BIAS-CORRECTED INFERENCE FOR A MODIFIED LEE–CARTER MORTALITY MODEL

2019 ◽  
Vol 49 (2) ◽  
pp. 433-455 ◽  
Author(s):  
Qing Liu ◽  
Chen Ling ◽  
Deyuan Li ◽  
Liang Peng
Keyword(s):  
Unit Root ◽  
Normal Limit ◽  
Mortality Rates ◽  
American Statistical Association ◽  
Mortality Model ◽  
Mortality Index ◽  
The Us ◽  
Modeling And Forecasting ◽  
Near Unit Root ◽  
Carter Model

AbstractAs a benchmark mortality model in forecasting future mortality rates and hedging longevity risk, the widely employed Lee–Carter model (Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.) suffers from a restrictive constraint on the unobserved mortality index for ensuring model’s identification and a possible inconsistent inference. Recently, a modified Lee–Carter model (Liu, Q., Ling, C. and Peng, L. (2018) Statistical inference for Lee–Carter mortality model and corresponding forecasts. North American Actuarial Journal, to appear.) removes this constraint and a simple least squares estimation is consistent with a normal limit when the mortality index follows from a unit root or near unit root AR(1) model with a nonzero intercept. This paper proposes a bias-corrected estimator for this modified Lee–Carter model, which is consistent and has a normal limit regardless of the mortality index being a stationary or near unit root or unit root AR(1) process with a nonzero intercept. Applications to the US mortality rates and a simulation study are provided as well.

TESTING FOR A UNIT ROOT IN LEE–CARTER MORTALITY MODEL

2017 ◽  
Vol 47 (3) ◽  
pp. 715-735 ◽  
Author(s):  
Xuan Leng ◽  
Liang Peng
Keyword(s):  
Unit Root ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Inference Procedure ◽  
Mortality Model ◽  
Mortality Index ◽  
R Packages ◽  
Mortality Projections ◽  
The U.S ◽  
Carter Model

AbstractMotivated by a recent discovery that the two-step inference for the Lee–Carter mortality model may be inconsistent when the mortality index does not follow from a nearly integrated AR(1) process, we propose a test for a unit root in a Lee–Carter model with an AR(p) process for the mortality index. Although testing for a unit root has been studied extensively in econometrics, the method and asymptotic results developed in this paper are unconventional. Unlike a blind application of existing R packages for implementing the two-step inference procedure in Lee and Carter (1992) to the U.S. mortality rate data, the proposed test rejects the null hypothesis that the mortality index follows from a unit root AR(1) process, which calls for serious attention on using the future mortality projections based on the Lee–Carter model in policy making, pricing annuities and hedging longevity risk. A simulation study is conducted to examine the finite sample behavior of the proposed test too.

scholarly journals NONPARAMETRIC TRANSFORMATION REGRESSION WITH NONSTATIONARY DATA

2014 ◽  
Vol 32 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Oliver Linton ◽  
Qiying Wang
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Kernel Regression ◽  
American Statistical Association ◽  
Correlation Structure ◽  
Regression Estimator ◽  
Statistical Association ◽  
Nonstationary Data ◽  
Nonparametric Transformation ◽  
Near Unit Root

We examine a kernel regression estimator for time series that takes account of the error correlation structure as proposed by Xiao et al. (2003, Journal of the American Statistical Association 98, 980–992). We show that this method continues to improve estimation in the case where the regressor is a unit root or a near unit root process.

ANALYTICAL EPIDEMIOLOGY OF GASTRIC CANCER IN THE REPUBLIC OF CRIMEA AND ITS CONFORMITY WITH ALL-RUSSIAN TRENDS

2018 ◽  
Vol 64 (5) ◽  
pp. 592-601
Author(s):  
Viktor Oleksenko ◽  
Kazim Aliev ◽  
I. Akinshevich ◽  
Ye. Chirva
Keyword(s):  
Gastric Cancer ◽  
Epidemiological Data ◽  
Mortality Rates ◽  
Similar Data ◽  
Results Of Treatment ◽  
Mortality Index ◽  
World Standard ◽  
The Russian Federation ◽  
The Republic ◽  
National Trends

