Influence on smoothness in penalized likelihood regression for binary data (Q1861631)

For independent, binary observations \(y_i\), \(i=1,\dots,n\), the distribution of \(y_i\) is supposed to be \(\exp(y_i\ln(\mu(t_i)/(1-\mu(t_i)))+\ln(1-\mu(t_i))\), where \(t_i\) is an independent variable and \(\mu\) is an unknown function. A penalized maximum likelihood estimator for \(\mu\) is considered with the smoothing parameter \(\lambda\). A generalized cross-validation technique for \(\lambda\) selection is described. Influence of changes in the data on the estimates of \(\lambda\) and \(\mu\) is investigated. Examples of biological data analysis are considered.