getInfRobIC             package:ROptEst             R Documentation

_G_e_n_e_r_i_c _F_u_n_c_t_i_o_n _f_o_r _t_h_e _C_o_m_p_u_t_a_t_i_o_n _o_f _O_p_t_i_m_a_l_l_y _R_o_b_u_s_t _I_C_s

_D_e_s_c_r_i_p_t_i_o_n:

     Generic function for the computation of optimally robust ICs  in
     case of infinitesimal robust models. This function is  rarely
     called directly.

_U_s_a_g_e:

     getInfRobIC(L2deriv, risk, neighbor, ...)

     ## S4 method for signature 'UnivariateDistribution, asCov,
     ##   ContNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, Finfo, trafo)

     ## S4 method for signature 'UnivariateDistribution, asCov,
     ##   TotalVarNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, Finfo, trafo)

     ## S4 method for signature 'RealRandVariable, asCov,
     ##   ContNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, Distr, Finfo, trafo)

     ## S4 method for signature 'UnivariateDistribution, asBias,
     ##   ContNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
                  upper, maxiter, tol, warn)

     ## S4 method for signature 'UnivariateDistribution, asBias,
     ##   TotalVarNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
                  upper, maxiter, tol, warn)

     ## S4 method for signature 'RealRandVariable, asBias,
     ##   ContNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
                  L2derivDistrSymm, Finfo, z.start, A.start, trafo, upper, maxiter, tol, warn)

     ## S4 method for signature 'UnivariateDistribution,
     ##   asHampel, UncondNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
                  upper, maxiter, tol, warn)

     ## S4 method for signature 'RealRandVariable, asHampel,
     ##   ContNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
                  L2derivDistrSymm, Finfo, z.start, A.start, trafo, upper, maxiter, tol, warn)

     ## S4 method for signature 'UnivariateDistribution,
     ##   asGRisk, UncondNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
                  upper, maxiter, tol, warn)

     ## S4 method for signature 'RealRandVariable, asGRisk,
     ##   ContNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, Distr, DistrSymm, L2derivSymm, 
                  L2derivDistrSymm, Finfo, z.start, A.start, trafo, upper, maxiter, tol, warn)

     ## S4 method for signature 'UnivariateDistribution,
     ##   asUnOvShoot, UncondNeighborhood':
     getInfRobIC(L2deriv, risk, neighbor, symm, Finfo, trafo, 
                  upper, maxiter, tol, warn)

_A_r_g_u_m_e_n_t_s:

 L2deriv: L2-derivative of some L2-differentiable family  of
          probability measures. 

    risk: object of class '"RiskType"'. 

neighbor: object of class '"Neighborhood"'. 

     ...: additional parameters. 

   Distr: object of class '"Distribution"'. 

    symm: logical: indicating symmetry of 'L2deriv'. 

DistrSymm: object of class '"DistributionSymmetry"'. 

L2derivSymm: object of class '"FunSymmList"'. 

L2derivDistrSymm: object of class '"DistrSymmList"'. 

   Finfo: Fisher information matrix. 

 z.start: initial value for the centering constant. 

 A.start: initial value for the standardizing matrix. 

   trafo: matrix: transformation of the parameter. 

   upper: upper bound for the optimal clipping bound. 

 maxiter: the maximum number of iterations. 

     tol: the desired accuracy (convergence tolerance).

    warn: logical: print warnings. 

_V_a_l_u_e:

     The optimally robust IC is computed.

_M_e_t_h_o_d_s:

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_C_o_v",  _n_e_i_g_h_b_o_r = "_C_o_n_t_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the classical optimal influence curve for L2
          differentiable  parametric families with unknown
          one-dimensional parameter. 

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_C_o_v",  _n_e_i_g_h_b_o_r = "_T_o_t_a_l_V_a_r_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the classical optimal influence curve for L2
          differentiable  parametric families with unknown
          one-dimensional parameter. 

     _L_2_d_e_r_i_v = "_R_e_a_l_R_a_n_d_V_a_r_i_a_b_l_e", _r_i_s_k = "_a_s_C_o_v",  _n_e_i_g_h_b_o_r = "_C_o_n_t_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the classical optimal influence curve for L2
          differentiable  parametric families with unknown
          k-dimensional parameter  (k > 1) where the underlying
          distribution is univariate. 

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_B_i_a_s",  _n_e_i_g_h_b_o_r = "_C_o_n_t_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the bias optimal influence curve for L2
          differentiable  parametric families with unknown
          one-dimensional parameter. 

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_B_i_a_s",  _n_e_i_g_h_b_o_r = "_T_o_t_a_l_V_a_r_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the bias optimal influence curve for L2
          differentiable  parametric families with unknown
          one-dimensional parameter. 

     _L_2_d_e_r_i_v = "_R_e_a_l_R_a_n_d_V_a_r_i_a_b_l_e", _r_i_s_k = "_a_s_B_i_a_s",  _n_e_i_g_h_b_o_r = "_C_o_n_t_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the bias optimal influence curve for L2
          differentiable  parametric families with unknown
          k-dimensional parameter  (k > 1) where the underlying
          distribution is univariate. 

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_H_a_m_p_e_l",  _n_e_i_g_h_b_o_r = "_U_n_c_o_n_d_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the optimally robust influence curve for L2
          differentiable  parametric families with unknown
          one-dimensional parameter. 

     _L_2_d_e_r_i_v = "_R_e_a_l_R_a_n_d_V_a_r_i_a_b_l_e", _r_i_s_k = "_a_s_H_a_m_p_e_l",  _n_e_i_g_h_b_o_r = "_C_o_n_t_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the optimally robust influence curve for L2
          differentiable  parametric families with unknown
          k-dimensional parameter  (k > 1) where the underlying
          distribution is univariate. 

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_G_R_i_s_k",  _n_e_i_g_h_b_o_r = "_U_n_c_o_n_d_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the optimally robust influence curve for L2
          differentiable  parametric families with unknown
          one-dimensional parameter. 

     _L_2_d_e_r_i_v = "_R_e_a_l_R_a_n_d_V_a_r_i_a_b_l_e", _r_i_s_k = "_a_s_G_R_i_s_k",  _n_e_i_g_h_b_o_r = "_C_o_n_t_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the optimally robust influence curve for L2
          differentiable  parametric families with unknown
          k-dimensional parameter  (k > 1) where the underlying
          distribution is univariate. 

     _L_2_d_e_r_i_v = "_U_n_i_v_a_r_i_a_t_e_D_i_s_t_r_i_b_u_t_i_o_n", _r_i_s_k = "_a_s_U_n_O_v_S_h_o_o_t",  _n_e_i_g_h_b_o_r = "_U_n_c_o_n_d_N_e_i_g_h_b_o_r_h_o_o_d" 
          computes the optimally robust influence curve for
          one-dimensional L2 differentiable parametric families and 
          asymptotic under-/overshoot risk. 

_A_u_t_h_o_r(_s):

     Matthias Kohl Matthias.Kohl@stamats.de

_R_e_f_e_r_e_n_c_e_s:

     Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats.
     *8*: 106-115.

     Rieder, H. (1994) _Robust Asymptotic Statistics_. New York:
     Springer.

     Kohl, M. (2005) _Numerical Contributions to the Asymptotic Theory
     of Robustness_.  Bayreuth: Dissertation.

_S_e_e _A_l_s_o:

     'InfRobModel-class'

