Here, we document the performance of different DFT and DFTB methods with respect to the C−O stretch vibration, both in terms of absolute frequencies and effects of hydrogen bonds on the frequencies. We demonstrate, that PBE/def2-TZVP is a suitable reference for the C−O stretch frequency in carboxylic acids. In the following text, the abbreviations ME (mean error), MAE (mean absolute error), MSE...

Error measures for the evaluation of forecasts are usually based on the size of the forecast errors. Common measures are e.g. the Mean Squared Error (MSE), the Mean Absolute Deviation (MAD) or the Mean Absolute Percentage Error (MAPE). Alternative measures for the comparison of forecasts are turning points or hits-and-misses, where an indicator loss function is used to decide, if a forecast is ...

The threshold region mean squared error (MSE) performance of the Capon-MVDR algorithm is predicted via an adaptation of an interval error based method referred to herein as the method of interval errors (MIE). MIE requires good approximations of two quantities: (i) interval error probabilities, and (ii) the algorithm asymptotic (SNR→ ∞) MSE performance. Exact pairwise error probabilities for th...

Consistent reconstruction is a method for producing an estimate x̃ ∈ R of a signal x ∈ R if one is given a collection ofN noisy linear measurements qn = 〈x, φn〉+ǫn, 1 ≤ n ≤ N , that have been corrupted by i.i.d. uniform noise {ǫn}n=1. We prove mean squared error bounds for consistent reconstruction when the measurement vectors {φn}n=1 ⊂ R are drawn independently at random from a suitable distrib...

A theoretical analysis of the overall mean squared error (MSE) in hybrid video coding is presented for the case of error prone transmission. The derived model for interframe error propagation includes the e ects of INTRA coding and spatial loop ltering and corresponds to simulation results very accurately. For a given target bit rate, only four parameters are necessary to describe the overall d...

Beamforming methods are used extensively in a variety of different areas, where one of their main goals is to estimate the source signal amplitude s(t) from the array observations y(t) = s(t)a + i(t) + e(t), t = 1,2,..., where a is the steering vector, i(t) is the interference, and e(t) is a Gaussian noise vector [1, 2]. To estimate s(t), we may use a beamformer with weights w so that s(t) = w*...

We employed a leave-one-out cross validation to determine optimally sized neighborhood. Variations between a single point and the other points within each filter size for all the points in the study area were evaluated, and the mean squared error (MSE) for each filter was calculated. The filter with the lowest MSE was considered as the optimal neighborhood. The method is useful in determining t...

A theoretical analysis of the overall mean squared error (MSE) in hybrid video coding is presented for the case of error prone transmission. The derived model for interframe error propagation includes the eeects of INTRA coding and spatial loop ltering and corresponds to simulation results very accurately. For a given target bit rate, only four parameters are necessary to describe the overall d...

The Weiss–Weinstein bound (WWB) provides a lower limit on the mean-squared error (MSE) achievable by an estimator of an unknown random parameter. In this correspondence, it is shown that some previously proposed simplified versions of the bound do not always hold for constrained parameters, i.e., parameters whose distribution has finite support. These simplifications can produce results which a...