class_docstr: A class that holds functions that are optimized/solved.
  
  The general setup of the class is simple.  Any method that starts with
  _opt_ creates a vector of estimating equations named est_vect such that
  np.dot(p, (est_vect))=0 where p is the weight on each
  observation as a 1 x n array and est_vect is n x k.  Then _modif_Newton is
  called to determine the optimal p by solving for the Lagrange multiplier
  (eta) in the profile likelihood maximization problem.  In the presence
  of nuisance parameters, _opt_ functions are  optimized over to profile
  out the nuisance parameters.
  
  Any method starting with _ci_limits calculates the log likelihood
  ratio for a specific value of a parameter and then subtracts a
  pre-specified critical value.  This is solved so that llr - crit = 0.
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docstr: Modified Newton's method for maximizing the log 'star' equation.  This
  function calls _fit_newton to find the optimal values of eta.
  
  Parameters
  ----------
  eta : ndarray, (1,m)
      Lagrange multiplier in the profile likelihood maximization
  
  est_vect : ndarray, (n,k)
      Estimating equations vector
  
  weights : 1darray
      Observation weights
  
  Returns
  -------
  params : 1xm array
      Lagrange multiplier that maximizes the log-likelihood
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code: def _modif_newton(self, eta, est_vect, weights):
      """
      Modified Newton's method for maximizing the log 'star' equation.  This
      function calls _fit_newton to find the optimal values of eta.
  
      Parameters
      ----------
      eta : ndarray, (1,m)
          Lagrange multiplier in the profile likelihood maximization
  
      est_vect : ndarray, (n,k)
          Estimating equations vector
  
      weights : 1darray
          Observation weights
  
      Returns
      -------
      params : 1xm array
          Lagrange multiplier that maximizes the log-likelihood
      """
      nobs = len(est_vect)
      f = lambda x0: -np.sum(
          self._log_star(x0, est_vect, weights, nobs)
      )
      grad = lambda x0: -self._grad(x0, est_vect, weights, nobs)
      hess = lambda x0: -self._hess(x0, est_vect, weights, nobs)
      kwds = {"tol": 1e-8}
      eta = eta.squeeze()
      res = _fit_newton(
          f, grad, eta, (), kwds, hess=hess, maxiter=50, disp=0
      )
      return res[0]
  
imports: import numpy
  from scipy import optimize
  from scipy.stats import chi2, skew, kurtosis
  from statsmodels.base.optimizer import _fit_newton
  import itertools
  from statsmodels.graphics import utils
label_desc: Use image node_id 5 for calling the _OptFuncts obj's underlying member method code with example usage: obj._modif_newton(eta, est_vect, weights) and returns: res