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\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural

\f0\fs24 \cf0 ============
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Description:
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============
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This is the main function to 
\f1\fs28 \cf2 \cb3 obtain nonlinear, data-adaptive dynamic equations from the observed longitudinal processes. The dynamic equation is numerically estimated  via  smoothing-based procedure on the pre-smoothed trajectories and derivatives
\f0\fs24 \cf0 \cb1 . 
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dimensional data is implemented with distance-based metric Multidimensional Scaling,
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mapping high-dimensional data to locations on a real interval, such that predictors that
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are close in a suitable sample metric also are located close to each other on the interval. 
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Established techniques from Functional Data Analysis can
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be applied for further statistical analysis once an underlying stochastic process and the
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corresponding random trajectory for each subject have been identified. 
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Reference: 
\f2\fs26 \cf2 \cb3  Nicolas Verzelen,\'a0 Wenwen Tao,\'a0 and\'a0Hans-Georg M\'fcller\
\pard\pardeftab720\sl280

\f3\fs22 \cf4 Inferring stochastic dynamics from functional data\
\pard\pardeftab720

\f4\fs24 \cf5 Biometrika
\f3\fs18 \'a0
\f4\fs24 (2012)\'a099(3):\'a0533-550\'a0first published online\'a0July 9, 2012\'a0doi:10.1093/biomet/ass015
\f3\fs22 \cf4 \
\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural

\f0\fs24 \cf0 \cb1 
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========
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Usage:
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========
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[mu,dyn_grid]=non_dyn(t,y,method,tout,N_f)\
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\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural
\cf0 =======\
Input:\
=======\
\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural
\cf0  t              :1 * N cell of observed time points. Need to be coherent for all subjects\
y              :1 * N cell of observed repeated measurements for each subject, corresponding to each cell of t.\
method    :a character string for the kernel to be used, default is 'gauss'
\f5 ; should be specified as one of the following
\f0 \
                 'epan' - epanechikov kernel\
                 'gauss' - gaussian kernel\
                 'gausvar' - variant of gaussian kernel\
                 'rect' - rectangular kernel\
                 'quar' - quartic kernel\
tout          : m * 1 vector of the output time grid ; default is equadistance 1*100 grid between min(t\{1\}) and max(t\{1\}).               \
N_f           :scalar that gives the output size of trajectory y grid; default is 200.\
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Details: i) Any unspecified or optional arguments can be set to "[]" for
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            default values;\

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=======
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Output:
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=======\
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\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural
\cf0 mu              :m * N_f matrix of the estimated dynamic surface on given time grid and trajectory grid (N_f equidistant grid on the support region)\
dyn_grid     :m * N_f matrix of the output grid corresponding to mu.
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\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural
\cf0 
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\
 See example_non_dyn.m
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}