We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman’s and Pearson’s chi-squares, namely “combined Neyman–Pearson chi-square” (χCNP2). ...Through analytical derivations and toy model simulations, we show that χCNP2 leads to a significantly smaller bias on the best-fit model parameters compared to those using either Neyman’s or Pearson’s chi-square. When the computational cost of using the Poisson-likelihood chi-square is high, χCNP2 provides a good alternative given its natural connection to the covariance matrix formalism.
Counting the types of squares rather than their occurrences, we consider the problem of bounding the number of distinct squares in a string. Fraenkel and Simpson showed in 1998 that a string of ...length n contains at most 2n distinct squares. Ilie presented in 2007 an asymptotic upper bound of 2n−Θ(logn). We show that a string of length n contains at most ⌊11n/6⌋ distinct squares. This new upper bound is obtained by investigating the combinatorial structure of double squares and showing that a string of length n contains at most ⌊5n/6⌋ particular double squares. In addition, the established structural properties provide a novel proof of Fraenkel and Simpson’s result.
ABSTRACT
Partial least squares path modeling (PLS‐PM) has become popular in various disciplines to model structural relationships among latent variables measured by manifest variables. To fully ...benefit from the predictive capabilities of PLS‐PM, researchers must understand the efficacy of predictive metrics used. In this research, we compare the performance of standard PLS‐PM criteria and model selection criteria derived from Information Theory, in terms of selecting the best predictive model among a cohort of competing models. We use Monte Carlo simulation to study this question under various sample sizes, effect sizes, item loadings, and model setups. Specifically, we explore whether, and when, the in‐sample measures such as the model selection criteria can substitute for out‐of‐sample criteria that require a holdout sample. Such a substitution is advantageous when creating a holdout causes considerable loss of statistical and predictive power due to an overall small sample. We find that when the researcher does not have the luxury of a holdout sample, and the goal is selecting correctly specified models with low prediction error, the in‐sample model selection criteria, in particular the Bayesian Information Criterion (BIC) and Geweke–Meese Criterion (GM), are useful substitutes for out‐of‐sample criteria. When a holdout sample is available, the best performing out‐of‐sample criteria include the root mean squared error (RMSE) and mean absolute deviation (MAD). We recommend against using standard the PLS‐PM criteria (R2, Adjusted R2, and Q2), and specifically the out‐of‐sample mean absolute percentage error (MAPE) for prediction‐oriented model selection purposes. Finally, we illustrate the model selection criteria's practical utility using a well‐known corporate reputation model.
The Normalized Difference Vegetation Index (NDVI) is one of the most commonly used vegetation indices for monitoring ecosystem dynamics and modeling biosphere processes. However, global NDVI products ...are usually provided with relatively coarse spatial resolutions that lack important spatial details. Producing NDVI time-series data with high spatiotemporal resolution is indispensable for monitoring land surfaces and ecosystem changes, especially in spatiotemporally heterogeneous areas. The Improved Flexible Spatiotemporal DAta Fusion (IFSDAF) method was developed in this study to fill this need. In accord with the distinctive characteristics of NDVIs with large data variance and high spatial autocorrelation compared with raw reflectance bands, the IFSDAF method first produces a time-dependent increment with linear unmixing and a space-dependent increment via thin plate spline interpolation. It then makes a final prediction by optimal integration of these two increments with the constrained least squares method. Moreover, the IFSDAF was developed with the capacity to use all available finer-scaled images, including those partly contaminated by clouds. NDVI images with coarse spatial resolution (MODIS) and fine spatial resolution (Landsat and Sentinel) in areas with great spatial heterogeneity and significant land cover changes were used to test the performance of the IFSDAF method. The root mean square error and relative root mean square error of predicted relative to observed results were 0.0884 and 22.12%, respectively, in heterogeneous areas, and 0.0546 and 25.77%, respectively, in areas of land-cover change. These promising results demonstrated the strength and robustness of the IFSDAF method in providing reliable NDVI datasets with high spatial and temporal resolution to support research on land surface processes. The efficiency of the proposed IFSDAF method can be greatly improved by using only the space-dependent increment. This simplification will make IFSDAF a feasible method for monitoring global vegetation.
