A SMOOTH NONPARAMETRIC CONDITIONAL DENSITY TEST FOR CATEGORICAL RESPONSES

We propose a consistent kernel-based specification test for conditional density models when the dependent variable is categorical/discrete. The method is applicable to popular parametric binary choice models such as the logit and probit specification and their multinomial and ordered counterparts, along with parametric count models, among others. The test is valid when the conditional density function contains both categorical and real-valued covariates. Theoretical support for the test and for a bootstrap-based version of the test is provided. Monte Carlo simulations are conducted to assess the finite-sample performance of the proposed method.

Dynamic Pricing Model of Power Options in a Fractional Market

In this paper, we study the new method of option pricing based on the risk preference. We define the equivalent classes of random events based on the historical information and the risk preference. The dynamic pricing model of power options has been studied. Applying the conditional density function of the stock price process, we have given the explicit solution of the model. And we analyze the influence of Hurst parameter on pricing formula.

EFFICIENCY BOUNDS FOR SEMIPARAMETRIC ESTIMATION OF INVERSE CONDITIONAL-DENSITY-WEIGHTED FUNCTIONS

Consider the unconditional moment restriction E[m(y, υ, w; π0)/fV|w (υ|w) −s (w; π0)] = 0, where m(·) and s(·) are known vector-valued functions of data (y┬, υ, w┬)┬. The smallest asymptotic variance that $\root \of n $-consistent regular estimators of π0 can have is calculated when fV|w(·) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that “plug-in” kernel-based estimators of π0 constructed from this type of moment restriction, such as Lewbel (1998, Econometrica 66, 105–121) and Lewbel (2007, Journal of Econometrics 141, 777–806), are semiparametric efficient.