def process_secondary_inputs(dict_):
    """
    This functions processes the secondary input parameters.

    Parameters
    ----------
    dict_: dict
        Estimation dictionary. Returned by grmpy.read(init_file).

    Returns
    -------
    trim: bool, default True
        Trim the data outside the common support, recommended.
    rbandwidth: float, default 0.05
        Bandwidth for the Double Residual Regression.
    reestimate_p: bool, default False
        Re-estimate P(Z) after trimming, not recommended.
    show_output: bool, default False
        Show intermediate outputs of the estimation process.
    """
    try:
        dict_["ESTIMATION"]["trim_support"]
    # Set default to True
    except KeyError:
        trim = True
    else:
        trim = dict_["ESTIMATION"]["trim_support"]

    try:
        dict_["ESTIMATION"]["reestimate_p"]
    # Set default to False
    except KeyError:
        reestimate_p = False
    else:
        reestimate_p = dict_["ESTIMATION"]["reestimate_p"]

    try:
        dict_["ESTIMATION"]["rbandwidth"]
    # Set default to 0.05
    except KeyError:
        rbandwidth = 0.05
    else:
        rbandwidth = dict_["ESTIMATION"]["rbandwidth"]

    try:
        dict_["ESTIMATION"]["show_output"]
    # Set default to True
    except KeyError:
        show_output = False
    else:
        show_output = dict_["ESTIMATION"]["show_output"]

    return trim, rbandwidth, reestimate_p, show_output