Dr Juhyun ParkLecturer in Statistics
- Nonparametric regression and functional data analysis
- Dynamic modelling of multi-dimensional curves
- Heavy tailed time series and extremes
- Longitudinal data analysis and medical statistics
- Multiple point processes for high frequency events
My main research area centres around functional data analysis and its applications. A typical functional data will be in the form of curves, or densely observed longitudinal data, such as spectrometric curves or cardiac frequency profiles. I focus on semi- or non-parametric approaches to analysing such data. Recent works are motivated by the need of developing methodologies for the analysis of multi-dimensional curves based on dynamic relations, and for extending to more general objects such as shapes or images.
Data as curves can also arise as intermediary from other forms of data, for example, risk neutral density functions, mortality curves, periodograms or intensity functions, and many nonparametric and functional data analysis techniques can be adopted to these type of data.
My interest also extends to regression models for extreme events, multiple point process models, ordinary differential equation models and medical statistics. In particular I am interested in extending these models to incorporate more complex data structure or high dimensional problems.
PhD Supervision Interests
1. Stochastic modelling and object oriented data analysis: This project develops a novel statistical methodology to analyse tree-like data (brain artery trees) based on a topological data representation. Standard methods try to extract high dimensional features from the representation for further analysis. This project considers a stochastic modelling approach similar to queueing models for statistical inference.
2. Prediction models for continuous monitoring data: It is easy to continuously collect and monitor various signals such as physiological or health related information, but is challenging to build a statistical model that takes such information into account. One can view such data as high-dimensional time series but there is more structural information/constraint that can be exploited. This project focuses on developing novel statistical methods using the ideas from functional data analysis and sparsity estimation.
3. Multivariate functional data analysis: Multivariate analysis is well developed for vector-like data, but not well developed for curve-like data such as continuous signals or functional data. Especially capturing (non-linear) dependence in high dimensional setting is challenging due to the inherent geometry of the data. This project develops novel statistical methods that combine the analytical (functional data analysis) and geometrical (shape analysis) approaches to analysing such type of data.
4. Spatial functional data and network regularisation: The spatial data has a natural network structure that is linked to each other through neighbours. When the dimension is high and the information is incomplete, it is difficult to estimate the underlying structure. This project considers to incorporate network regularisation methods in the context of spatial data analysis to tackle statistical inference problems.
Removing phase variability to extract a mean shape for juggling trajectories
Brunel, N., Park, J. 29/10/2014 In: Electronic Journal of Statistics. 8, 2, p. 1848-1855. 8 p.
Measuring similarity and improving stability in biomarker identification methods applied to Fourier-transform infrared (FTIR) spectroscopy
Trevisan, J., Park, J., Angelov, P., Ahmadzai, A., Gajjar, K., Scott, A.D., Carmichael, P.L., Martin, F. 04/2014 In: Journal of Biophotonics. 7, 3-4, p. 254-265. 12 p.
Functional synchrony for point processes
Park, J. 2014 In: Contributions in infinite-dimensional statistics and related topics. Societa Editorice Esculapio p. 203-208. 6 p.
Shape invariant modeling of pricing kernels and risk aversion
Grith, M., Haerdle, W., Park, J. 2013 In: Journal of Financial Econometrics. 11, 2, p. 370-399. 30 p.
Estimation of a functional single index model
Ferraty, F., Park, J., Vieu, P. 2011 In: Recent Advances in Functional Data Analysis and Related Topics. Berlin : Physica-Verlag HD p. 111-116. 6 p.
Long-range dependence analysis of Internet traffic
Park, C., Hernandez-Campos, F., Le, L., Marron, J.S., Park, J., Pipiras, V., Smith, F.D., Smith, R.L., Trovero, M., Zhu, Z. 2011 In: Journal of Applied Statistics. 38, 7, p. 1407-1433. 27 p.
Local additive estimation.
Park, J., Seifert, B. 03/2010 In: Journal of the Royal Statistical Society: Series B (Statistical Methodology). 72, 2, p. 171-191. 21 p.
Robust estimation of the Hurst parameter and selection of an onset scaling.
Park, J., Park, C. 10/2009 In: Statistica Sinica. 19, 4, p. 1531-1555. 25 p.
Structural components in functional data.
Park, J., Gasser, T., Rousson, V. 1/07/2009 In: Computational Statistics and Data Analysis. 53, 9, p. 3452-3465. 14 p.
Shape invariant modelling pricing kernels and risk aversion. SFB 649 Discussion Papers SFB649DP2009-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
Grith, M., Härdle, W., Park, J. 2009 Berlin : Humboldt University
Supporting mathematics undergraduates in learning statistics using self-learning materials
Park, J., Sperrin, M. 2009 In: JSM Proceedings, Washington, USA.
On properties of local additive estimation based on the smooth backfitting estimator.
Park, J., Seifert, B. 2008
On the effect of curve alignment and functional PCA
Park, J. 2008 In: Functional and operatorial statistics. Springer p. 243-245. 3 p.
On the choice of an auxiliary function in the M/G/∞ estimation.
Park, J. 15/08/2007 In: Computational Statistics and Data Analysis. 51, 12, p. 5477-5482. 6 p.
Nonparametric inference about service time distribution from indirect measurements.
Park, J., Hall, P. 1/11/2004 In: Journal of the Royal Statistical Society: Series B (Statistical Methodology). 66, 4, p. 861-875. 15 p.