These observations prove that the sample median
(Me(x) = 10) is the best kernel size for capturing the whole amplitude peak.
We use Industry Discretion as our measure of managerial discretion and classify the industries associated with our sample firms into High Discretion (Industry Discretion above the sample median
) and Low Discretion (Industry Discretion below the sample median
The estimation results are for small firms (firm size below the sample median
) in columns 1 and 3 and large firms (firm size above the sample median
) in columns 2 and 4.
Using nonlinear least squares to estimate these parameters from the I-15 data yields [d.sub.j] = 247.20 and [s.sub.j] = 27.36, implying a speed-density elasticity of -0.521 at the sample median
Despite the similarity of some subgroups with the sample median
, the median returns of the remaining subgroups differed more substantially (especially for trips placing a different number of sets or landing in a different region).
In the sign test, the sample median
was 1.017, with 160 values above, 126 values below and 8 equal to the hypothesized median (Z = 0.05, P = 0.05).
In this study, smokers with family incomes equal to or below the study sample median
were more likely to respond to price increases by quitting than smokers with family incomes above the median (e.g., 10% quitting compared with 3% quitting in response to a 50% price increase).
Although the sample mean is more efficient than the sample median
when the data are drawn from a normal distribution, this will not be true in general.
In order to investigate the effect of cash holdings, we divide the sample into low and high pre-crisis cash holding groups based on below and above the sample median
cash holdings, respectively, and examine the effect of internal/external finance dependence on financing and investments during the crisis.
Central Limit Theorem for the Sample Median
. Let [[??].sub.m] be the sample median
for the sample [x.sub.1], [x.sub.2],..., [x.sub.n] n = 2k - 1, k [member of] [Z.sup.+].
(1) [FCF.sub.i] is a dummy variable that takes a value of one if repurchasing firm i has free cash flows (cash flows greater than the sample median
and Tobin's q less than 1) and zero otherwise.