observation. See, e.g., reviews of Carroll, Rupert and Stefanski (1995); Chen, Hong and Nekipelov (2009); the problem is examined in Cunha, Heckman and Schennach (2010). Suppose that g is the density of a mismeasured variable, x $^{∗}$, z is observed and has density w$_{1}$ ; z = x $^{∗}$+ u, where u is measurement/contamination error independent of x ∗ with a density, f. Another observation, x, on x ∗ is available: x = x ∗ + u$_{x}$, where u$_{x}$ is not necessarily independent but E ( u$_{x}$ | x $^{∗}$, u ) = 0 . Example 2. Errors in variables regression (EIV) model with Berkson type measurement error. Review Chen, Hong and Nekipelov (2009); examined by Newey (2001), univariate case in Schennach (2007) and Zinde-Walsh (2009), multivariate Zinde-Walsh (2010). Consider x = x ∗ + u$_{x}$ ; (1) z = x ∗ + u. (2) y = g ( x $^{∗}$) + u$_{y}$ ; (3) x = x ∗ + u$_{x}$ ; (4) z = x ∗ + u. (5) 3