This function contructs the selection event by computing c_k, d_k and e_k which are the constants in the quadratic inequalities which characterize the model selection event. The function is used internally by the function solve_selection_event, which returns the intervals of the OLS estimator where the selection event takes place.
construct_selection_event(a,b,R_M_k,kappa_M_k,R_M_phat,kappa_M_phat)
Constant c_k in the quadratic inequality c_k*Z^2+d_k*Z+e_k>=0 which characterizes the model selection event of the selected model compared to model k (see Lemma 1 for details)
Constant d_k in the quadratic inequality c_k*Z^2+d_k*Z+e_k>=0 which characterizes the model selection event of the selected model compared to model k (see Lemma 1 for details)
Constant e_k in the quadratic inequality c_k*Z^2+d_k*Z+e_k>=0 which characterizes the model selection event of the selected model compared to model k (see Lemma 1 for details)
Residual vector of type "matrix" and dimension nx1 (see Lemma 1 for details)
Vector of type "matrix" and dimension nx1: useful in orthogonal decomposition of y (see Lemma 1 for details)
The orthogonal projection matrix of model k
Adjustment factor for model complexity kappa of model k
The orthogonal projection matrix of the selected model
Adjustment factor for model complexity kappa of the selected model
Pirenne, S. and Claeskens, G. (2024). Exact Post-Selection Inference for Adjusted R Squared.