*! version 1.0.0 30jul2013
help clrbound

Title

clrbound -- Compute a one-sided bound estimate

Syntax

clrbound (depvar1 indepvars1 range1)
( depvar2 indepvars2 range2 ) ...
( depvarN indepvarsN rangeN )
[if] [in]
[,
lower | upper
method("series"|"local")
level(numlist)
noais
minsmooth(#)
maxsmooth(#)
noundersmooth
bandwidth(numlist)
rnd(#)
norseed
seed(#)
]

Description

clrbound estimates the one-sided lower or upper intersection bounds of a parameter. The variables are defined similarly as for clr2bound; see clr2bound. clrbound requires the package moremata.

Options

lower specifies whether the estimation is for the lower bound or the upper bound. By default, it will return the upper intersection bound. Specifying lower, clrbound will return the lower intersection bound.

method(string) specifies the method of estimation. By default, clr2bound will conduct parametric estimation. Specifying method("series"), clr2bound will conduct series estimation with cubic B-splines. Specifying
method("local"), will result in local linear estimation.

level(numlist) specifies confidence levels. numlist has to be filled with real numbers between 0 and 1. In particular, if this option is specified as level(0.5), the result is the half-median-unbiased estimator of the parameter of the interest. The default is level(0.5 0.9 0.95 0.99).

noais determines whether the adaptive inequality selection would be applied or not. The adaptive inequality selection (AIS) helps to get sharper bounds by using the problem-dependent cutoff to drop irrelevant grid points of the
range. The default is to use AIS.

minsmooth(#) and
maxsmooth(#)
specify the minimum and maximum possible numbers of approximating functions considered in the cross validation procedure for B-splines.
Specifically, the number of approximating functions is set to the minimizer of the leave-one-out least squares cross validation score within this range.
For example, if a user inputs minsmooth(5) and maxsmooth(9), the number of approximating functions is chosen from the set {5,6,7,8,9}.
The procedure calculates this number separately for each inequality. The default is minsmooth(5) and maxsmooth(20). If under-smoothing is performed, the number of approximating functions ultimately used will be given by the largest integer smaller than ( the number of approximating functions times the under-smoothing factor ), see option noundersmooth below. This option is only available for series estimation.

bandwidth(#) specifies the value of the bandwidth used in the local linear estimation. By default, clr2bound calculates a bandwidth for each inequality. With undersmoothing, we use the rule of thumb bandwidth When the bandwidth(#) is specified, clr2bound uses the given bandwidth as the global bandwidth for every inequality. This option is only available for local linear estimation.

noundersmooth determines whether under-smoothing is carried out, with the default being to under-smooth. In series estimation, under-smoothing is implemented by first computing the number of approximating functions as the minimizer of the leave-one-out least squares cross validation score. The noundersmooth option simply uses this number. Without this option, we then set the number of approximating functions to K, given by the largest integer which is smaller than or equal to ( the number of approximating functions times n^1/5 times n^-2/7. For local linear estimation under-smoothing is done by using the bandwidth which is multiplied by n^1/5 times n^-2/7 from origianl bandwith. This option is only available for series and local linear estimation.

rnd(#) specifies the number of columns of the random matrix generated from the standard normal distribution. This matrix is used for computation of critical values. For example, if the number is 10000 and the level is 0.95, we choose the 0.95 quantile from 10000 randomly generated elements. The default is rnd(10000).

norseed determines whether the seed number for the simulation used in the calculation would be reset. If a user wants to use this command for simulations such as Monte Carlo method, he can prevent the command from resetting the seed number every lap by using this option. The default is to reset the seed number.

seed(#) specifies the seed number for the random number generation described above. To prevent the estimation result from changing one particular values to another randomly, clr2bound always conducts set seed # initially.
The default is seed(0).