Gastric cancer (GC) is one of the most common malignant tumor, both world-wide and in the Russian Federation (RF), possessing one of the highest mortality rates. The aim of current research was to analyze the main epidemiological data, the rates reflecting the diagnostics and results of treatment of GC patients in the Republic of Crimea (RC) and to compare with national trends. Using the extensive, intensive, standardized rates, estimated by world standard method, structural analysis of the epidemiology of GC in RC for the period from 2007 to 2016 was carried out. The obtained results made it possible to compare these data with the main GC rates in RF. Results of the study. The incidence of GC in RC decreased during 10 years, for men - 16,42 (4th place), for women - 6,68 (9th place) per 100 000 of the population. By 2021 a further decline in morbidity in men is expected to be 30,27% and a possible increase in the female incidence rate - by 17,54%. The average age of GC patients in RC was 66,5 years. Index accuracy was 0,75, which testified to satisfactory conditions of specialized treatment for this tumor. Mortality from GC at the 1st year of life in RC was higher than in RF - 56,0%, which was due to low active diagnostics - 3,6% and accordingly a high proportion of GC patients of IV stage - 43,3%. Ratio index in RC for 10 years was higher than in RF and increased from 3,5 to 4,4; prevalence rate of GC in RC was lower - 84,1 per 100 000 of the population in comparison with RF, GC mortality index - 15,3 per 100 000 of the population that was lower than in RF. The proportion of patients who have been observed for 5 years or more in RC was 57,3% that was more than in RF. Conclusions. The rates reflecting early diagnostics of GC in RC are worse than all-Russian ones, which makes it necessary to develop medical examination program for the population of RC for this malignancy. The growth of ratio index, the lower mortality rates and the greater proportion of people who have been observed for 5 years or more indicates the best results of treatment of patients with GC in RC compared with similar data in RF.

Modeling and Forecasting Mortality Rates

2011 ◽  
Author(s):  
Daniel Mitchell ◽  
Patrick L. Brockett ◽  
Rafael Mendoza-Arriaga ◽  
Kumar Muthuraman
Keyword(s):  
Mortality Rates ◽  
Modeling And Forecasting

scholarly journals Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model

2021 ◽  
Vol 18 (4) ◽  
pp. 2204
Author(s):  
Ana Debón ◽  
Steven Haberman ◽  
Francisco Montes ◽  
Edoardo Otranto
Keyword(s):  
Historical Data ◽  
Mortality Rates ◽  
Parametric Model ◽  
Mortality Data ◽  
Block Bootstrap ◽  
Functional Anova ◽  
Model Block ◽  
The Usa ◽  
Data Constraints ◽  
Carter Model

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model’s fit to historical data and the model’s forecasting of the future. This paper’s main objective is to evaluate if differences between models are reflected in different mortality indicators’ forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model’s predictions must be checked in terms of their probabilities and the mortality indicators of interest.

scholarly journals COVID-19 in Latin America: a first glance to the mortality

2020 ◽  
pp. 1-3 ◽  
Author(s):  
Nubia Muñoz
Keyword(s):  
Latin America ◽  
Latin American ◽  
Mortality Rates ◽  
European Countries ◽  
Death Rates ◽  
Death Toll ◽  
The United Kingdom ◽  
Health Authorities ◽  
The Us ◽  
Latin American Countries

It is too early to know which will be the final death toll from the Covid-19 or SARS-CoV-2 virus epidemy in Latin America since the epidemy is still active and we will not know when it will end. The curve for new infections and deaths has not reached yet a peak (Figure 1). In addition, we know little about the epidemiology of this new virus. The daily litany of the number of people infected with the number of admissions to hospitals and intensive care units and the number of deaths guides health authorities to plan health services and politicians to gauge the degree of confinement necessary to control the transmission of the virus, but it says little about the magnitude of the problem if we do not relate it to the population at risk. At the end of the pandemic, we will be able to estimate age-standardized death rates for the different countries, but until then the crude death rates will provide a first glance or snapshot of the death toll and impact of the pandemic from March to May 2020. These rates are well below those estimated in other countries in Europe and North America: Belgium (82.6), Spain (58.0), the United Kingdom (57.5), Italy (55.0), France (42.9), Sweden (41.4), and the US (30.7). (Johns Hopkins CSSE, May 30, 2020). However, in the European countries and the US the number of deaths has reached a peak, while this is not the case in Latin American countries. (Figure 1). It should be taken into account that the above rates are crude and therefore, some of the differences could be due to the fact that European countries have a larger proportion of the population over 70 years of age in whom higher mortality rates have been reported.

