The framework is quite general allowing the parameters defining the additional and maintained conditional moment restrictions to differ and permitting the conditioning variates to differ likewise.
In consequence, the threshold point can be adaptively estimated even under conditional moment restrictions.
By using the conditional moment restrictions, as we expect, we can increase the efficiency of the resulting estimator [8 10].
Possible methods include using conditional variance restrictions as in Graham (2008), or using variation in network/group size as in Lee (2007).
This indicates that using the conditional moment restrictions, the estimates are more accurate, regardless of the samples size and the different unknown parameter.
Specifically, based on the empirical likelihood method, we consider the parameter estimation problem for Poisson autoregressive model with conditional moment restrictions.
Root-n-consistent estimators of the regression coefficients in the linear censored regression model under conditional quantile restrictions on the error terms were proposed by Powell (Journal of Econometrics 25 (1984) 303 325, 32 (1986a) 143 155).
Our approach yields more efficient estimates compared to the maximum likelihood estimator, the least squares estimator and the weighted least squares estimator, which do not utilize the conditional moment restrictions.
Here, we assume that we have some auxiliary information that can be represented as the following conditional moment restrictions: E bigl(g(X_{t},ldots,X_{t-p}; theta_{0})|X t-1) bigr)=0 (1.2) for each (t=0, 1, 2,ldots) , where the unknown parameter vector (theta _{0}in R^{d}), (X(t-1)=(X_{t-1}, ldots, X_{t-p})) and (g(x;theta)in R^{r}) is some function with (rgeq d).
The second is a nonstationary model with a conditional independence restriction.
