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행렬 X가 불완전열계수인 경우의 능형회귀에서 오차분산과 능형모수의 추정
김종덕 부산 외국어 대학교 2007 外大論叢 Vol.33 No.-
A reasonable way for the estimation of the biasing parameter in ridge regression is to choose a value which minimizes the mean squared error of the estimator. However, this does not yield a closed-form solution. Thus Hoerl, Kennard, and Baldwin (1975) showed an optimal choice of the biasing parameter to be ĉ=pÔ2/ββ, by using two special matrix X with size n×p is p. In this paper, a detailed description of the process was given for the result. However, this can be applied only to the case of full column rank of X. The mean squared error of the estimator was developed for the two special situations in the case of non-full column rank of X. Then the optimal value of the biasing parameter tumed out to be ĉ=pÔ2/ββ if the rank of X is r(<min(n-1,p). Thus this can be regarded as a general optimal equation of biasing parameter for rank(X)=r(≤ min(n-1,p).
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모야모야 병 : 소아와 어른에 있어서 자기공명영상 소견의 차이
김종덕 대한영상의학회 1995 대한영상의학회지 Vol.33 No.6
Purpose : To evaluate whether there are any differences in MR findings between the childhood and adultmoyamoya disease. Materials and Methods : We compared the brain MR findings in 22 children(13 boys and 9 girls, 2-18 years of age) who had moyamoya disease with 15 adult patients(7 men and 8 women, 19-55 years of age). The MRfindings were classified as parenchymal-(infarctions and intracranial hemorrhages) and vascularabnormalities(intracranial vascular patency and moyamoya vessels). The difference in each of these MR findings wasanalyzed using Chi-square test and Fisher's exact test(two-tailed). Out of 22 children, two children with normalMR finding were excluded from the statistical analysis. Moyamoya diseases were diagnosed angiographically in alladult patients. In children, they were diagnosed by MR imaging, MR angiography(6) and/or conventional cerebralangiography(18). Results : In children, cerebral infarctions were observed in 20 of 22 patients(91%)(cortex 86%, periventricular white matter/centrum semiovale 32%, basal ganglia 10%). In two patients, there was no parenchymalabnormality. Intracranial hemorrhages were not demonstrated in any patients. In adults, intracranialhemorrhages(intracerebral hematoma, intraventricular hemorrhage, alone or combined) were demonstrated in 10 of 15patients(67%). Cerebral infarctions with or without intracranial hemorrhage were detected in 10 of 15patients(67%)(cortex 40%, periventricular white matter/centrum semiovale 53%, basal ganglia 20%). The differencein parenchymal abnormalities between the childhood and the adult moyamoya disease was statisticallysignificant(p=0.000164). There was no significant difference between the two groups with regard to the occlusivechanges of the internal carotid and middle cerebral arteries or to moyamoya vessels(p>0.01). Conclusion : Thisstudy could prove the fact that the principal clinical symptoms in the childhood moyamoya disease were due tocerebral infarction and those in the adult cases were due to infarction and intracranial hemorrhage. In addition, cortical infarction was more prevalent in children and infarction in periventricular white matter/centrumsemivoale and basal ganglia was more frequent in adults. There was no significant difference in vascularabnormalities between the two groups. enisci weredi
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