Linear Regression with Truncated and Censored Data

Linear regression with censored data is a regression model, the dependent variable of which is censored, that is, the variable is transformed if it is less or (greater) than a certain threshold.

Unlike the censored data model, in the truncated data model, observation is entirely excluded if the response is less (or greater) of a certain threshold.

Let the time series be given according to the linear regression model:

The εt errors are a sequence of independent identically distributed random variables. Errors can have the normal and logistic probability distribution or the probability distribution of the first-type extremum (Gumbel distribution). The main characteristics of these distributions are given in the table:

Characteristic\
Distribution
Normal Logistic Gumbel
Density
Distribution function
Mean: 0 0 -0.57721566…
Variance 1

The censored regression is defined as follows:

The truncated regression is defined as follows: yt = zt is present only if lzrt.

On estimating censored or truncated regression, it is necessary to use the observations y1,…,yT and l1,…,lT, r1,…,rt to estimate the parameters β1,…+βn,σ.

See also:

Library of Methods and Models | Linear Regression | ISmCensoredTruncatedRegression