The following proposition gives an important result forΓββ. Proposition 2 Let{λi,Σ}i=1dbe the eigenvalues ofΣ=E(XXT), we have1/C≤λi,Σ≤C. Moreover, for anyϕ∈Hd, there is a positive constantCββsuch that, Cββ‖ϕ‖2≤⟨ϕ,Γββϕ⟩≤C‖ϕ‖2, ...
program myratio, rclass version 17 summarize length local length = r(mean) summarize turn local turn = r(mean) return scalar ratio = `length'/`turn' end Our program callssummarizeand stores the mean of the variablelengthin a local macro. The program then repeats this procedure for the sec...
In those cases, the Kalman filter is commonly applied (Welch and Bishop, 2004); however, the use of constrained estimation techniques such as the moving horizon estimation (MHE) can lead to significant improvements of the estimation result by adding system knowledge (Darby and Nikolaou, 2007; ...
If this 22 regress postestimation — Postestimation tools for regress were not a manual, having found evidence of omitted variables, we would never have run the estat hettest, estat szroeter, and estat imtest commands, at least not until we solved the omitted-variable problem. Technical note ...
Main result In this section, some sufficient conditions are provided to guarantee the ultimate boundedness of dynamics (7), (10). Then, according to the proposed sufficient conditions, the design approach of the stubborn filter and remote estimator are presented. Before stating our main results, ...
This result is not consistent with that obtained by Combellie et al.37 because most of the stations used in their study are located 150 km away from the epicentre and only data with PTW 30 s are used to calculate the two early parameters. If they use longer PTW, they should come ...
The deviation of α and in particular of αmax from α is a result of the fact that the PDF for most angles β is not symmetric (see specific example in Figure 4). It is largest for angles β near π/4 and 3π/4 (see Figure 1). However, both are much smaller than the ...
The b value obtained in the pre-April 16 period is slightly smaller than that obtained in the post-April 16 period, but this result is not statistically significant. If we remove the M JMA 6.4 earthquake (only M > 6 aftershock in all the time periods) that occurred 2.6 h after the ...
x∈Rn,n≥2 respectively. The operator |⋅| denotes the absolute value of a scalar or the number of elements of a vector. Without any specification, ‖⋅‖ denotes the Euclidean norm of the inputted vector. At first, the following result [30] is provided to guarantee the finite-time ...
n˜k=nkck,HkML is the ML estimation for the kth subcarrier. From Eq. (4.28), it follows that the estimated channel transfer function is contaminated by the noise. We use two means to characterize the errors as a result of this noise. The first one is the mean square error (MSE),...