Here, we address the problem of trend estimation for functional time series. Existing contributions either deal with detecting a functional trend or assuming a simple model. They consider neither the estimation of a general functional trend nor the analysis of functional time series with a functional trend component. Similarly to univariate time series, we propose an alternative methodology to analyze functional time series, taking into account a functional trend component. We propose to estimate the functional trend by using a tensor product surface that is easy to implement, to interpret, and allows to control the smoothness properties of the estimator. Through a Monte Carlo study, we simulate different scenarios of functional processes to show that our estimator accurately identifies the functional trend component. We also show that the dependency structure of the estimated stationary time series component is not significantly affected by the error approximation of the functional trend component. We apply our methodology to annual mortality rates in France.
We propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the $L^2$-distance between the spectral density operator of a non-stationary process and its best ($L^2$-)approximation by a spectral density operator corresponding to a stationary process. This distance can easily be estimated by sums of Hilbert-Schmidt inner products of periodogram operators (evaluated at different frequencies), and asymptotic normality of an appropriately standardized version of the estimator can be established for the corresponding estimate under the null …
In this paper, the motility model for the developed country, which United State possesses the largest economy in the world and thus serves as an ideal representation, is investigated. Early surveillance of the causes of death is critical which can allow the preparation of preventive steps against critical disease such as dengue fever. Studies reported that some search queries, especially those diseases related terms on Google Trends are essential. To this end, we include either main cause of death or the extended or the more general terminologies from Google Trends to decode the mortality rela…
In the study of life tables the random variable of interest is usually assumed discrete since mortality rates are studied for integer ages. In dynamic life tables a time domain is included to account for the evolution effect of the hazard rates in time. In this article we follow a survival analysis approach and use a nonparametric description of the hazard rates. We construct a discrete time stochastic processes that reflects dependence across age as well as in time. This process is used as a bayesian nonparametric prior distribution for the hazard rates for the study of evolutionary life tabl…
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly smoothing raw rates across dimensions, such as calendar year and age. The GP model quantifies uncertainty associated with smoothed historical experience and generates full stochastic trajectories for out-of-sample forecasts. Our framework is well suited for updating projections when newly available data arrives, and for dealing with "edge" issues where credibili…
Nonparametric Efficient Estimation of Dynamic Treatment Regimes with Competing Risks
University of Minnesota（明尼苏达大学）；Edward Hines Jr. VA Hospital（爱德华·海恩斯少将退伍军人医院）；Augusta University（奥古斯塔大学）；Veterans Affairs Health Care System（退伍军人保健系统）；HealthPartners Institute（健康伙伴研究所）
In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA is to assume that data are continuous functions and that each continuous function is considered as a single observation. Thus, FDA deals with large-scale and complex data. However, visualization and exploratory data analysis, which is very important in practice, can be challenging due to the complexity of the continuous functions. Here we propose some nonpara…
Spatiotemporal simulation of minimum and maximum temperature is a fundamental requirement for climate impact studies and hydrological or agricultural models. Particularly over regions with variable orography, these simulations are difficult to produce due to terrain driven nonstationarity. We develop a bivariate stochastic model for the spatiotemporal field of minimum and maximum temperature. The proposed framework splits the bivariate field into two components of "local climate" and "weather." The local climate component is a linear model with spatially varying process coefficients capturing …
Non-ignorable dropout is common in studies with long follow-up time, and it can bias study results unless handled carefully. A double-sampling design allocates additional resources to pursue a subsample of the dropouts and find out their outcomes, which can address potential biases due to non-ignorable dropout. It is desirable to construct semiparametric estimators for the double-sampling design because of their robustness properties. However, obtaining such semiparametric estimators remains a challenge due to the requirement of the analytic form of the efficient influence function (EIF), the …
Mechanistic models fit to streaming surveillance data are critical to understanding the transmission dynamics of an outbreak as it unfolds in real-time. However, transmission model parameter estimation can be imprecise, and sometimes even impossible, because surveillance data are noisy and not informative about all aspects of the mechanistic model. To partially overcome this obstacle, Bayesian models have been proposed to integrate multiple surveillance data streams. We devised a modeling framework for integrating SARS-CoV-2 diagnostics test and mortality time series data, as well as seropreva…
Rank-Based Estimation of U-Shaped Biomarker Risk Curves and Critical Points for Time-to-Event Outcomes
Emory University Rollins School of Public Health（埃默里大学罗林斯公共卫生学院）；Department of Biostatistics Johns Hopkins Bloomberg School of Public Health（约翰霍普金斯大学彭博公共卫生学院生物统计系）；Eli Lilly and Company（礼来公司）；Department of Neurology Johns Hopkins School of Medicine（约翰霍普金斯大学医学院神经病学系）
