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Estimators for derivatives associated with a density function can be useful in identifying its modes and inflection points. In addition, these estimators play an important role in plug-in methods associated with bandwidth selection in nonparametric kernel density estimation. In this paper, we extend the nonparametric class of density estimators proposed by Mynbaev and Martins-Filho (2010) to the estimation of m-order density derivatives. Contrary to some existing derivative estimators, the estimators in our proposed class have a full asymptotic characterization, including uniform consistency and asymptotic normality. An expression for the bandwidth that minimizes an asymptotic approximation for the estimators’ integrated squared error is provided. A Monte Carlo study sheds light on the finite sample performance of our estimators and contrasts it with that of density derivative estimators based on the classical Rosenblatt–Parzen approach.

The chapter studies strategic default using an experimental approach.

The experiment considers a stochastic asset process and a loan with no down-payment. The treatments are two asset volatilities (high and low) and the absence and presence of social interactions via a direct effect on the subject's payoff.

I demonstrate that (i) people appear to follow the prediction of the strategic default model quite closely in the high asset volatility treatment, and that (ii) incorporating social interactions delays the strategic default beyond what is considered optimal.

The study tests adequately the strategic default using a novel experimental design and analyzes the neighbor's effect on that decision.