arXiv subjects

Yiping Guo

Publications and source records attributed to Yiping Guo.

6 recordsLinked to original sources

arXiv2023

Fast Estimation of the Renshaw-Haberman Model and Its Variants

In mortality modelling, cohort effects are often taken into consideration as they add insights about variations in mortality across different generations. Statistically speaking, models such as the Renshaw-Haberman model may provide a better fit to historical data compared to their counterparts that incorporate no cohort effects. However, when such models are estimated using an iterative maximum likelihood method in which parameters are updated one at a time, convergence is typically slow and may not even be reached within a reasonably established maximum number of iterations. Among others, the slow convergence problem hinders the study of parameter uncertainty through bootstrapping methods. In this paper, we propose an intuitive estimation method that minimizes the sum of squared errors between actual and fitted log central death rates. The complications arising from the incorporation of cohort effects are overcome by formulating part of the optimization as a principal component analysis with missing values. Using mortality data from various populations, we demonstrate that our proposed method produces satisfactory estimation results and is significantly more efficient compared to the traditional likelihood-based approach.

stat.ME↗

arXiv2023

Kriging Methods for Modelling Spatial Basis Risk in Weather Index Insurances: A Technical Note

The use of weather index insurances is subject to spatial basis risk, which arises from the fact that the location of the user's risk exposure is not the same as the location of any of the weather stations where an index can be measured. To gauge the effectiveness of weather index insurances, spatial interpolation techniques such as kriging can be adopted to estimate the relevant weather index from observations taken at nearby locations. In this paper, we study the performance of various statistical methods, ranging from simple nearest neighbor to more advanced trans-Gaussian kriging, in spatial interpolations of daily precipitations with data obtained from the US National Oceanic and Atmospheric Administration. We also investigate how spatial interpolations should be implemented in practice when the insurance is linked to popular weather indexes including annual consecutive dry days ($CDD$) and maximum five-day precipitation in one month ($MFP$). It is found that although spatially interpolating the raw weather variables on a daily basis is more sophisticated and computationally demanding, it does not necessarily yield superior results compared to direct interpolations of $CDD$/$MFP$ on a yearly/monthly basis. This intriguing outcome can be explained by the statistical properties of the weather indexes and the underlying weather variables.

stat.AP↗

arXiv2023

Robust Parameter Estimation for the Lee-Carter Family: A Probabilistic Principal Component Approach

The well-known Lee-Carter model uses a bilinear form $\log(m_{x,t})=a_x+b_xk_t$ to represent the log mortality rate and has been widely researched and developed over the past thirty years. However, there has been little attention being paid to the robustness of the parameters against outliers, especially when estimating $b_x$. In response, we propose a robust estimation method for a wide family of Lee-Carter-type models, treating the problem as a Probabilistic Principal Component Analysis (PPCA) with multivariate $t$-distributions. An efficient Expectation-Maximization (EM) algorithm is also derived for implementation. The benefits of the method are threefold: 1) it produces more robust estimates of both $b_x$ and $k_t$, 2) it can be naturally extended to a large family of Lee-Carter type models, including those for modelling multiple populations, and 3) it can be integrated with other existing time series models for $k_t$. Using numerical studies based on United States mortality data from the Human Mortality Database, we show the proposed model performs more robust compared to conventional methods in the presence of outliers.

stat.ME↗

arXiv2022

On Robust Probabilistic Principal Component Analysis using Multivariate $t$-Distributions

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to change the underlying Gaussian distributions to multivariate $t$-distributions. Based on the representation of $t$-distribution as a scale mixture of Gaussian distributions, a hierarchical model is used for implementation. However, in the existing literature, the hierarchical model implemented does not yield the equivalent interpretation. In this paper, we present two sets of equivalent relationships between the high-level multivariate $t$-PPCA framework and the hierarchical model used for implementation. In doing so, we clarify a current misrepresentation in the literature, by specifying the correct correspondence. In addition, we discuss the performance of different multivariate $t$ robust PPCA methods both in theory and simulation studies, and propose a novel Monte Carlo expectation-maximization (MCEM) algorithm to implement one general type of such models.

stat.ME↗

arXiv2020

Conditional Density Estimation via Weighted Logistic Regressions

Compared to the conditional mean as a simple point estimator, the conditional density function is more informative to describe the distributions with multi-modality, asymmetry or heteroskedasticity. In this paper, we propose a novel parametric conditional density estimation method by showing the connection between the general density and the likelihood function of inhomogeneous Poisson process models. The maximum likelihood estimates can be obtained via weighted logistic regressions, and the computation can be significantly relaxed by combining a block-wise alternating maximization scheme and local case-control sampling. We also provide simulation studies for illustration.

stat.ME↗

arXiv2003

Make search become the internal function of Internet

Domain Resource Integrated System (DRIS) is introduced in this paper. DRIS is a distributed information retrieval system, which will solve problems like poor coverage, long update interval in current web search system. The most distinct character of DRIS is that it's a public opening system, and acts as an internal component of Internet, but not the production of a company. The implementation of DRIS is also represented.

cs.IR↗