Variance

Most of the statistical procedures in meta-analysis are based on the estimation of average effect sizes from a set of primary studies. The optimal weight for averaging a set of independent effect sizes is the inverse variance of each effect size, but in practice these weights have to be estimated, being affected by sampling error. When assuming a random-effects model, there are two alternative procedures for averaging independent effect sizes: Hunter and Schmidt’s estimator, which consists of weighting by sample size as an approximation to the optimal weights; and Hedges and Vevea’s estimator, which consists of weighting by an estimation of the inverse variance of each effect size. In this article, the bias and mean squared error of the two estimators were assessed via Monte Carlo simulation of meta-analyses with the standardized mean difference as the effect-size index. Hedges and Vevea’s estimator, although slightly biased, achieved the best performance in terms of the mean square...

We have analyzed the seasonal variation of short-period (<2 h) gravity wave activity in the troposphere and lower stratosphere using the wind observations made with VHF radar at Gadanki (13.5
N, 79.2
E), India. Four years of high resolution (
3 min) wind data (2003–2006) have been used to study variance and momentum flux of short-period gravity waves. Both horizontal and vertical variances show annual variation. Variances in the upper troposphere (12–16 km) and lower stratosphere (18–21 km) are found to maximize in the wet months of June–July–August coinciding with the peaks of outgoing longwave radiation (OLR) and the rain rate (surface and Tropical Rainfall Measuring Mission [TRMM] 2 km rainfall). An additional strong peak of variance is observed in the height ranges of 4–12 km during spring which corresponds to TRMM storm height maximum. The measurements suggest deep convective activity to be the main source of short period gravity waves. Variances in the UTLS region are found to correlate well with square of wind shear indicating possible in situ generation of the gravity waves. Topographic generation of short period gravity waves does not seem to be important for this site. An interannual variability is observed in the measured wave activity. Zonal momentum flux shows annual variation with westward preference in the wet season whereas the meridional flux does not indicate any clear variation.

In 2007, the SAVI was launched as an index designed to measure the market's expectation of the 3-month market volatility. The SAVI soon became the benchmark for measuring the market sentiment, and in this light can be thought of as a market "fear" index. Two years later, in 2009 the Johannesburg Stock Exchange updated the SAVI to reect a new way of measuring the expected volatility, one that is consistent with the theoretical framework, risk-management and the way traders trade options. The new SAVI is calculated as the at-the-money volatility adjusted for the volatility skew as determined by the actively traded options in
the market. The aim of this note is to introduce the new SAVI calculation method, and briefly discuss the benets of the new SAVI.

Testing hypothesis about variance parameters arises in contexts where uniformity is important and also in relation to checking assumptions as a preliminary to analysis of variance, discriminant analysis and so forth. In this paper, a bootstrap graphical method is ...