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lianxh
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. ssc install lianxh
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. help lianxh
⛳ Stata 系列推文:
作者:赵玉 (山东大学)
邮箱:zhaoyu_yep@163.com
目录
在连享会以往的推文中,我们介绍了分位数回归的基本方法(具体链接链接见「6. 相关推文」),包括总体分位数,样本分位数以及面板分位数回归模型。
分位数方法之所以被广泛使用,关键取决于快速算法的存在。尽管在算法上目前已有很多改进,但计算时间仍然是不可忽略的。本文主要向大家介绍一种分位数回归命令 qrprocess,这一命令与 Stata 官方命令 qreg
的估计结果相近,但运算速度约为前者的 30 倍。
引述一段 Chernozhukov, V., I. Fernández-Val, and B. Melly. 2020a. Fast algorithms for the quantile regression process. Working paper. -PDF- 在结论部分的观点:
Instead of bootstrapping the quantile regression estimates, it is possible to bootstrap the score (or estimating equation) of the estimator. This approach amounts in fact to using the one-step estimator to compute the bootstrap estimate when we take the sample estimate as a preliminary guess. This inference procedure, which has been suggested for quantile regression by Chernozhukov and Hansen (2006) and Belloni et al. (2017), is extremely fast and can also be used to perform uniform inference. Its drawback is the necessity to choose a smoothing parameter to estimate the conditional density of the response variable given the covariates.
The simulations we report in Section 6 show that the preprocessing algorithm is 30 times faster than Stata’s built-in algorithm when we have 50, 000 observations, 20 regressors and we estimate 99 quantile regressions. The onestep estimator further divides the computing time by almost 4. The preprocessing step applied to the bootstrap of a single quantile regression divides the computing time by about 10. The score multiplier bootstrap further divides the computing time by 10 compared to the preprocessing algorithm. Thus, these new algorithms open new possibilities for quantile regression methods. For instance, in the application reported in Section 7, we could estimate 91 different quantile regressions in a sample of 2, 194, 021 observations, with 14 regressors and bootstrap 100 times the estimates in about 30 minutes on a laptop. The same estimation with the built-in commands of Stata would take over two months. The codes in Stata and some rudimentary codes in R are available from the authors.
令
其中,
qrprocess 命令是 Chernozhukov, Fernández-Val and Melly (2020) 编写的 Stata 新命令,安装命令如下:
. ssc install qrprocess, replace
该命令依赖于 moremata,需预先安装:
. ssc install moremata, replace
如果无法直接安装,可以使用如下推文中介绍的手动安装方法:
亦可直接执行如下命令:
. net install moremata, from(https://file.lianxh.cn/StataCMD/moremata) replace force
qrprocess 命令语法结构如下:
. help qrprocess
. qrprocess depvar [indepvars] [if] [in] [weight] [, options]
. depvar:被解释变量;
. indepvars:解释变量;
. Options:
. quantile(numlist):指定要估计的分位数;默认值为0.5(中位数)
. method([mtype], [mopts]):指定用于计算分位数回归估计的算法方法以及控制算法结束的参数
. vce([vtype], [vopts]):指定用于估计标准误差
. functional:提供置信区间、假设检验
. level(#):设置置信水平;默认值为水平为0.95
. noprint:禁止显示结果
我们使用 qrprocess 命令来实现分位数回归模型,这里我们使用 Stata 自带的数据 auto.dta。
首先进行中位数回归:
. sysuse auto, clear
. qrprocess price mpg weight length foreign // 中位数回归
Quantile regression
No. of obs. 74
Algorithm: qreg.
Variance: kernel estimate of the sandwich as proposed by Powell(1990).
--------------------------------------------------------------------------
price Coef. Std. Err. t P>t [95% Conf. Interval]
--------------------------------------------------------------------------
Quant. 0.5
mpg 6.297878 134.9509 0.05 0.963 -262.9217 275.5175
weight 3.933588 2.487104 1.58 0.118 -1.026785 8.893961
length -41.25191 72.577 -0.57 0.572 -186.0022 103.4984
foreign 3377.771 1411.45 2.39 0.019 562.7222 6192.82
_cons 344.6489 7452.584 0.05 0.963 -14519.06 15208.36
--------------------------------------------------------------------------
有上述结果可知,mpg 每增加一单位,会使价格中位数增加 6.30 个单位,即当汽车每加仑能行走的公里数提高一个单位,中档价位的汽车便会增加 6.30 个单位,但统计结果上并不显著。
进一步地,用 bootstrap 标准误差估计 0.25、0.5、0.75 分位点上的回归结果:
. qrprocess price mpg weight length foreign, vce(boot) quantile(0.25 0.5 0.75)
(bootstrapping .......................)
Quantile regression
No. of obs. 74
Algorithm: qreg.
Variance: empirical bootstrap.
-------------------------------------------------------------------------
price Coef. Std. Err. t P>t [95% Conf. Interval]
-------------------------------------------------------------------------
Quant. 0.25
mpg 6.85905 54.47329 0.13 0.900 -101.8122 115.5303
weight 1.903734 1.398422 1.36 0.178 -.8860422 4.69351
length 2.037834 27.91324 0.07 0.942 -53.64756 57.72323
foreign 2253.604 935.7526 2.41 0.019 386.8291 4120.38
_cons -2097.658 3569.829 -0.59 0.559 -9219.271 5023.956
-------------------------------------------------------------------------
Quant. 0.5
mpg 6.297878 134.9509 0.05 0.963 -262.9217 275.5175
weight 3.933588 2.487104 1.58 0.118 -1.026785 8.893961
length -41.25191 72.577 -0.57 0.572 -186.0022 103.4984
foreign 3377.771 1411.45 2.39 0.019 562.7222 6192.82
_cons 344.6489 7452.584 0.05 0.963 -14519.06 15208.36
-------------------------------------------------------------------------
Quant. 0.75
mpg -47.17156 166.7631 -0.28 0.778 -379.8547 285.5116
weight 9.139458 2.530752 3.61 0.001 4.090746 14.18817
length -226.8545 85.49465 -2.65 0.010 -397.4116 -56.2973
foreign 3343.127 1130.874 2.96 0.004 1087.096 5599.159
_cons 22606.38 12346.16 1.83 0.071 -2023.526 47236.29
-------------------------------------------------------------------------
估计 0.1,0.2,…,0.9 分位数的离散分位数回归过程,并绘制所有系数:
. qrprocess price mpg weight length foreign, quantile(0.1(0.01)0.9) noprint
. plotprocess
关于 qrprocess
的基本介绍在这里就结束了,想要深入了解的学者可以阅读下方的参考资料,或者 help qrprocess
查看相关命令的应用与介绍。
Note:产生如下推文列表的 Stata 命令为:
lianxh 分位数
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New!
lianxh
命令发布了:
随时搜索连享会推文、Stata 资源,安装命令如下:
. ssc install lianxh
使用详情参见帮助文件 (有惊喜):
. help lianxh