•IFSDAF was proposed to fuse NDVI data with different resolutions.•IFSDAF performs well in areas with great spatial heterogeneity.•IFSDAF can capture land cover changes in the fused image.•IFSDAF optimizes the combination of temporal and spatial information.•IFSDAF can use partially cloud contaminated fine-resolution images as input.
Quantized Kernel Least Mean Square Algorithm Badong Chen; Songlin Zhao; Pingping Zhu ...
IEEE transaction on neural networks and learning systems,
2012-Jan., 2012, 2012-Jan, 2012-1-00, 20120101, Letnik:
23, Številka:
1
Journal Article
In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind ...this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.
Display omitted
•We address shortcomings of RMSE calculation of 5-parameter single diode PV models.•We propose an exact solution for RMSE of 5-parameter single diode PV models.•The proposed RMSE ...expression is based on Lambert W function.•Precision of calculation to solve the Lambert W function is addressed.•Results and applications show why the proposed RMSE expression must be adopted.
In the literature, one can find a lot of methods and techniques employed to estimate single diode solar photovoltaic (PV) cell parameters. The efficiency of these methods is usually tested by calculating the Root Mean Square Error (RMSE) between the measured and estimated values of the solar PV cell output current. In this work, first, the values of RMSE calculated using 69 different methods published in many journal papers for the well-known RTC France solar PV cell are presented and discussed. Second, a novel exact analytical solution for RMSE calculation based on the Lambert W function is proposed. The results obtained show that the RMSE values were not calculated correctly in most of the methods presented in the literature since the exact expression of the calculated cell output current was not used. Third, the precision of calculation of the methods used for analytical solving of Lambert W equation is presented and discussed. Fourth, the applicability of the proposed solution methodology in accordance with current-voltage characteristics measured in the laboratory for solar modules of Clean Energy Trainer Setup is checked. Identification of its unknown parameters is presented using three optimization techniques. Further, the proposed solution methodology is proven for Solarex MSX–60 PV module, and the most promising 5-parameter single diode parameters are estimated based on minimization of the precise RMSE values calculated. Finally, this work aimed to develop a good base for proper investigation and implementation of optimization algorithms to solve the parameter estimation problem of 5-parameter single diode PV equivalent circuits.
Visible light communication (VLC) has been proposed as a promising way for next generation wireless communication networks to mitigate the scarcity of the radio frequency (RF) spectrum, and has ...consequently attracted much attention. This paper introduces a single-input single-output (SISO) VLC system under the joint effects of statistical random channel and signal-dependent shot noise (SDSN). Moreover, it estimates the channel of the considered system using maximum likelihood (ML), least square (LS), linear minimum mean square error (LMMSE), maximum posteriori probability (MAP) and minimum mean square error (MMSE) estimators. Furthermore, a Bayesian Cramér-Rao lower bound (BCRLB) is derived for the proposed system and it is compared to the mean square error (MSE) of the proposed estimators. The problem of unknown SDSN factor, <inline-formula><tex-math notation="LaTeX">\zeta ^{2}</tex-math></inline-formula>, at the receiver side is discussed and two solutions are investigated. The receiver of a VLC system under SDSN and random channel gain <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula> is designed and its BER is studied. Finally, Monte Carlo simulation results of the proposed estimators, which show the dramatic effect of the SDSN on the considered system, are provided. In particular, the presence of noise variance, as well as the SDSN factor, causes an increase in the MSE of the system, while increasing the power reinforces the system performance.
A scaled difference test statistic
that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (Psychometrika 66:507–514,
...2001
). The statistic
is asymptotically equivalent to the scaled difference test statistic
introduced in Satorra (Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker, pp. 233–247,
2000
), which requires more involved computations beyond standard output of SEM software. The test statistic
has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the implicit function theorem, this note develops an improved scaling correction leading to a new scaled difference statistic
that avoids negative chi-square values.
In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability ...is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, we propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, we compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. We show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.
PDF
