Asymptotic normality of least-square estimators in multivariate singular linear models

Optimization ◽  
1975 ◽  
Vol 6 (2) ◽  
pp. 285-299
Author(s):  
Wolfgang H. Schmidt
Nutrients ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 548
Author(s):  
Chia-Wen Lu ◽  
Yi-Chen Lee ◽  
Chia-Sheng Kuo ◽  
Chien-Hsieh Chiang ◽  
Hao-Hsiang Chang ◽  
...  

The association between serum concentrations of zinc, copper, or iron and the risk of metabolic syndrome are inconclusive. Therefore, we conduct a case-control study to explore the relationship between serum levels of zinc, copper, or iron and metabolic syndrome as well as each metabolic factor and insulin resistance. We enrolled 1165 adults, aged ≥ 40 (65.8 ± 10) years in a hospital-based population to compare the serum levels of zinc, copper, and iron between subjects with and without metabolic syndrome by using multivariate logistic regression analyses. The least square means were computed by general linear models to compare serum concentrations of zinc, copper, and iron in relation to the number of metabolic factors. The mean serum concentrations of zinc, copper, and iron were 941.91 ± 333.63 μg/L, 1043.45 ± 306.36 μg/L, and 1246.83 ± 538.13 μg/L, respectively. The odds ratios (ORs) of metabolic syndrome for the highest versus the lowest quartile were 5.83 (95% CI: 3.35–10.12; p for trend < 0.001) for zinc, 2.02 (95% CI: 1.25–3.25; p for trend: 0.013) for copper, and 2.11 (95% CI: 1.24–3.62; p for trend: 0.021) for iron after adjusting for age, sex, personal habits, body mass index, and homeostatic model assessment insulin resistance. Additionally, the serum zinc, copper, and iron concentrations increased as the number of metabolic factors rose (p for trend < 0.001). This was the first study to clearly demonstrate that higher serum levels of zinc, copper, and iron were associated with the risk of metabolic syndrome and the number of metabolic factors independent of BMI and insulin resistance.


2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.


2004 ◽  
Vol 35 (12) ◽  
pp. 1-9
Author(s):  
Masashi Kitahara ◽  
Taichi Hayasaka ◽  
Naohiro Toda ◽  
Shiro Usui

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