A Comparison of Priors When Using Bayesian Regression to Estimate Oral Reading Fluency Slopes

Bayesian regression has emerged as a viable alternative for the estimation of curriculum-based measurement (CBM) growth slopes. Preliminary findings suggest such methods may yield improved efficiency relative to other linear estimators and can be embedded into data management programs for high-frequency use. However, additional research is needed, as Bayesian estimators require multiple specifications of the prior distributions. The current study evaluates the accuracy of several combinations of prior values, including three distributions of the residuals, two values of the expected growth rate, and three possible values for the precision of slope when using Bayesian simple linear regression to estimate fluency growth slopes for reading CBM. We also included traditional ordinary least squares (OLS) as a baseline contrast. Findings suggest that the prior specification for the residual distribution had, on average, a trivial effect on the accuracy of the slope. However, specifications for growth rate and precision of slope were influential, and virtually all variants of Bayesian regression evaluated were superior to OLS. Converging evidence from both simulated and observed data now suggests Bayesian methods outperform OLS for estimating CBM growth slopes and should be strongly considered in research and practice.

\({\mathbb{T}}\)-Proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or a widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

T-proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

Blind Deblurring Based on Sigmoid Function

Blind image deblurring, also known as blind image deconvolution, is a long-standing challenge in the field of image processing and low-level vision. To restore a clear version of a severely degraded image, this paper proposes a blind deblurring algorithm based on the sigmoid function, which constructs novel blind deblurring estimators for both the original image and the degradation process by exploring the excellent property of sigmoid function and considering image derivative constraints. Owing to these symmetric and non-linear estimators of low computation complexity, high-quality images can be obtained by the algorithm. The algorithm is also extended to image sequences. The sigmoid function enables the proposed algorithm to achieve state-of-the-art performance in various scenarios, including natural, text, face, and low-illumination images. Furthermore, the method can be extended naturally to non-uniform deblurring. Quantitative and qualitative experimental evaluations indicate that the algorithm can remove the blur effect and improve the image quality of actual and simulated images. Finally, the use of sigmoid function provides a new approach to algorithm performance optimization in the field of image restoration.

Fast leave-one-out methods for inference, model selection, and diagnostic checking

In this article, we describe jackknife2, a new prefix command for jackknifing linear estimators. It takes full advantage of the available leave-one-out formula, thereby allowing for substantial reduction in computing time. Of special note is that jackknife2 allows the user to compute cross-validation and diagnostic measures that are currently not available after ivregress 2sls, xtreg, and xtivregress.

Systematic bias of selected estimates applied in vertical displacement analysis

In surveying problems we almost always use unbiased estimators; however, even unbiased estimator might yield biased assessments, which is due to data. In statistics one distinguishes several types of such biases, for example, sampling, systemic or response biases. Considering surveying observation sets, bias from data might result from systematic or gross errors of measurements. If nonrandom errors in an observation set are known, then bias can easily be determined for linear estimates (e.g., least squares estimates). In the case of non-linear estimators, it is not so simple. In this paper we are focused on a vertical displacement analysis and we consider traditional least squares estimate, two Msplitestimates and two basic robust estimates, namely M-estimate, R-estimate. The main aim of the paper is to assess estimate biases empirically by applying Monte Carlo method. The smallest biases are obtained for M- and R-estimates, especially for a high magnitude of a gross error. On the other hand, there are several cases when Msplitestimates are the best. Such results are acquired when the magnitude of a gross error is moderate or small. The outcomes confirm that bias of Msplitestimates might vary for different point displacements.

Testing normality of chosen R-estimates used in deformation analysis

The normal distribution is one of the most important distribution in statistics. In the context of geodetic observation analyses, such importance follows Hagen’s hypothesis of elementary errors; however, some papers point to some leptokurtic tendencies in geodetic observation sets. In the case of linear estimators, the normality is guaranteed by normality of the independent observations. The situation is more complex if estimates and/or the functional model are not linear. Then the normality of such estimates can be tested theoretically or empirically by applying one of goodness-of-fit tests.This paper focuses on testing normality of selected variants of the Hodges-Lehmann estimators (HLE). Under some general assumptions the simplest HLEs have asymptotical normality. However, this does not apply to the Hodges-Lehmann weighted estimators (HLWE), which are more applicable in deformation analysis. Thus, the paper presents tests for normality of HLEs and HLWEs. The analyses, which are based on Monte Carlo method and the Jarque–Bera test, prove normality of HLEs. HLWEs do not follow the normal distribution when the functional model is not linear, and the accuracy of observation is relatively low. However, this fact seems not important from the practical point of view.