arXiv subjects

Lingyu He

Publications and source records attributed to Lingyu He.

3 recordsLinked to original sources

arXiv2022

Robust PCA for High Dimensional Data based on Characteristic Transformation

In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic function is constructed to improve the robustness of the classical PCA. Besides the typical outliers, the proposed method has the unique advantage of dealing with heavy-tail-distributed data, whose covariances could be nonexistent (positively infinite, for instance). The proposed approach is also a case of kernel principal component analysis (KPCA) method and adopts the robust and non-linear properties via a bounded and non-linear kernel function. The merits of the new method are illustrated by some statistical properties including the upper bound of the excess error and the behaviors of the large eigenvalues under a spiked covariance model. In addition, we show the advantages of our method over the classical PCA by a variety of simulations. At last, we apply the new robust PCA to classify mice with different genotypes in a biological study based on their protein expression data and find that our method is more accurately on identifying abnormal mice comparing to the classical PCA.

stat.ME↗

arXiv2021

A Forecast-driven Hierarchical Factor Model with Application to Mortality Data

Mortality forecasting plays a pivotal role in insurance and financial risk management of life insurers, pension funds, and social securities. Mortality data is usually high-dimensional in nature and favors factor model approaches to modelling and forecasting. This paper introduces a new forecast-driven hierarchical factor model (FHFM) customized for mortality forecasting. Compared to existing models, which only capture the cross-sectional variation or time-serial dependence in the dimension reduction step, the new model captures both features efficiently under a hierarchical structure, and provides insights into the understanding of dynamic variation of mortality patterns over time. By comparing with static PCA utilized in Lee and Carter 1992, dynamic PCA introduced in Lam et al. 2011, as well as other existing mortality modelling methods, we find that this approach provides both better estimation results and superior out-of-sample forecasting performance. Simulation studies further illustrate the advantages of the proposed model based on different data structures. Finally, empirical studies using the US mortality data demonstrate the implications and significance of this new model in life expectancy forecasting and life annuities pricing.

stat.AP↗

arXiv2021

Mortality Forecasting using Factor Models: Time-varying or Time-invariant Factor Loadings?

Many existing mortality models follow the framework of classical factor models, such as the Lee-Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as $κ_t$ in the Lee-Carter model). Factor loadings, which capture the linear relationship between age variables and latent common factors (such as $β_x$ in the Lee-Carter model), are assumed to be time-invariant in the classical framework. This assumption is usually too restrictive in reality as mortality datasets typically span a long period of time. Driving forces such as medical improvement of certain diseases, environmental changes and technological progress may significantly influence the relationship of different variables. In this paper, we first develop a factor model with time-varying factor loadings (time-varying factor model) as an extension of the classical factor model for mortality modelling. Two forecasting methods to extrapolate the factor loadings, the local regression method and the naive method, are proposed for the time-varying factor model. From the empirical data analysis, we find that the new model can capture the empirical feature of time-varying factor loadings and improve mortality forecasting over different horizons and countries. Further, we propose a novel approach based on change point analysis to estimate the optimal `boundary' between short-term and long-term forecasting, which is favoured by the local linear regression and naive method, respectively. Additionally, simulation studies are provided to show the performance of the time-varying factor model under various scenarios.

stat.ME↗