A comparison of the Lee–Carter model and AR–ARCH model for forecasting mortality rates

2012 ◽  
Vol 50 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Rosella Giacometti ◽  
Marida Bertocchi ◽  
Svetlozar T. Rachev ◽  
Frank J. Fabozzi
Keyword(s):  
Mortality Rates ◽  
Arch Model ◽  
Carter Model

scholarly journals Applying Heath-Jarrow-Morton Model to Forecasting the US Treasury Daily Yield Curve Rates

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Valerii Maltsev ◽  
Michael Pokojovy
Keyword(s):  
Predictive Power ◽  
Yield Curve ◽  
Real Data ◽  
Stochastic Evolution ◽  
Infinite Dimensions ◽  
No Arbitrage ◽  
Hjm Model ◽  
Concise Review ◽  
The Us ◽  
Modeling And Forecasting

The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the underlying correlation structure. Aimed at researchers and practitioners, the purpose of this article is to present a self-contained, but concise review of the abstract HJM framework founded upon the theory of interest and stochastic partial differential equations in infinite dimensions. To illustrate the predictive power of this theory, we apply it to modeling and forecasting the US Treasury daily yield curve rates. We fit a non-parametric model to real data available from the US Department of the Treasury and illustrate its statistical performance in forecasting future yield curve rates.

scholarly journals Racism as a Leading Cause of Death: Measuring Excess Deaths in the US

2021 ◽  
Author(s):  
Daisy Massey ◽  
Jeremy Faust ◽  
Karen Dorsey ◽  
Yuan Lu ◽  
Harlan Krumholz
Keyword(s):  
Black Women ◽  
Mortality Rate ◽  
Black Men ◽  
Cause Of Death ◽  
White Women ◽  
Black People ◽  
Mortality Rates ◽  
White People ◽  
The Us ◽  
Excess Deaths

Background: Excess death for Black people compared with White people is a measure of health equity. We sought to determine the excess deaths under the age of 65 (<65) for Black people in the United States (US) over the most recent 20-year period. We also compared the excess deaths for Black people with a cause of death that is traditionally reported. Methods: We used the Multiple Cause of Death 1999-2019 dataset from the Center of Disease Control (CDC) WONDER to report age-adjusted mortality rates among non-Hispanic Black (Black) and non-Hispanic White (White) people and to calculate annual age-adjusted <65 excess deaths for Black people from 1999-2019. We measured the difference in mortality rates between Black and White people and the 20-year and 5-year trends using linear regression. We compared age-adjusted <65 excess deaths for Black people to the primary causes of death among <65 Black people in the US. Results: From 1999 to 2019, the age-adjusted mortality rate for Black men was 1,186 per 100,000 and for White men was 921 per 100,000, for a difference of 265 per 100,000. The age-adjusted mortality rate for Black women was 802 per 100,000 and for White women was 664 per 100,000, for a difference of 138 per 100,000. While the gap for men and women is less than it was in 1999, it has been increasing among men since 2014. These differences have led to many Black people dying before age 65. In 1999, there were 22,945 age-adjusted excess deaths among Black women <65 and in 2019 there were 14,444, deaths that would not have occurred had their risks been the same as those of White women. Among Black men, 38,882 age-adjusted excess <65 deaths occurred in 1999 and 25,850 in 2019. When compared to the top 5 causes of deaths among <65 Black people, death related to disparities would be the highest mortality rate among both <65 Black men and women. Comment: In the US, over the recent 20-year period, disparities in mortality rates resulted in between 61,827 excess deaths in 1999 and 40,294 excess deaths in 2019 among <65 Black people. The race-based disparity in the US was the leading cause of death among <65 Black people. Societal commitment and investment in eliminating disparities should be on par with those focused on other leading causes of death such as heart disease and cancer.

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