ltsReg                 package:rrcov                 R Documentation

_R_o_b_u_s_t _r_e_g_r_e_s_s_i_o_n _w_i_t_h _h_i_g_h _b_r_e_a_k_d_o_w_n _p_o_i_n_t

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

     Carries out least trimmed squares (LTS) regression.

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

     ltsReg(x, y, intercept=TRUE, alpha=NULL, nsamp=500, adjust=FALSE, mcd=TRUE, qr.out=FALSE, yname=NULL, seed=0)

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

       x: a matrix or data frame containing the explanatory variables. 

       y: the response: a vector of length the number of rows of 'x'. 

intercept: if true, a model with constant term will be itted; otherwise
          no constant term will be included. Default is 'intercept =
          TRUE'  

   alpha: the percentage of squared residuals whose sum will be
          minimized. Its default value is 0.5.  In general, alpha must
          be a value between 0.5 and 1. 

   nsamp: number of subsets used for initial estimates. Default is
          'nsamp = 500' 

  adjust: whether to perform intercept adjustment at each step. This
          could be quite time consuming, therefore the default is
          'adjust = FALSE' 

     mcd: whether to compute robust distances using Fast-MCD.

  qr.out: whether to return the QR decomposition. Default is 'qr.out =
          FALSE'

   yname: the name of the dependent variable. Default is 'yname = NULL'

    seed: starting value for random generator. Default is 'seed = 0'

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

     The LTS regression method minimizes the sum of the h smallest
     squared  residuals, where h must be at least half the number of
     observations. The  default value of h is roughly 0.5n where n is
     the total number of observations,  but the user may choose any
     value between n/2 and n. The computations are performed  using the
     Fast LTS algorithm proposed by Rousseeuw and Van Driessen (1999).

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

     An object of class '"lts"'. This is a list with components

    crit: the value of the objective function of the LTS regression
          method, i.e. the sum of the h smallest squared raw residuals. 

coefficients: vector of coefficient estimates (including the
          intercept,when intercept=TRUE), obtained after reweighting 

    best: the best subset found and used for computing the raw
          estimates. The size of 'best' is equal to 'quan'. 

fitted.values: vector like y containing the fitted values of the
          response after reweighting. 

residuals: vector like y containing the residuals from the weighted
          least squares regression. 

   scale: scale estimate of the reweighted residuals.  

rsquared: robust version of R squared.  

   alpha: same as the input parameter 'alpha'. 

    quan: the number h of observations that have determined the least
          trimmed squares estimator 

intercept: same as the input parameter 'intercept'.  

raw.coefficients: vector of raw coefficient estimates (including the
          intercept,when intercept=TRUE). 

raw.scale: scale estimate of the raw residuals. 

raw.resid: vector like y containing the raw residuals from the
          regression. 

  lts.wt: vector like y containing weights that can be used in a
          weighted least squares. These weights are 1 for points with
          reasonably small raw residuals, and 0 for points with large
          raw residuals. 

  method: character string naming the method (Least Trimmed Squares). 

       X: the input data as a matrix. 

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

     p. j. Rousseeuw (1984), Least Median of Squares Regression.
     _Journal of the American Statistical Association_, *79*, pp.
     871-881. 

     P. J. Rousseeuw and A. M. Leroy (1987)  _Robust Regression and
     Outlier Detection._ Wiley. 

     P. J. Rousseeuw and K. van Driessen (1999) Computing LTS
     Regression for Large Data Sets,  Technical Report, University of
     Antwerp, submitted

     P. J. Rousseeuw and K. van Driessen (1999)  A fast algorithm for
     the minimum covariance determinant estimator.  _Technometrics_,
     *41*, 212-223.

     Pison, G., Van Aelst, S., and Willems, G. (2002),  Small Sample
     Corrections for LTS and MCD,  _Metrika_, *55*, 111-123.

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

     'covMcd'

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

     data(heart)
     ltsReg(heart.x, heart.y)

