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: Transforms the log of observation probabilities in terms of the
  Lagrange multiplier to the log 'star' of the probabilities.
  
  Parameters
  ----------
  eta : float
      Lagrange multiplier
  
  est_vect : ndarray (n,k)
      Estimating equations vector
  
  wts : nx1 array
      Observation weights
  
  Returns
  ------
  data_star : ndarray
      The weighted logstar of the estimting equations
  
  Notes
  -----
  This function is only a placeholder for the _fit_Newton.
  The function value is not used in optimization and the optimal value
  is disregarded when computing the log likelihood ratio.
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code: def _log_star(self, eta, est_vect, weights, nobs):
      """
      Transforms the log of observation probabilities in terms of the
      Lagrange multiplier to the log 'star' of the probabilities.
  
      Parameters
      ----------
      eta : float
          Lagrange multiplier
  
      est_vect : ndarray (n,k)
          Estimating equations vector
  
      wts : nx1 array
          Observation weights
  
      Returns
      ------
      data_star : ndarray
          The weighted logstar of the estimting equations
  
      Notes
      -----
      This function is only a placeholder for the _fit_Newton.
      The function value is not used in optimization and the optimal value
      is disregarded when computing the log likelihood ratio.
      """
      data_star = np.log(weights) + (
          np.sum(weights) + np.dot(est_vect, eta)
      )
      idx = data_star < 1.0 / nobs
      not_idx = ~idx
      nx = nobs * data_star[idx]
      data_star[idx] = np.log(1.0 / nobs) - 1.5 + nx * (2.0 - nx / 2)
      data_star[not_idx] = np.log(data_star[not_idx])
      return data_star
  
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 2 for calling the _OptFuncts obj's underlying member method code with example usage: obj._log_star(eta, est_vect, weights, nobs) and returns: data_star