

Building on the work of Barras, Scaillet and Wermers (BSW, 2010), we propose a modified approach to inferring performance for a cross-section of investment funds. Our model assumes that funds belong to groups of different abnormal performance or alpha. Using the structure of the probability model, we simultaneously estimate the alpha locations and the fractions of funds for each group, taking multiple testing into account. Our approach allows for tests with imperfect power that may falsely classify good funds as bad, and vice versa. Examining both mutual funds and hedge funds, we find smaller fractions of zero-alpha funds and more funds with abnormal performance, compared with the BSW approach. We also use the model as prior information about the cross-section of funds to evaluate and predict fund performance.

We outline a general method that estimates smooth functionals of a probability distribution from a sample of observations, restricting the framework to local polynomial fitting. The construction of the estimators is based on a weighted least squares criterion and reproducing kernel Hilbert spaces theory. We briefly discuss their asymptotic properties and review applications to classical bivariate risk measures estimation.