  This paper extends three Lasso inferential methods, Debiased Lasso,
$C(\alpha)$ and Selective Inference to a survey environment. We establish the
asymptotic validity of the inference procedures in generalized linear models
with survey weights and/or heteroskedasticity. Moreover, we generalize the
methods to inference on nonlinear parameter functions e.g. the average marginal
effect in survey logit models. We illustrate the effectiveness of the approach
in simulated data and Canadian Internet Use Survey 2020 data.
