Analysis of variance for functional data by Jin-Ting Zhang PDF

By Jin-Ting Zhang

"Preface useful info research has been a well-liked statistical study subject for the final 3 many years. sensible info are usually acquired through gazing a few matters through the years, house or different continua densely. they're often gathered from a variety of study parts, together with audiology, biology, kid's development experiences, ergonomics, environmentology, me- teorology, and women's healthiness reports among Read more...

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The measurements are shown as circles, and the standard regression spline fit, the first-, second-, and third-iteration regression spline fits are shown as the dotdashed, dashed, dotted, and solid curves, respectively. It is seen that the usual regression spline fit is indeed affected by the outlier, the first-iteration regression spline fit improves the usual regression spline fit and it is improved by the second-iteration regression spline fit. The second- and third-iteration regression spline fits are close to each other.

For convenience, it may be called a regression spline of degree k with knots τ1 , τ2 , · · · , τK . 15) associated with k = 1, 2, and 3 are usually called linear, quadratic, and cubic regression splines, respectively. We can see that within any subinterval or local neighborhood [τr , τr+1 ), we have k r βk+l (t − τl )k , βs ts + f (t) = s=0 l=1 which is a kth degree polynomial. (βk + r βk+l ). βk+r . βk+r for r = 1, 2, · · · , K. ). 16) where p = K + k + 1 denotes the number of the basis functions involved.

Let ⎤ ⎡ 1 (t1 − t0 ) · · · (t1 − t0 )p ⎥ ⎢ .. .. 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.

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