We investigate the problem of nonparametric density estimation on \(\mathbb {R}_{+}\) in the presence of incomplete responses under a Missing At Random (MAR) mechanism. Since standard symmetric kernel estimators are known to suffer from severe boundary effects on positive supports, we develop an inverse-probability-weighted gamma kernel methodology specifically designed to accommodate simultaneously the support constraint and the missingness structure. The proposed procedure is built from an ideal reweighted estimator involving the unknown observation probabilities and from a feasible estimator obtained by replacing these propensity scores with a nonparametric Nadaraya–Watson-type estimate based on fully observed auxiliary covariates. Under suitable regularity and smoothing assumptions, we derive a detailed asymptotic theory for both estimators. In particular, we establish explicit pointwise expansions for the bias and variance, obtain the corresponding mean squared error and mean integrated squared error, and prove asymptotic normality in the interior region. These results extend the classical gamma-kernel framework for complete data to the substantially more delicate setting of MAR incompleteness, and they quantify the additional stochastic cost induced by propensity-score estimation. The finite-sample behavior of the method is assessed through an extensive Monte Carlo study covering several positive-supported models, varying dependence levels between the study variable and the auxiliary covariates, and multiple missingness rates. The numerical evidence shows that the proposed estimator retains the boundary-adaptive advantages of gamma kernels while providing stable and accurate recovery of the target density under incomplete observation. A real-data analysis further illustrates its practical relevance for distributional inference with positive-valued variables subject to missingness.
