A new approach for evaluating time-trends in extreme values accounting also for spatial dependence is proposed. Based on exceedances over a space-time threshold, estimators for a trend function and for extreme value parameters are given, leading to a homogenization procedure for then applying stationary extreme value processes. Extremal dependence over space is further evaluated through variogram analysis including anisotropy. We detect significant inhomogeneities and trends in the extremal behaviour of daily precipitation data over a time period of 84 years and from 68 observational weather stations in North-West Germany. We observe that the trend is not monotonous over time in general.
Asymptotic normality of the estimators under maximum domain of attraction conditions are proven.
Model averaging with mixed criteria for estimating high quantiles of extreme values: Application to heavy rainfall
Honam Research Division, Electronics and Telecommunications Research Institute（韩国电子与电信研究院湖南研究部）；Department of Statistics, Chonnam National University（全南大学统计系）
Modeling extremes of climate variables in the framework of climate change is a particularly difficult task, since it implies taking into account spatio-temporal nonstationarities. In this paper, we propose a new method for estimating extreme precipitation at the points where we have not observations using information from marginal distributions and dependence structure. To reach this goal we combine two statistical approaches of extreme values theory allowing on the one hand to control temporal and spatial non-stationarities via a tail trend function with a spatio-temporal structure in the mar…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled isotonic es- timators at an interior point are shown to converge to Chernoff's distribution under minimal conditions on the stationary errors. Since the isotonic estimators suffer from the spiking problem at the end point, two modifications are proposed. The estima- tion errors for both estimators of the boundary point are shown to have interesting limiting …
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the c…
Max-stable processes have been expanded to quantify extremal dependence in spatio-temporal data. Due to the interaction between space and time, spatio-temporal data are often complex to analyze. So, characterizing these dependencies is one of the crucial challenges in this field of statistics. This paper suggests a semiparametric inference methodology based on the spatio-temporal F-madogram for estimating the parameters of a space-time max-stable process using gridded data. The performance of the method is investigated through various simulation studies. Finally, we apply our inferential proce…
The evaluation of possible climate change consequence on extreme rainfall has significant implications for the design of engineering structure and socioeconomic resources development. While many studies have assessed the impact of climate change on design rainfall using global and regional climate model (RCM) predictions, to date, there has been no comprehensive comparison or evaluation of intensity-duration-frequency (IDF) statistics at regional scale, considering both stationary versus nonstationary models for the future climate. To understand how extreme precipitation may respond to future …
Severe thunderstorms can have devastating impacts. Concurrently high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are known to be conducive to severe weather, so high values of PROD=$\sqrt{\mathrm{CAPE}} \times$SRH have been used to indicate high risk of severe thunderstorms. We consider the extreme values of these three variables for a large area of the contiguous US over the period 1979-2015, and use extreme-value theory and a multiple testing procedure to show that there is a significant time trend in the extremes for PROD maxima in April, May and…
We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero, derive an asymptotic confidence interval for a single random effect at the parametric rate $\sqrt{n}$, and propose an empirical Bayes estimator for a part of the mean vector in ANOVA type models that performs asymptotically as well as the oracle Bayes estimator. We support our results with numerical simulations and provide comparisons with oracle estimators. …
Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and environmental science settings. The approach presented here relaxes the asymptotic assumption typical of the traditional extreme value (EV) theory, and accounts for the possible underlying variability in the distribution of event magnitudes and occurrences, which are described through a latent temporal process. Focusing on daily rainfall extremes, the structure o…
One of the commonly used approaches to modeling extremes is the peaks-over-threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high or low so that the exceedance has approximately a generalized Pareto distribution (GPD). This method requires the selection of a threshold that might affect the estimates. Here we propose an alternative method, the Log-Histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned his…
For a panel model considered by Abadie et al. (2010), the counterfactual outcomes constructed by Abadie et al., Hsiao et al. (2012), and Doudchenko and Imbens (2017) may all be confounded by uncontrolled heterogenous trends. Based on exact-matching on the trend predictors, I propose new methods of estimating the model-specific treatment effects, which are free from heterogenous trends. When applied to Abadie et al.'s (2010) model and data, the new estimators suggest considerably smaller effects of California's tobacco control program.
