Sentence examples for unbounded variance from inspiring English sources
Similar to [14, 36], we assume that the channel state has unbounded variance.
In addition, inner and outer bounds on the capacity region are derived in the regime of high state power, i.e., the channel state sequence has unbounded variance.
In contrast, the slope of power laws for avalanche dynamics is typically more shallow than −2, that is, these distributions do not have a mean and display unbounded variance, that is, non-existing first and second moments.
In the case of the random design nonparametric regression, to correct for the unbounded finite-sample variance of the local polynomial estimator using a 'global' bandwidth, several remedies are available.
In the case of the multivariate random design nonparametric regression, an interpolation method is proposed to overcome the problem of unbounded finite sample variance for the local linear estimator (LLE) using a global bandwidth.
In the case of the random design nonparametric regression, to correct for the unbounded finite-sample variance of the local linear estimator (LLE), Seifert and Gasser (J. Amer. Statist. Assoc. 91 (1996) 267 275) apply the idea of ridge regression to the LLE, and propose the local linear ridge regression estimator (LLRRE).
The latter two models assumed constant modifying variances because models with varying modifying variances resulted in unbounded estimates.
If the mean and variance were continuous and unbounded variables then they could be represented with Gaussian distributions and a Kalman filter could be used to optimally estimate them.
In this case, the mixture likelihood is unbounded because infinite values emerge if the variance of one of the components is zero.
The prior distributions for unknown variance parameters were set as unbounded uniform, which makes the Bayesian posterior distribution mathematically identical to the likelihood.
Note that the Wiener phase noise spectrum becomes unbounded at, which is a consequence of the variance increasing linearly with time.
