Response to Editor’s comments:
The manuscript has been extensively checked for grammar and English language expression.
Where necessary, edits have been made to the text to improve it readability.
The review was conducted according to the PRISMA statement. This statement is now
referenced in the paper and a completed PRISMA checklist is attached to this response to
reviewers. The checklist items marked as n/a are not relevant to this paper as it was not a
meta-analysis or review of results, rather the review describes the statistical analysis
approaches used in the published studies.
Reviewer: Han Lin L Shang
Reviewer's report: This paper provides a review on functional data analysis, which is an
increasingly popular field in statistics. The authors revisit the applications of functional data
analysis, and they covered the realms of data reduction, clustering, functional linear
modelling and forecasting.
RESPONSE: The authors thank the reviewer.
Major compulsory revisions
1) Please define what you meant by the time series analysis. I am not sure univariate time
series and multivariate time series techniques could be replaced by a functional time series
approach. Please specify: which type of time series is suitable for analysing via a functional
time series approach, and why that would be the case?
RESPONSE: “The time series analysis” has been removed from the manuscript. We did not
use any time series analysis ourselves in this manuscript but did review the reported FDA
techniques for time series data within the biomedical and public health settings.
2) Page 12, “Although some authors believe that FDA can be considered as a smoothed
version of multivariate data analysis, smoothing techniques should still be used to reduce
some of the inherent randomness in the observed data.” Some may disagree with this view,
because they prefer to incorporate the smoothness via roughness penalty approach, instead of
smoothing data directly. You may consider to state the existence of at least two ways of
smoothing in functional data analysis.
RESPONSE: We appreciate that some people prefer to incorporate the smoothness via a
roughness penalty approach, instead of smoothing the data directly. However, we believe
that the smoothing method reduces the observational errors and these types of errors always
exist in the time series data and so should be preferred. No change was made to the
manuscript in relation to this point.
3) Page 18, “more recent work has shown the advantage of direct application of smoothing
techniques to reduce the inherent randomness in the observed data”. Please cite references.
RESPONSE: The references have been added on page 18, para 2, last sentence, as suggested.
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4) Page 20, “been used in a number of demographic applications and there have been various
extensions and modifications proposed”. Please cite references.
RESPONSE: The references have been added on page 20, line 2 from bottom, as suggested
5) Page 21, “it establishes FDA as a preferred modelling approach for time series data”,
really? If so, please state why? Note this comment relates to 1).
RESPONSE: The statement has been changed in the manuscript on page 21. However, the
authors believe that FDA provides a relatively novel modelling and prediction approach for
time series data.
6) This paper has focused on application of FDA, with little or none on the theoretical aspect
of FDA. It would be more complete if the authors would extend their researcher by adding
references of theoretical results.
RESPONSE: The authors agreed with the reviewer’s comment about the lack of theoretical
detail in the paper. However, because this paper is a systematic reviewed of published FDA
applications, it is beyond its scope to do so. The reference list does include major texts and
some theoretical papers and the interested author can read those.
Minor essential revisions
1) Page 4, the multivariate approach also suffers from the high correlated measurement
within each functional object.
RESPONSE: This statement has been added to the paper on page 4, para 2, line 4, as
suggested.
2) Page 5, contained in the function and its derivatives (see the work by Andre Mas and his
colleagues)
RESPONSE: This has been added to the text on page 5, line 4 from bottom, as suggested.
3) Page 9, “Excluded studies as this stage” should be Excluded studies at this stage
RESPONSE: The typo has been corrected on page 9, para 2, line 2, as suggested.
4) Page 13, “while still holding as much as possible of the variation in the data set”. Please
replace the variation by the total variation
RESPONSE: The variation has been replaced by total variation on page 13, para 1, line 3, as
suggested.
5) Page 19, line 2, conventional statistical algorithms an can even... Please rewritten it.
RESPONSE: The typo has been corrected on page 19, line 2, as suggested.
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Reviewer: YUKUN WU
Reviewer's report: The authors did some literature search on the application of functional
data analysis (FDA) in the field of helth sciences. It is not easy to cover every aspect of FDA
in depth. For example, smoothing methods can be a paper by itself.
RESPONSE: The authors thank the reviewer.
