By Esposito P.
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Additional info for Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity
The alternative of interest was that cells grown in the presence of vitamin E would be capable of many more cell divisions. Under the null hypothesis, the labels “treated” and “untreated” provide no information about the outcomes: The observations are expected to have more or less the same values in each of the two experimental groups. If they do differ it should only be as a result of some uncontrollable random ﬂuctuation. Thus, if this null or no-difference hypothesis were true, I was free to exchange the labels.
X, y)n . 2. Following Hall and Wilson , we compute the bivariate mean (x ∗ , y ∗ ) of the bootstrap sample, and its covariance matrix ∗ . 3. We draw n pairs (εi , ηi ) from the bivariate normal distribution with mean (x ∗ , y ∗ ) and covariance matrix ∗ , and use them to form xi∗ = x ∗ + (xi − hεi ) 1 + h2 /σx2∗ , yi∗ = y ∗ + (yi − hni ) 1 + h2 /σy2∗ . 4. Finally, we use (x1∗ , y1∗ ), (x2∗ , y2∗ ), . . , (xn∗ , yn∗ ) to estimate the correlation coefﬁcient. com/downloads/libraries sbootstrap(data, median) Sample Calculation with Stata .
Instead of giving 6 That is, a normal distribution with mean 0 and variance 1. 26 2 Estimating Population Parameters equal probability to each of the observations in the original sample, greater weight is given to some of the observations and less weight to others. 5, 4, 7, 8. Bootstrap samples containing 7 and 8 are much more likely to have large means, so instead of drawing bootstrap samples such that every observation has the same probability 1/10 of being included, we weight the sample so that larger values are more likely to be drawn, selecting −2 with probability 1/55 for example, −1 with probability 2/55, and so forth, with the probability of selecting 8 being 9/55th’s.
Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity by Esposito P.