leastFavorableRadius         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 _L_e_a_s_t _F_a_v_o_r_a_b_l_e _R_a_d_i_i

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

     Generic function for the computation of least favorable radii.

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

     leastFavorableRadius(L2Fam, neighbor, risk, ...)

     ## S4 method for signature 'L2ParamFamily,
     ##   UncondNeighborhood, asGRisk':
     leastFavorableRadius(L2Fam, neighbor, risk, rho, upRad = 1, 
                 z.start = NULL, A.start = NULL, upper = 100, maxiter = 100, 
                 tol = .Machine$double.eps^0.4, warn = FALSE)

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

   L2Fam: L2-differentiable family of probability measures. 

neighbor: object of class '"Neighborhood"'. 

    risk: object of class '"RiskType"'. 

     ...: additional parameters 

   upRad: the upper end point of the radius interval to be searched. 

     rho: The considered radius interval is: [r*rho, r/rho] with 0 <
          rho < 1. 

 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. 

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

     The least favorable radius and the corresponding inefficiency  are
     computed.

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

     _L_2_F_a_m = "_L_2_P_a_r_a_m_F_a_m_i_l_y", _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",  _r_i_s_k = "_a_s_G_R_i_s_k" 
          computation of the least favorable radius. 

_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., Kohl, M. and Ruckdeschel, P. (2001) The Costs of not
     Knowing the Radius. Submitted. Appeared as discussion paper Nr.
     81.  SFB 373 (Quantification and Simulation of Economic
     Processes), Humboldt University, Berlin; also available under
     <URL:
     www.uni-bayreuth.de/departments/math/org/mathe7/RIEDER/pubs/RR.pdf>

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

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

     'radiusMinimaxIC'

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

     N <- NormLocationFamily(mean=0, sd=1) 
     leastFavorableRadius(L2Fam=N, neighbor=ContNeighborhood(),
                          risk=asMSE(), rho=0.5)

