Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing

1990 ◽  
Vol 6 (1) ◽  
pp. 63-74 ◽  
Author(s):  
R.A.L. Carter ◽  
M.S. Srivastava ◽  
V.K. Srivastava ◽  
A. Ullah

We first present an unbiased estimator of the MSE matrix of the Stein-rule estimator of the coefficient vector in a normal linear regression model. The Steinrule estimator can be used with both its estimated MSE matrix and with the least-squares MSE matrix to form confidence ellipsoids. We derive the approximate expected squared volumes and coverage probabilities of these confidence sets and discuss their ranking. These results can be applied to the conditional prediction of the mean of the endogenous variable. We also consider the power of F-tests which employ the Stein-rule estimator in place of the least-squares estimator.

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.


1998 ◽  
Vol 7 (1) ◽  
pp. 53-61
Author(s):  
Henrich Cheng ◽  
Matt Fraidakis ◽  
Birger Blombäck ◽  
Paul Lapchak ◽  
Barry Hoffer ◽  
...  

One novel method to deliver trophic factor locally in the CNS is to mix it into fibrin glue. In the present studies, [125I]-labeled GDNF-containing fibrin glue balls were used to determine binding and spread of the trophic factor. First, the binding of different concentrations of [125I]-labelèd GDNF in fibrin glue was determined in vitro. Within the six concentrations used (from 200 nM to 0.004 nM, 0 M as control), there was a strong linear correlation between the [125I]-GDNF concentration and the recovered radioactivity (r = 0.992). The mean bound radioactivity in 16 samples with 4 nM [125I]-GDNF was 71262 + 2710 CPM, and accounted for 89.8% of the mean initial count of free [125I]-GDNF (79369 + 3499 CPM). Second, [125I]-GDNF-containing glue balls were implanted into the anterior chamber of adult rats. The implanted fibrin glue balls decreased in size with time, but could still be identified on the irises 2 wk after implantation. Radioactivity was concentrated at the implantation sites in the early stages with a distribution in the surrounding iris tissue, which became separated into focal radioactive spots at the third week. Counts of radioactivity were significantly higher in the [125I]-GDNF glue ball-implanted irises than controls until 14 days after implantation. A study of the [125I] decay over time using least-squares linear regression demonstrated first-order kinetics (r = —0.98, p < 0.02) with k = 0.0091 and T 1/2 = 76 h. Finally, [125I]-GDNF–containing glue balls were implanted in the spinal cord of adult rats. Radioactivity was concentrated at the implantation sites in the early stages and was later distributed more widely in the surrounding thoracic cord. The [125I]-GDNF–containing glue degraded over time and became a porous meshwork with decreasing radioactivity at the later time points. Radioactivity in the spinal cords subjected to implantation of [125I]-GDNF–containing glue balls was higher than in controls for 14 days. Study of the [125I] decay by time with least-squares linear regression demonstrated first-order kinetics (r = -0.97, p = 0.001) with T 1/2 = 75.6 h. We conclude that the trophic factor GDNF becomes bound in the fibrin glue matrix from which it is gradually released. Our results suggest that fibrin glue is an effective substrate for keeping a trophic factor localized in situ for a finite period, protected from the circulation, surrounding aqueous humor or CSF.


Filomat ◽  
2016 ◽  
Vol 30 (15) ◽  
pp. 3949-3961 ◽  
Author(s):  
Xu Gong ◽  
Fenghua Wen ◽  
Zhifang He ◽  
Jia Yang ◽  
Xiaoguang Yang ◽  
...  

The extreme return and extreme volatility have great influences on the investor sentiment in stock market. However, few researchers have taken the phenomenon into consideration. In this paper, we first distinguish the extreme situations from non-extreme situations. Then we use the ordinary generalized least squares and quantile regression methods to estimate a linear regression model by applying the standardized AAII, the return and volatility of SP 500. The results indicate that, except for extremely negative return, other return sequences can cause great changes in investor sentiment, and non-extreme return plays a leading role in affecting the overall American investor sentiment. Extremely positive (negative) return can rapidly improve (further reduce) the level of investor sentiment when investors encounter extremely pessimistic situations. The impact gradually decreases with improvement of the sentiment until the situation turns optimistic. In addition, we find that extreme and non-extreme volatility cannot a_ect the overall investor sentiment.


2018 ◽  
Vol 27 (2) ◽  
pp. 166-172 ◽  
Author(s):  
Ali Gholami ◽  
Farhad Zamani ◽  
Bayan Hosseini ◽  
Rahim Sharafkhani ◽  
Mansooreh Maadi ◽  
...  

Objective: This study was designed to examine the effect of metabolic syndrome (MetS) on health-related quality of life (HRQOL) in patients with suspected nonalcoholic steatohepatitis (NASH). Subjects and Methods: Three hundred thirty-two patients (236 males and 96 females) with suspected NASH from the Amol cohort study were included in this study. MetS was diagnosed based on Adult Treatment Panel III criteria and HRQOL was measured using the 12-Item Short-Form Health Survey (SF-12) questionnaire (with 8 subscales and 2 summary components). A multivariable linear regression model was used to assess the independent effect of MetS on HRQOL. Results: The mean age of the study population was 42 ± 13 years (range 18–82). The prevalence of MetS was 43.4% (n = 144) and the mean scores on the Physical Component Summary (PCS) and the Mental Component Summary were 72.4 ± 20.86 and 42.7 ± 12.42, respectively. The multivariable linear regression model showed that MetS was negatively associated with 4 subscales of HRQOL that included: role limitations due to physical problems (RP) (B = –14.05, p = 0.004), bodily pain (BP) (B = –7.37, p = 0.02), vitality (VT) (B = –7.72, p = 0.022), and role limitations due to emotional problems (RE) (B = –12.67, p = 0.005) after adjustment for other variables. Also, MetS had a borderline association with the general health and mental health subscales and the PCS (p < 0.1). Conclusion: In this study, there was a strong association between MetS and 4 subscales (RP, BP, VT, and RE) of HRQOL in patients with suspected NASH; this could be considered as a part of health policy to improve general health.


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