Empirical likelihood confidence intervals for density function in errors-in-variables model

The paper proposes empirical likelihood confidence intervals for the density function in
the errors-in-variables model. We show that the empirical likelihood produces confidence
intervals having theoretically accurate coverage rate for both ordinary and super smooth
measurement errors. Some simulation studies are conducted to compare the finite sample
performances of the empirical likelihood confidence intervals and the z-type confidence
intervals based on Fan (1991)’s asymptotic normality theories.