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and truncated at each end to present curves of equal length. Measurements were recorded once per day per cycle from 8days before the day of ovulation and until 15days after the ovulation.A woman may have one or several cycles. The length of the observation period is 24days Some measurements from some subjects were missing due to various reasons The data set consists of two groups :the conceptive progesterone curves (22menstrual cycles)For more detail about this
data set, see Yen and Jaffe (1991), Brumback and Rice (1998) and Fan Zhang (2000),among others
Figure 1.1 (a) presents a spaghetti plot for 22 raw conceptive progesterone curves Dots indicaed with straight line segments .The problem of missing vales is not serious here because each cyxle curve has at least 17 out of 24 measure ments. Overall, the raw curves present a similar pattern:before the ovulation day (Day 0 ), the raw curves are quit flat ,but after the ovulation day; they generally move upward.However,it is easy to see that within a cycle curve, the measurements vary qround some underlying curve which appears to be smooth, and for diffeent cycles, the underlying smooth curve are different from each other Figure1.1 (b) presents the pointwise means dot-dashed curve )with 95% pointwise standard deviation (SD)band (cross-dashed curves).They were obtained in simple way :at each distinct design time point t,the mean and standard deviation were computed using the cross-section data at t, it can be seen that the pointwise mean curve is rather smooth ,although it is not difficult to discover that there is still some noise appeared in the pointwise menn curve
Figure 1.2 (a) presents a spaghetti plot for the 69 raw nonconceptive progesterone curves.Compared to the conceptive progesterone curves.these curves behave quite similarly before the day of ovulation,but generally show a different trend after the ovulation day. It is easy to see that,like the the conceptive progesterone curves the underlying individual cycle of the nonconceptive progesterone curves appear to be smooth ,and so is their underlyling mean cuve.A naïve estimate of the underlying mean curve is the pointwise mena curve, shown as dot-dashed curve in Figure1.2(b).The 95%poinwise SD band (cross-dashed curves)provides a rough estimate
For the accuracy of the naïve estimate
The progesterone data have been used for illustrations of nonparametric regression methods by several authors ,For example, Fan ang Zhang (2000)used them to illustrate their two-stp method for estimating the underlying mean function for longitudinal data or functional data .Brumback and Rice(1998)used them to illustrate a smoothing spline mixed-effects modeling technique for estimating both mean and individual function,while WU and Zhang (2002a)used them to illustrate a local polynomial mixed-effects modeling approach.
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Answer 1

并且削在每个末端提出相等的长度曲线。 测量一次每天被记录了每个周期从8days在天之前排卵和直到15days在排卵以后。妇女也许有一个或几个周期。 观察期的长度是24days有些测量从有些主题是错过由于数据集包括二个小组的各种各样的原因：有构思力的孕酮为关于这个数据集的更多细节弯曲(22menstrual
周期)，看见Yen，并且Jaffe (1991)， Brumback和Rice (1998)和风扇张(2000)，在其他中
图1.1 (a)礼物意粉剧情为22个未加工的有构思力的孕酮曲线小点indicaed与直线段。因为每cyxle曲线有至少17出于24项措施ments，错过谷的问题这里不是严肃的。 总之，未加工的曲线提出一个相似的样式：在排卵天(天0)之前，未加工的曲线在排卵天以后平展被放弃，但; 他们一般移动向上。然而，看是容易的在周期曲线之内，测量变化qround一些看来是光滑的部下的曲线，和为diffeent周期，部下的光滑的曲线是与彼此不同pointwise意味小点该死的曲线)与95% pointwise标准偏差的Figure1.1 (b)礼物(SD)带(十字架该死的曲线)。他们获得了用简单的方式：在每分明设计时间点t，卑鄙和标准偏差使用短剖面数据被计算了在t，它能被看见pointwise手段曲线是相当光滑的，虽然发现是不难的仍然有一些噪声在pointwise menn曲线表
1.2 (a)礼物出现意粉剧情为未加工的nonconceptive孕酮弯曲的69。比较对有构思力的孕酮curves.these曲线在天排卵之前相当相似地表现，但在排卵天以后一般显示一个不同的趋向。 看，象有构思力的孕酮曲线nonconceptive孕酮曲线的部下的单独周期看来是光滑的是容易的，和，因此是他们underlyling的卑鄙cuve。强调的naïve估计 卑鄙曲线是pointwise mena曲线，显示作为小点该死的曲线在Figure1.2 (b)。95%poinwise SD带(十字架该死的曲线)为孕酮数据
为非参数退化方法例证
使用了naïve估计的准确性提供粗略估计,例如，几位作者扇动ang张(2000)使用他们说明他们的two-stp方法为估计部下的平均值函数为纵向数据或功能数据。brumback和Rice (1998)使用他们说明塑造估计的使光滑的多槽轴混杂作用两个的技术,而吴和张(2002a)使用他们说明塑造方法的地方多项混杂作用。