Extropy, introduced as a complementary dual to Shannon entropy, provides an alternative measure of uncertainty with valuable interpretations in information theory, statistics, and signal processing. For a continuous random variable with density f, the extropy is defined by \(J(f) = -\frac{1}{2} \int f(x)^2 \, dx\) , making its estimation closely connected to nonparametric density estimation. In this paper, we propose a new nonparametric estimator for extropy based on a locally tilted Kernel Density Estimator (KDE). The method applies an exponential tilting transformation to the classical KDE, reducing bias in squared-density functionals. We derive theoretical properties including consistency and asymptotic normality of the proposed estimator. Simulation studies illustrate its competitive performance relative to plug-in KDE and k-nearest-neighbor methods, and applications to real-world datasets demonstrate its practical utility. The paper contributes a novel bias-reduced approach to estimating extropy and other integral functionals of density functions.
