Géraldine Laurent

Parametric conditional variance estimation in location-scale models with censored data

Abstract: Suppose the random vector (X,Y ) satisfies the regression model Y = m(X)+σ(X)ε, where m(·) = E(Y |·), σ2(·) = Var(Y |·) belongs to some parametric class {σθ(·) : θ ∈ Θ} and ε is independent of X. The response Y is subject to random right censoring and the covariate X is completely observed. A new estimation procedure is proposed for σθ(·) when m(·) is unknown. It is based on nonlinear least squares estimation extended to conditional variance in the censored case. The consistency and asymptotic normality of the proposed estimator are established. The estimator is studied via simulations and an important application is devoted to fatigue life data analysis. MSC 2010 subject classifications: Primary 62N01, 62N02; secondary 62N05.

Computational Treatment of the Error Distribution in Nonparametric Regression with Right-Censored and Selection-Biased Data

Consider the regression model Y = m(X) + φ(X)e, where m(X) = E[Y ∣X] and φ2(X) = V ar[Y ∣X] are unknown smooth functions and the error e (with unknown distribution) is independent of X. The pair (X, Y) is subject to parametric selection bias and the response to right censoring. We construct a new estimator for the cumulative distribution function of the error e, and develop a bootstrap technique to select the smoothing parameter involved in the procedure. The estimator is studied via extended simulations and applied to real unemployment data.