optIC                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.

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

     optIC(model, risk, ...)

     ## S4 method for signature 'L2ParamFamily, asCov':
     optIC(model, risk)

     ## S4 method for signature 'InfRobModel, asRisk':
     optIC(model, risk, z.start = NULL, A.start = NULL, upper = 1e4, 
                  maxiter = 50, tol = .Machine$double.eps^0.4, warn = TRUE)

     ## S4 method for signature 'InfRobModel, asUnOvShoot':
     optIC(model, risk, upper = 1e4, maxiter = 50, 
                  tol = .Machine$double.eps^0.4, warn = TRUE)

     ## S4 method for signature 'FixRobModel, fiUnOvShoot':
     optIC(model, risk, sampleSize, upper = 1e4, maxiter = 50, 
                  tol = .Machine$double.eps^0.4, warn = TRUE, Algo = "A", cont = "left")

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

   model: probability model. 

    risk: object of class '"RiskType"'. 

     ...: additional parameters. 

 z.start: initial value for the centering constant. 

 A.start: initial value for the standardizing matrix. 

   upper: upper bound for the optimal clipping bound. 

 maxiter: the maximum number of iterations. 

     tol: the desired accuracy (convergence tolerance).

    warn: logical: print warnings. 

sampleSize: integer: sample size. 

    Algo: "A" or "B". 

    cont: "left" or "right". 

_D_e_t_a_i_l_s:

     In case of the finite-sample risk '"fiUnOvShoot"' one can choose
     between two algorithms for the computation of this risk where the
     least favorable contamination is assumed to be left or right of
     some bound. For more details we refer to Section 11.3 of Kohl
     (2005).

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

     Some optimally robust IC is computed.

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

     _m_o_d_e_l = "_L_2_P_a_r_a_m_F_a_m_i_l_y", _r_i_s_k = "_a_s_C_o_v" computes classical optimal
          influence curve for L2 differentiable  parametric families.

     _m_o_d_e_l = "_I_n_f_R_o_b_M_o_d_e_l", _r_i_s_k = "_a_s_R_i_s_k" computes optimally robust
          influence curve for  robust models with infinitesimal
          neighborhoods and various asymptotic risks. 

     _m_o_d_e_l = "_I_n_f_R_o_b_M_o_d_e_l", _r_i_s_k = "_a_s_U_n_O_v_S_h_o_o_t" computes optimally
          robust influence curve for  robust models with infinitesimal
          neighborhoods and asymptotic under-/overshoot risk. 

     _m_o_d_e_l = "_F_i_x_R_o_b_M_o_d_e_l", _r_i_s_k = "_f_i_U_n_O_v_S_h_o_o_t" computes optimally
          robust influence curve for  robust models with fixed
          neighborhoods and finite-sample 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:

     Huber, P.J. (1968) Robust Confidence Limits. Z.
     Wahrscheinlichkeitstheor. Verw. Geb. *10*:269-278.

     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:

     'InfluenceCurve-class', 'RiskType-class'

_E_x_a_m_p_l_e_s:

     B <- BinomFamily(size = 25, prob = 0.25) 

     ## classical optimal IC
     IC0 <- optIC(model = B, risk = asCov())
     plot(IC0) # plot IC
     checkIC(IC0, B)

