Quantile (including median) regression with                    (STB-9: sg11.1)
               bootstrapped standard errors
-------------------------------------------

	^bsqreg^ [depvar [varlist] [^if^ exp] [^in^ range] ]
	       [^, l^evel^(^#^) qu^antile^(^#^) ^r^eps^(^#^) wlsi^ter^(^#^)^ ]

To reset problem-sizes limits, see ^help matsize^.


Description
-----------

^bsqreg^ estimates quantile (including median) regression models, also known as
least absolute value (LAV) models and minimum L1-norm models.  ^bsqreg^ is an
alternative to ^qreg^; it produces the same parameter estimates but produces 
bootstrapped standard errors.  Rogers (1992) reported that the standard errors
produced by ^qreg^ appear quite satisfactory except in the case of heterosce-
dastic errors; use of ^bsqreg^ is recommended in that case.



Description, continued
----------------------

Users are warned that ^bsqreg^ is only partially like an estimation command.
^bsqreg^, typed without arguments, does replay estimates; coefficients can be
obtained from ^_b[]^; ^predict^ can be used after estimation to obtain predicted
values and residuals.  In all other ways, however, ^bsqreg^ is NOT an estimation
command.  In particular, standard errors cannot be obtained from ^_se[]^; ^test^
and ^correlate, _coef^ cannot be used; and ^predict^ cannot be used except for 
predicted values and residuals.

In all cases, Stata itself does not know about these limitations and will 
fulfill reqeusts, but with obviously incorrect results.  (It is agreed that
this behavior is intolerable and it will be addressed when Stata 3.1 is 
released -- when internal changes can be made to Stata itself.)

^bsqreg^ will allow at most 20 independent variables for users of DOS or Mac-
intosh regular Stata (see CRC 1992b; the maximum is really larger than 20).   

^bsqreg^ will allow at most 255 independent variables for users of Intercooled
or Unix Stata,  assuming ^matsize^ has been set to 255 or more (see CRC 1992b;
the maximum is really more than 255).


Options
-------

^level(^#^)^ specifies the significance level in percent for confidence intervals
    of the coefficients; see [4] estimate.

^quantile(^#^)^ specifies the quantile to be estimated and must be between 0 and 1,
    exclusive.  The default value of 0.5 corresponds to the median.

^nolog^ suppresses the iteration log.

^reps(^#^)^ specifies the number of bootstrap replications to be performed for
    estimating the standard errors.  The defulat is ^reps(20)^.

^wlsiter(^#^)^ should never need to be specified; see [5s] qreg.









Examples
--------


 . ^bsqreg y x^
 . ^bsqreg y x, reps(40)^
 . ^bsqreg y x, quantile(.75)^
 . ^bsqreg y x, quantile(.75) reps(40)^


 . ^bsqreg price weight length foreign^
 . ^predict hat^                                   (to obtain predicted values)
 . ^predict r, resid^                              (to obtain residuals)
 . ^bsqreg^                                        (to redisplay results)


 . ^test weight=0^                                 (DO NOT DO THIS!)







References
----------

CRC. 1992.  crc18: Important differences between regular and Intercooled
     Stata.  ^Stata Technical Bulletin^ 9: 3-4.

Gould, W. 1992.  sg11.1: Quantile regression with bootstrapped standard
     errors.  ^Stata Technical Bulletin^ 9: 19-21.

Rogers, W. 1992.  sg11: Quantile regression standard errors.  ^Stata Technical^
     ^Bulletin^ 9: 16-19.



Also see
--------

    STB:  sg11.1 (STB-9)
 Manual:  [4] estimate, [5s] qreg
On-line:  ^help^ for ^predict^, ^qreg^; ^boot^, ^bootcmd^, ^jknife^