Estimation of a regression function corresponding to latent variables

•We estimate the regression function for a linear latent variable model.•We use a nonparametric least squares estimates.•We require no assumptions on the structure or smoothness of the regression function.•The strong consistency of the estimates is shown.

The problem of estimation of a univariate regression function from latent variables given an independent and identically distributed sample of the observable variables in the corresponding common factor analysis model is considered. Nonparametric least squares estimates of the regression function are defined. The strong consistency of the estimates is shown for subgaussian random variables whose characteristic function vanishes nowhere. This consistency result does not require any assumptions on the structure or the smoothness of the regression function.