optRisk               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 _t_h_e _m_i_n_i_m_a_l _r_i_s_k

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

     Generic function for the computation of the optimal (i.e.,
     minimal)  risk for a probability model.

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

     optRisk(model, risk, ...)

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

     ## S4 method for signature 'FixRobModel, fiUnOvShoot':
     optRisk(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:

     The minimal risk 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" asymptotic covariance of
          L2 differentiable parameteric family. 

     _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" asymptotic risk of a
          infinitesimal robust model. 

     _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" finite-sample
          under-/overshoot risk of a robust model with fixed
          neighborhood. 

_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:

     'RiskType-class'

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

     optRisk(model = NormLocationScaleFamily(), risk = asCov())

