Estimating average growth trajectories in shape-space using kernel smoothing

In this paper, we show how a dense surface point distribution model of the human face can be computed and demonstrate the usefulness of the high-dimensional shape-space for expressing the shape changes associated with growth and aging. We show how average growth trajectories for the human face can be computed in the absence of longitudinal data by using kernel smoothing across a population. A training set of three-dimensional surface scans of 199 male and 201 female subjects of between 0 and 50 years of age is used to build the model

Functional principal component analysis of spatially correlated data

This paper focuses on the analysis of spatially correlated functional data. We propose a parametric model for spatial correlation and the between-curve correlation is modeled by correlating functional principal component scores of the functional data. Additionally, in the sparse observation framework, we propose a novel approach of spatial principal analysis by conditional expectation to explicitly estimate spatial correlations and reconstruct individual curves. Assuming spatial stationarity, empirical spatial correlations are calculated as the ratio of eigenvalues of the smoothed covariance surface Cov (Xi(s),Xi(t))(Xi(s),Xi(t)) and cross-covariance surface Cov (Xi(s),Xj(t))(Xi(s),Xj(t)) at locations indexed by i and j. Then a anisotropy Matérn spatial correlation model is fitted to empirical correlations. Finally, principal component scores are estimated to reconstruct the sparsely observed curves. This framework can naturally accommodate arbitrary covariance structures, but there is an enormous reduction in computation if one can assume the separability of temporal and spatial components. We demonstrate the consistency of our estimates and propose hypothesis tests to examine the separability as well as the isotropy effect of spatial correlation. Using simulation studies, we show that these methods have some clear advantages over existing methods of curve reconstruction and estimation of model parameters

Search for Evergreens in Science: A Functional Data Analysis

Evergreens in science are papers that display a continual rise in annual citations without decline, at least within a sufficiently long time period. Aiming to better understand evergreens in particular and patterns of citation trajectory in general, this paper develops a functional data analysis method to cluster citation trajectories of a sample of 1699 research papers published in 1980 in the American Physical Society (APS) journals. We propose a functional Poisson regression model for individual papers' citation trajectories, and fit the model to the observed 30-year citations of individual papers by functional principal component analysis and maximum likelihood estimation. Based on the estimated paper-specific coefficients, we apply the K-means clustering algorithm to cluster papers into different groups, for uncovering general types of citation trajectories. The result demonstrates the existence of an evergreen cluster of papers that do not exhibit any decline in annual citations over 30 years.Comment: 40 pages, 9 figure

The Evolution of Cross-Region Price Distribution in Russia

The behavior of the entire cross-section distribution of prices in Russian regions is analyzed from 1992 through 2000, using non-parametric techniques. The cost of a staples basket is used as a price representative. Price dispersion measured as the standard deviation of prices is found to be diminishing since about 1994; and the shape of the cross-region distribution of prices tends to be more regular over time. To characterize intra-distribution mobility, a transition probability function (stochastic kernel) is estimated. It is also used to derive a long-run limit of the price distribution. Overall, the results suggest that, excluding a few years following the price liberalization, price convergence has been happening among Russian regions.http://deepblue.lib.umich.edu/bitstream/2027.42/40102/3/wp716.pd

Particle Efficient Importance Sampling

The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers. Despite a number of successful applications in high dimensions, it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases. We solve this problem by recognising that the EIS framework has an offline sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the look-ahead construction of the importance sampler. We apply the method for a range of univariate and bivariate stochastic volatility specifications. We also develop a new application of the EIS approach to state space models with Student's t state innovations. Our results show that the particle EIS method strongly outperforms both the standard EIS method and particle filters for likelihood evaluation in high dimensions. Moreover, the ratio between the variances of the particle EIS and particle filter methods remains stable as the time series dimension increases. We illustrate the efficiency of the method for Bayesian inference using the particle marginal Metropolis-Hastings and importance sampling squared algorithms

The Evolution of Cross-Region Price Distribution in Russia

The behavior of the entire cross-section distribution of prices in Russian regions is analyzed from 1992 through 2000, using non-parametric techniques. The cost of a staples basket is used as a price representative. Price dispersion measured as the standard deviation of prices is found to be diminishing since about 1994; and the shape of the cross-region distribution of prices tends to be more regular over time. To characterize intra-distribution mobility, a transition probability function (stochastic kernel) is estimated. It is also used to derive a long-run limit of the price distribution. Overall, the results suggest that, excluding a few years following the price liberalization, price convergence has been happening among Russian regions.price convergence, price dispersion, distribution dynamics, market integration, Russia