The paper presents a method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in high-dimensional models. The method is based on the lasso and involves "desparsifying" the estimator by inverting the KKT conditions. It is shown to be asymptotically optimal in terms of semiparametric efficiency. The method is extended to generalized linear models with convex loss functions and is analyzed for Gaussian, sub-Gaussian, and bounded correlated designs. The paper discusses the challenges of constructing confidence intervals and tests in high-dimensional sparse models, where traditional methods fail due to the non-trivial limiting distributions of sparse estimators. The proposed method uses a residual-based bootstrap scheme and is shown to be consistent for high-dimensional settings. The paper also discusses related work, including methods for quantifying uncertainty in high-dimensional models, and provides theoretical results for linear and generalized linear models. The method is shown to be asymptotically normal and to achieve semiparametric efficiency under certain conditions. The paper also discusses the use of nodewise regression to approximate the inverse of the matrix of second-order derivatives and provides theoretical results for the asymptotic normality of the estimator. The method is shown to be robust to non-Gaussian designs and errors, and the paper provides theoretical results for non-Gaussian models. The paper concludes with a discussion of the implications of the results for statistical inference in high-dimensional models.The paper presents a method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in high-dimensional models. The method is based on the lasso and involves "desparsifying" the estimator by inverting the KKT conditions. It is shown to be asymptotically optimal in terms of semiparametric efficiency. The method is extended to generalized linear models with convex loss functions and is analyzed for Gaussian, sub-Gaussian, and bounded correlated designs. The paper discusses the challenges of constructing confidence intervals and tests in high-dimensional sparse models, where traditional methods fail due to the non-trivial limiting distributions of sparse estimators. The proposed method uses a residual-based bootstrap scheme and is shown to be consistent for high-dimensional settings. The paper also discusses related work, including methods for quantifying uncertainty in high-dimensional models, and provides theoretical results for linear and generalized linear models. The method is shown to be asymptotically normal and to achieve semiparametric efficiency under certain conditions. The paper also discusses the use of nodewise regression to approximate the inverse of the matrix of second-order derivatives and provides theoretical results for the asymptotic normality of the estimator. The method is shown to be robust to non-Gaussian designs and errors, and the paper provides theoretical results for non-Gaussian models. The paper concludes with a discussion of the implications of the results for statistical inference in high-dimensional models.