LBEa                   package:LBE                   R Documentation

_O_p_t_i_m_a_l _s_e_t_t_i_n_g _f_o_r _t_h_e _p_a_r_a_m_e_t_e_r _a

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

     The LBEa function is called by the main function LBE for choosing
     the greatest value of a such that the upper bound of the
     asymptotic standard deviation is less than a threshold l. A plot
     illustrating the relation between a and l for a fixed number of
     tested hypotheses can also be displayed.

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

     LBEa(m, l = 0.05, fig = TRUE, a.rng = NA)

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

       m: Total number of tested hypotheses. 

       l: Threshold for the upper bound of the asymptotic standard
          deviation (default value is 0.05). 

     fig: Logical value for plotting the standard deviation versus a. 

   a.rng: Range of values of a to consider. If a.rng==NA, a.rng is set
          such that the standard deviation is less than 0.5. 

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

     The procedure LBE is based on the expectation of a particular
     transformation of the p-values leading to a straightforward
     estimation of the key quantity pi0 that is the proportion of true
     null hypotheses: $
     pi0(a)={(1/m)*sum_{i=1}^{m}[-ln(1-pi)]^a]}/Gamma(a+1) $ where a
     belongs to the interval [1;inf[.    As there is a balance between
     bias (decreasing as a increase) and variance (increasing as a
     increase), for a specified number m of tested hypotheses, we have
     proposed to choose the greatest value of a such that the upper
     bound of the asymptotic standard deviation of the estimator of pi0
     is smaller than the threshold l. The function LBEa allows to plot
     the standard deviation versus a in order to help for the choice of
     the threshold l (for a specific number m of tested hypotheses).

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

      a : Greatest value of a such that the the upper bound of the
          asymptotic standard deviation of the estimator of pi0 is
          smaller than the threshold l. 

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

     Cyril Dalmasso

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

     Dalmasso C, Broet P, Moreau T (2005). A simple procedure for
     estimating the false discovery rate. Bioinformatics.
     Bioinformatics, 21: 660 - 668.

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

     'LBE', 'LBEplot', 'LBEsummary', 'LBEwrite'

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

     ## start
     data(hedenfalk.pval)
     m <- length(hedenfalk.pval)
     LBEa(m,l=0.05)
     ## end

