User:Bonvoisin

I am interested in various mathematical topics: measure theory, probability, statistics, biostatistics and econometrics. In econometrics one topic I am particularly interested in is "Indirect inference".

Indirect inference

Indirect inference is a parameter estimation method that is mostly used in econometrics. It is essentially useful when likelihood related methods are too complex or too computing time consuming.

Model

Let a statistical model defined by a parametric family $$P_\theta,\ Y_i \sim P_\theta, i=1,...,N $$, the indirect method for estimating $$\theta$$ has several steps:
 * 1) Auxiliary parameter estimate:

$$\hat{\beta}=argmax \ Q_N(y_N,\beta)$$
 * 1) Simulated auxiliary parameter estimate:

$$\hat{\beta}_{SN}(\theta)=\frac{1}{S}\sum argmax \ Q_N(z_N^s(\theta),\beta)$$
 * 1) Indirect estimate:

$$\hat{\theta}_{SN}= argmin \ ^t(\hat{\beta}-\hat{\beta}_{SN}(\theta))\Omega (\hat{\beta}-\hat{\beta}_{SN}(\theta))$$