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are obtained via the method of inversion of certain discrepancy statistics arising in hypothesis testing problems. The advantage of this approach is that it avoids the estimation of nuisance parameters such as the derivative of the unknown function, which existing methods are forced to deal with. While the methodology is motivated by earlier work in the indepen…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural semiparametric way. The local M-estimators of the unknown functional-coefficient functions are proposed by using local linear approximation, and their asymptotic distributions are then established under weak spatial mixing conditions allowing the data processes to be either stationary or nonstationary with spatial trends. Application to a soil data set is demonstrated wi…
Accurate estimation of daily rainfall return levels associated with large return periods is needed for a number of hydrological planning purposes, including protective infrastructure, dams, and retention basins. This is especially relevant at small spatial scales. The ERA-5 reanalysis product provides seasonal daily precipitation over Europe on a 0.25 x 0.25 grid (about 27 x 27 km). This translates more than 20,000 land grid points and leads to models with a large number of parameters when estimating return levels. To bypass this abundance of parameters, we build on the regional frequency anal…
We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we provide a formula for computing the distribution of the turning point location and consequently to estimate a confidence interval for the location. We test this formula in simulated data series having a trend with asymmetric minimum, investigating the coverage rate as a function of a bandwidth parameter. The method is applied to estimate the confidence interval …
Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run parameter, $K$, that determines how exceedances are declustered. We extend a class of estimators of the reciprocal mean cluster size, known as the extremal index, establish consistency and asymptotic normality,…
We consider the problem of estimating a function from $n$ noisy samples whose discrete Total Variation (TV) is bounded by $C_n$. We reveal a deep connection to the seemingly disparate problem of Strongly Adaptive online learning (Daniely et al, 2015) and provide an $O(n \log n)$ time algorithm that attains the near minimax optimal rate of $\tilde O (n^{1/3}C_n^{2/3})$ under squared error loss. The resulting algorithm runs online and optimally adapts to the unknown smoothness parameter $C_n$. This leads to a new and more versatile alternative to wavelets-based methods for (1) adaptively estimat…
The University of Tokyo（东京大学）；Center for Spatial Information Science, The University of Tokyo（东京大学空间信息科学中心）
Despite increasing accessibility to function data, effective methods for flexibly estimating underlying functional trend are still scarce. We thereby develop functional version of trend filtering for estimating trend of functional data indexed by time or on general graph by extending the conventional trend filtering, a powerful nonparametric trend estimation technique, for scalar data. We formulate the new trend filtering by introducing penalty terms based on $L_2$-norm of the differences of adjacent trend functions. We develop an efficient iteration algorithm for optimizing the objective func…
The Hodrick-Prescott filter represents one of the most popular method for trend-cycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick-Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal-noise matrix ratio to the parameters of the VARMA representation of the model. We then show that the parameters can be estimated using a recently introduced method, called "Moment Estimation Through Aggregation (META)". This method replaces the traditional multivariate li…
We discuss and extend methods for estimating Markovian-Regime-Switching (MRS) and trend models for wholesale electricity prices. We argue the existing methods of trend estimation used in the electricity price modelling literature either require an ambiguous definition of an extreme price, or lead to issues when implementing model selection [23]. The first main contribution of this paper is to design and infer a model which has a model-based definition of extreme prices and permits the use of model selection criteria. Due to the complexity of the MRS models inference is not straightforward. In …
Measles is a significant source of global disease burden and child mortality. Measles vaccination through routine immunization (RI) programs in high-burden settings remains a challenge due to poor health care infrastructure and access. Supplementary immunization activities (SIA) in the form of vaccination campaigns are therefore implemented to prevent measles outbreaks by reducing the size of the susceptible population. The SIA efficacy, defined as the fraction of susceptible population immunized by an SIA, is a critical metric for assessing campaign effectiveness. We propose a discrete-time h…
We address the problem of estimating smoothly varying baseline trends in time series data. This problem arises in a wide range of fields, including chemistry, macroeconomics, and medicine; however, our study is motivated by the analysis of data from low cost air quality sensors. Our methods extend the quantile trend filtering framework to enable the estimation of multiple quantile trends simultaneously while ensuring that the quantiles do not cross. To handle the computational challenge posed by very long time series, we propose a parallelizable alternating direction method of moments (ADMM) a…
Structural Nested Mean Models Under Parallel Trends Assumptions
CUNY School of Public Health（纽约市立大学公共卫生学院）；Ghent University（根特大学）；University of California Irvine（加州大学尔湾分校）；University of Pennsylvania（宾夕法尼亚大学）；Harvard TH Chan School of Public Health（哈佛大学陈曾熙公共卫生学院）
The present paper introduces a new model used to study and analyse the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) epidemic-reported-data from Spain. This is a Hidden Markov Model whose hidden layer is a regeneration process with Poisson immigration, Po-INAR(1), together with a mechanism that allows the estimation of the under-reporting in non-stationary count time series. A novelty of the model is that the expectation of the innovations in the unobserved process is a time-dependent function defined in such a way that information about the spread of an epidemic, as modelled thr…