Some comments follow:
1). The authors seemed to submit the article without careful proofreading. There are some
obvious language problems:
RESPONSE: The authors have extensively revised the manuscript for both grammar and
English expression.
Line 5 of paragraph 1 on page 6, "... peocesses, [l]and usage ...";
RESPONSE: Corrected on page 6, para 1, line 6.
Line 4 of paragraph 2 on page 6, "issues [has] have also ...";
RESPONSE: The grammar has been corrected, as suggested on page 6, para 2, line 4
First sentence of paragraph 3 on page 18 (section discussion) is grammatically
incorrect;
RESPONSE: The sentence has been edited on page 18.
Line 2 on page 19, "... algorithms [an] can even ...";
RESPONSE: The typo has been corrected on page 19, line 2, as suggested.
Sentence 2 of paragraph 2 on page 12, "A common approach ..." is ambiguous;
RESPONSE: The sentence has been rewritten on page 12, para 1, sentence 2, as suggested.
The conclusion part in abstract needs to be carefully rewritten. It does not answer the
question of the title (value) at all.
RESPONSE: The conclusion has been rewritten with particular focus on the research
questions.
2). Due to its non-parametric assumption, a drawback of FDA is its ability of forecasting and
corresponding interpretation, especially in a health data setting. Can the authors discuss it
more?
RESPONSE: We disagree. The beauty of FDA is that it makes no parametric assumptions
about age or time effects, in contrast to most other methods commonly used to model trends
in time series data.
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3). It is doubtful that the authors could conclude FDA as a preferred model[l]ing approaching
for time series data (page 21, paragraph 1 of section "conclusion") based only on the searched
articles.
RESPONSE: The statement “………preferred modelling approach….” has been changed, as
suggested by the other two reviewers.
4). The title looks not relevant to the contents, or vise versa.
RESPONSE: The title has been revised.
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Reviewer: Hongtu Zhu
Reviewer's report:I am happy to see that FDA is becoming a standard method and has been
widely used in various scientific studies. The authors are congratulated for giving a nice and
comprehensive review on the applications of FDA in such studies.
RESPONSE: The authors thank the reviewer.
Personally, I would like to see more comments on the FDA methodologies in the longitudinal
data analysis and biomedical imaging analysis.
RESPONSE: This is noted but was not added to the paper, because it was not requested by
other reviewers.
1. Recently, various FDA methods have been developed to model longitudinal data. Please
see Müller, H.G. (2011). Functional data analysis. International Encyclopedia of
Statistical Science Ed. Lovric, M. Springer Science Business Media, Heidelberg.
Extended online version available in StatProb: The Encyclopedia Sponsored by
Statistics and Probability Societies, id 242,
RESPONSE: The reference has been added on page 5, line 7, as suggested.
2. Moreover, various FDA methods have been developed to model high-dimensional
neuroimaging data. Please see
Yuan, Y., Zhu, H.T., Styner, M., J. H. Gilmore., and Marron, J. S. Varying
coefficient model for modeling diffusion tensors along white matter bundles.
Annals of Applied Statistics, in press, 2012.
Hua, Z.W., Dunson, D., Gilmore, J.H., Styner, M., and Zhu, HT. Semiparametric
Bayesian Local Functional Models for Diffusion Tensor Tract Statistics.
NeuroImage, in press, 2012.
Zhu, HT., Kong, L., Li, R., Styner, M., Gerig, G., Lin, W. and Gilmore, J. H.
FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics, NeuroImage,
56, 1412-1425, 2011.
Zhu, H.T., Styner, M., Tang, N.S., Liu, Z.X., Lin, W.L., Gilmore, J.H. FRATS:
functional regression analysis of DTI tract statistics. IEEE Transactions on
Medical Imaging, 29, 1039-1049, 2010.
In particular, the authors showed that compared with standard linear models,
functional linear model leads to a much gain in statistical efficiency. Please see
Hua et al (2012) and Zhu et al. (2011).
RESPONSE: We thank the reviewer for bringing these new papers to our attention. However
as our systematic review was restricted to studies published before the end of 2010, they have
not been included. To do so would mean that we would have to search and review the
literature again more completely to also identify other studies that may have been published
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post 2010. However, the 2010 article has been added (Table 1) and revised the findings in the
manuscript .
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