In general, the AW-XWVD outperformed the S-transform as a phase estimator and the S-transform estimates never meet the CRLB for all signals even at SNR of 10 dB.
To facilitate interpretation of results mean differences were back-transformed from the square root transformed estimates to the original density scales, with reference values corresponding approximately to median values in the study population (i.e. percent density 30%, dense area 35 cm, lucent area 90 cm).
Because of the log-transformation, we applied Duan's "smearing estimate" to back-transform estimates to original (untransformed) units of cm; this method adjusts for bias arising in retransformation of estimates from nonparametric or generalized linear models [ 27].
Transform estimates that drug prohibition has cost between £100bn and £200bn over the past 20 years.
About the Fourier transform estimates of ({sigma}_{Omega,h,phi,k}) with (Omegain H^{1}({{S}^{n-1}})), we have the following.
Of course, we remark that our result is mainly influenced by the idea and the technique established in [15]: Littlewood-Paley theory for product theory, Fourier transform estimates, etc. Remark 1.4.
In [19], Al-Salman, Al-Qassem and Pan proved that T is bounded on L p (ℝ n × ℝ m ) for 1 < p < ∞ when Ω ∈ L log L 2(Sn-1× Sm-1) and h ∈ Δ α for some α > 1, where their technique mostly based on refining the Duoandikoetxea-Rubia's Fourier transform estimates and Littlewood-paley theory.
Transformed estimates derived from the least squares means for this model and their standard errors are plotted in Figure 3.
All comparisons were based on threshold cycle number itself, rather than transformed estimates of RNA quantity, because the former value best reflects experimental error.
Transformed estimates were back transformed for presentation.
The pooled estimates calculated based on the untransformed and logit transformed estimates are presented in Table 3.
