Estimates for the SVD of the Truncated Fourier Transform on $$L^2(\cosh (b|\cdot |))$$ and Stable Analytic Continuation

Abstract

We consider a linear model where the coefficients -intercept and slopes -are random and independent from regressors which support is a proper subset. When the slopes do not have heavy tails, the joint density of the random coefficients is identified. Lower bounds on the supremum risk for the estimation of the density are derived for this model and a related white noise model. We present an estimator, its rates of convergence, and a data-driven rule which delivers adaptive estimators. The corresponding R package is RandomCoefficients.

Relaxing monotonicity in endogenous selection models and application to surveys

“…Condition (8) allows for dependence between H and Y and R to be partly based on Y , even conditionally. It provides an alternative identification strategy.…”

“…Remark 7. The techniques in [8], which are used in [7], also allow to estimate by a simple series estimator, under proper integrability, E [φ(Y )|X = x] for almost every x ∈ supp(X) even if we observe X only when it falls in an interval which is a proper subset of supp(X) (a type of censoring…”