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which is an unbiased estimator of the variance of the mean in terms of the observed sample variance and known quantities. If the autocorrelations are identically zero, this expression reduces to the well-known result for the variance of the mean for independent data. The effect of the expectation operator in these expressions is that the ...
The bias is a trivial calculation, but the variance of ¯ is more involved since the jackknife replicates are not independent. For the special case of the mean, one can show explicitly that the jackknife estimate equals the usual estimate:
Consider the model of a normal distribution with unknown mean but known variance: { P θ = N(θ, σ 2) | θ ∈ R}. The data consists of n independent and identically distributed observations from this model: X = (x 1, …, x n). We estimate the parameter θ using the sample mean of all observations:
Because the Markowitz or Mean-Variance Efficient Portfolio is calculated from the sample mean and covariance, which are likely different from the population mean and covariance, the resulting investment portfolio may allocate too much weight to assets with better estimated than true risk/return characteristics.
(A portfolio is mean-variance efficient if there is no portfolio that has a higher return and lower risk than those for the efficient portfolio. [1]) Mean-variance efficiency of the market portfolio is equivalent to the CAPM equation holding. This statement is a mathematical fact, requiring no model assumptions.
Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained or residual variation ; likewise, when discussing variance as such, this is referred to as unexplained or residual variance .
Software is widely available for fitting this type of multilevel model. In this case, if the variance of the normal variable is zero, the model reduces to the standard (undispersed) logistic regression. This model has an additional free parameter, namely the variance of the normal variable.
This metric is well suited to intermittent-demand series (a data set containing a large amount of zeros) because it never gives infinite or undefined values [1] except in the irrelevant case where all historical data are equal.