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Conversely, a “large" R 2 (scaled by the sample size so that it follows the chi-squared distribution) counts against the hypothesis of homoskedasticity. An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a ...
where T is the sample size, is the residual and is the row of the design matrix, and is the Bartlett kernel [8] and can be thought of as a weight that decreases with increasing separation between samples. Disturbances that are farther apart from each other are given lower weight, while those with equal subscripts are given a weight of 1.
Unlike the asymptotic White's estimator, their estimators are unbiased when the data are homoscedastic. Of the four widely available different options, often denoted as HC0-HC3, the HC3 specification appears to work best, with tests relying on the HC3 estimator featuring better power and closer proximity to the targeted size , especially in ...
The simplest method for correcting the reticulocyte count, to obtain a more accurate daily production index, is to divide the corrected count by a factor of 2 (or multiply with ½) whenever polychromasia (the presence of immature marrow reticulocytes or "shift" cells) is observed on the smear or the immature fraction on the automated counter is ...
Generally Bessel's correction is an approach to reduce the bias due to finite sample size. Such finite-sample bias correction is also needed for other estimates like skew and kurtosis, but in these the inaccuracies are often significantly larger. To fully remove such bias it is necessary to do a more complex multi-parameter estimation.
For example, in a medical study patients are recruited as a sample from a population, and their characteristics such as blood pressure may be viewed as arising from a random sample. Under certain assumptions (typically, normal distribution assumptions) there is a known ratio between the true slope, and the expected estimated slope.
For example, for = 0.05 and m = 10, the Bonferroni-adjusted level is 0.005 and the Šidák-adjusted level is approximately 0.005116. One can also compute confidence intervals matching the test decision using the Šidák correction by computing each confidence interval at the ⋅ {\displaystyle \cdot } (1 − α) 1/ m % level.
Heckman's correction involves a normality assumption, provides a test for sample selection bias and formula for bias corrected model. Suppose that a researcher wants to estimate the determinants of wage offers, but has access to wage observations for only those who work.