By Jin-Ting Zhang
"Preface useful facts research has been a well-liked statistical learn subject for the final 3 a long time. practical info are usually received through gazing a few matters over the years, house or different continua densely. they're often accumulated from a number of study parts, together with audiology, biology, kid's progress reviews, ergonomics, environmentology, me- teorology, and women's health and wellbeing reports among others within the kind of curves, surfaces, or different advanced items. Statistical inference for sensible facts regularly refers to estimation and speculation trying out approximately useful data. Read more...
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Extra resources for Analysis of variance for functional data
It is one of the reasons why cubic smoothing splines are popular in statistical applications. 24) be all the distinct design time points and be sorted in increasing order. 23) when k = 2. Let f = (f1 , · · · , fK )T , where fr = f (τr ), r = 1, 2, · · · , K.
X = ⎣ ... ⎦, . . 1 (tn − t0 ) · · · (tn − t0 )p and W = diag(Kh (t1 − t0 ), · · · , Kh (tn − t0 )), be the design matrix and the weight matrix for the LPK ﬁt around t0 . 5) where y = (y1 , · · · , yn )T and β = (β0 , β1 , · · · , βp )T . eTr+1,p+1 S−1 n Tn y, where er+1,p+1 denotes a (p + 1)-dimensional unit vector whose (r + 1)st entry is 1 and the other entries are 0, and Sn = XT WX, Tn = XT W. 22 NONPARAMETRIC SMOOTHERS FOR A SINGLE CURVE When t0 runs over the whole support T of the design time points, a whole (r) range estimation of f (r) (t) is obtained.
This is a twosample problem for functional data. It can be handled using the methods developed in Chapter 5. Another question also arises naturally. Is there any signiﬁcant diﬀerence between the covariance functions of girls and boys? This problem will be handled in an exercise problem in Chapter 10. Then comes a related question. How to test if there is any signiﬁcant diﬀerence between the mean growth curves of girls and boys when there is no knowledge about if the covariance functions of girls and boys are equal.
Analysis of variance for functional data by Jin-Ting Zhang