Erratum to: Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data

1 Erratum to: Comput Stat DOI 10.1007/s00180-015-0612-8

In the original publication of the article, the formula in Sect. 3.2 is incorrect. The correct version of the formula is given below:

$$\begin{aligned} {{{\bar{\varvec{\theta }}} }^{(k + 1)}}= & {} {{{\bar{\varvec{\theta }}} }^{(k)}} + {\left( {\sum \limits _{i = 1}^m {\varvec{H}_{\varvec{i}}}^T{{\varvec{\Lambda } _{\varvec{i}}}}{{\varvec{V}_{\varvec{i}}}}^{\!\!-1}{{\tilde{\varvec{\Lambda }}_i}}{\varvec{H}_{\varvec{i}}}} + {\hat{\varvec{G}}} \right) ^{- 1}} \\&\left. \times \left( {\sum \limits _{i = 1}^m {\varvec{H}_{\varvec{i}}}^T{{\varvec{\Lambda }_{\varvec{i}}}}{{\varvec{V}_{\varvec{i}}}^{\!\!-1}{{\tilde{\varvec{S}}}_i}} - {\hat{\varvec{G}}} {\varvec{\theta }} } \right) \right| _{{\varvec{\theta }} = {{{\bar{\varvec{\theta }}} }^{(k)}},{\varvec{\Omega }} = {{\bar{{\varvec{\Omega }} }}^{(k)}}} \\ {{\bar{{\varvec{\Omega }} }}^{(k + 1)}}= & {} \left\{ \left( {\sum \limits _{i = 1}^m {{\varvec{H}_{{i}}}^T{{\varvec{\Lambda }}_{{i}}}}{{\varvec{V}_{{i}}}}^{\!\!-1}{{\tilde{\varvec{\Lambda }}_i}{\varvec{H}_{{i}}}} +\hat{\varvec{G}}} \right) ^{\!\!-1}{{\varvec{\Gamma } _n}}\left( {{\varvec{\theta }} ,{\varvec{\Omega }} } \right) \right. \\&\left. \left. \times {{\left( {\sum \limits _{i = 1}^m {{\varvec{H}_{{i}}}^T{{\varvec{\Lambda }} _{{i}}}{{\varvec{V}_{{i}}}}^{\!\!-1}{{{\tilde{\varvec{\Lambda }} }}_i}{\varvec{H}_{{i}}}} + {\hat{\varvec{G}}}} \right) }^{\!\!-1}} \right\} \right| _{{{\varvec{\theta }}} = {{{\bar{\varvec{\theta }}} }^{(k)}},{\varvec{\Omega }} = {{\bar{\varvec{\Omega }}}^{(k)}}} \end{aligned}$$