def calc_bias_abc(second_order_influence):
    """
    Calculates the approximate bias of the MLE estimates for use in calculating
    the approximate bootstrap confidence (ABC) intervals.

    Parameters
    ----------
    second_order_influence : 2D ndarray.
        Should have one row for each observation. Should have one column for
        each parameter in the parameter vector being estimated. Elements should
        denote the second order empirical influence of the associated
        observation on the associated parameter.

    Returns
    -------
    bias : 1D ndarray.
        Contains the approximate bias of the MLE estimates for use in the ABC
        confidence intervals.

    References
    ----------
    Efron, Bradley, and Robert J. Tibshirani. An Introduction to the Bootstrap.
        CRC press, 1994. Section 22.6, Equation 22.35.
    """
    num_obs = second_order_influence.shape[0]
    constant = 2.0 * num_obs**2
    bias = second_order_influence.sum(axis=0) / constant
    return bias