Estimation of the parameters in a two linear regression equations system with identical parameter vectors

For two normal linear models with some of the parameters identical, a new estimator of the parameters is proposed and its statistical property is established. Two seemingly unrelated regression models with identical parameters are also considered. An efficient feasible estimator is obtained.62F10

Estimation of means of multivariate normal populations with order restriction

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case.Multivariate normal mean Order restrict Graybill-Deal estimator Isotonic regression

Analysis of Factors Influencing Wave Overtopping Discharge from Breakwater Based on an MIV-BP Estimation Model

Aiming at the problem of calculating the overtopping of single-slope breakwaters, a mean impact value-backpropagation (MIV-BP) estimation model for predicting overtopping was established. Experimental data from the Tianjin Research Institute of Water Transport Engineering (TIWTE) were utilized to further enrich the dataset of the CLASH project for single-slope wave overtopping discharge. This paper established a comprehensive prediction model based on an ensemble learning average method combination strategy. There are 10 input parameters in the model, including the offshore effective wave height, average wave period, offshore water depth, toe submergence, toe width, slope tangent, armor rock surface roughness factor, crest height with respect to the static water level, wall height with respect to the static water level, and crest width; the output parameter is the mean overtopping discharge. Subsequently, a comparative analysis was conducted between this estimation model, the Chinese standard formula calculation model, and the European Van der Meer formula calculation model. Compared with the two formulas mentioned above, this estimation model’s coefficient of correlation increased by 0.23 and 0.26, respectively. Finally, a weight evaluation analysis of the 10 main factors affecting overtopping was carried out based on a MIV-BP neural network model. In the analysis, a positive correlation was found for factors, such as the wave height, average wave period, and water depth at the structure toe; a negative correlation was found for factors, such as the slope, crest height with respect to the static water level, wall height with respect to the static water level, and crest width. Overall, the results provide a significant basis and reference for optimizing the design of the wave overtopping control