Mathematics

Research

14 pages, 3324 KiB

Open AccessArticle

Forecasting Canadian Age-Specific Mortality Rates: Application of Functional Time Series Analysis

by Azizur Rahman and Depeng Jiang

Mathematics 2023, 11(18), 3808; https://doi.org/10.3390/math11183808 - 5 Sep 2023

Viewed by 1087

In the insurance and pension industries, as well as in designing social security systems, forecasted mortality rates are of major interest. The current research provides statistical methods based on functional time series analysis to improve mortality rate prediction for the Canadian population. The [...] Read more.

In the insurance and pension industries, as well as in designing social security systems, forecasted mortality rates are of major interest. The current research provides statistical methods based on functional time series analysis to improve mortality rate prediction for the Canadian population. The proposed functional time series-based model was applied to the three-mortality series: total, male and female age-specific Canadian mortality rate over the year 1991 to 2019. Descriptive measures were used to estimate the overall temporal patterns and the functional principal component regression model (fPCA) was used to predict the next ten years mortality rate for each series. Functional autoregressive model (fAR (1)) was used to measure the impact of one year age differences on mortality series. For total series, the mortality rates for children have dropped over the whole data period, while the difference between young adults and those over 40 has only been falling since about 2003 and has leveled off in the last decade of the data. A moderate to strong impact of age differences on Canadian age-specific mortality series was observed over the years. Wider application of fPCA to provide more accurate estimates in public health, demography, and age-related policy studies should be considered. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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24 pages, 12683 KiB

Open AccessArticle

Spatial Autocorrelation of Global Stock Exchanges Using Functional Areal Spatial Principal Component Analysis

by Tzung Hsuen Khoo, Dharini Pathmanathan and Sophie Dabo-Niang

Mathematics 2023, 11(3), 674; https://doi.org/10.3390/math11030674 - 28 Jan 2023

Cited by 1 | Viewed by 1656

Abstract

This work focuses on functional data presenting spatial dependence. The spatial autocorrelation of stock exchange returns for 71 stock exchanges from 69 countries was investigated using the functional Moran’s I statistic, classical principal component analysis (PCA) and functional areal spatial principal component analysis [...] Read more.

This work focuses on functional data presenting spatial dependence. The spatial autocorrelation of stock exchange returns for 71 stock exchanges from 69 countries was investigated using the functional Moran’s I statistic, classical principal component analysis (PCA) and functional areal spatial principal component analysis (FASPCA). This work focuses on the period where the 2015–2016 global market sell-off occurred and proved the existence of spatial autocorrelation among the stock exchanges studied. The stock exchange return data were converted into functional data before performing the classical PCA and FASPCA. Results from the Monte Carlo test of the functional Moran’s I statistics show that the 2015–2016 global market sell-off had a great impact on the spatial autocorrelation of stock exchanges. Principal components from FASPCA show positive spatial autocorrelation in the stock exchanges. Regional clusters were formed before, after and during the 2015–2016 global market sell-off period. This work explored the existence of positive spatial autocorrelation in global stock exchanges and showed that FASPCA is a useful tool in exploring spatial dependency in complex spatial data. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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17 pages, 2652 KiB

Open AccessArticle

Estimation of Coefficient of Variation Using Calibrated Estimators in Double Stratified Random Sampling

by Usman Shahzad, Ishfaq Ahmad, Amelia V. García-Luengo, Tolga Zaman, Nadia H. Al-Noor and Anoop Kumar

Mathematics 2023, 11(1), 252; https://doi.org/10.3390/math11010252 - 3 Jan 2023

Cited by 10 | Viewed by 2138

Abstract

One of the most useful indicators of relative dispersion is the coefficient of variation. The characteristics of the coefficient of variation have contributed to its widespread use in most scientific and academic disciplines, with real life applications. The traditional estimators of the coefficient [...] Read more.

One of the most useful indicators of relative dispersion is the coefficient of variation. The characteristics of the coefficient of variation have contributed to its widespread use in most scientific and academic disciplines, with real life applications. The traditional estimators of the coefficient of variation are based on conventional moments; therefore, these are highly affected by the presence of extreme values. In this article, we develop some novel calibration-based coefficient of variation estimators for the study variable under double stratified random sampling (DSRS) using the robust features of linear (L and TL) moments, which offer appropriate coefficient of variation estimates. To evaluate the usefulness of the proposed estimators, a simulation study is performed by using three populations out of which one is based on the COVID-19 pandemic data set and the other two are based on apple fruit data sets. The relative efficiency of the proposed estimators with respect to the existing estimators has been calculated. The superiority of the suggested estimators over the existing estimators are clearly validated by using the real data sets. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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23 pages, 884 KiB

Open AccessArticle

Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data

by Larbi Ait-Hennani, Zoulikha Kaid, Ali Laksaci and Mustapha Rachdi

Mathematics 2022, 10(23), 4508; https://doi.org/10.3390/math10234508 - 29 Nov 2022

Cited by 1 | Viewed by 1078

Abstract

In this paper, we study the nonparametric estimation of the expected shortfall regression when the exogenous observation is functional. The constructed estimator is obtained by combining the double kernels estimator of both conditional value at risk and conditional density function. The asymptotic proprieties [...] Read more.

In this paper, we study the nonparametric estimation of the expected shortfall regression when the exogenous observation is functional. The constructed estimator is obtained by combining the double kernels estimator of both conditional value at risk and conditional density function. The asymptotic proprieties of this estimator are established under weak dependency condition. Precisely, we assume that the observations are generated from quasi-associated functional time series and we prove the almost complete convergence of the constructed estimator. This asymptotic result is obtained under a standard condition of functional time series analysis. The finite sample performance of this estimator is evaluated using artificial data. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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37 pages, 491 KiB

Open AccessArticle

Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes

by Sultana Didi and Salim Bouzebda

Mathematics 2022, 10(22), 4356; https://doi.org/10.3390/math10224356 - 19 Nov 2022

Cited by 8 | Viewed by 1086

Abstract

In this study, we look at the wavelet basis for the nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We employ a martingale approach to [...] Read more.

In this study, we look at the wavelet basis for the nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We employ a martingale approach to obtain the asymptotic properties of these wavelet estimators. These findings are established under rather broad assumptions. All we assume about the data is that they are ergodic, but beyond that, we make no assumptions. In this paper, the mean integrated squared error findings in the independence or mixing setting were generalized to the ergodic setting. The theoretical results presented in this study are (or will be) valuable resources for various cutting-edge functional data analysis applications. Applications include conditional distribution, conditional quantile, entropy, and curve discrimination. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

16 pages, 3588 KiB

Open AccessArticle

Forecasting Day-Ahead Traffic Flow Using Functional Time Series Approach

by Ismail Shah, Izhar Muhammad, Sajid Ali, Saira Ahmed, Mohammed M. A. Almazah and A. Y. Al-Rezami

Mathematics 2022, 10(22), 4279; https://doi.org/10.3390/math10224279 - 16 Nov 2022

Cited by 20 | Viewed by 2434

Abstract

Nowadays, short-term traffic flow forecasting has gained increasing attention from researchers due to traffic congestion in many large and medium-sized cities that pose a serious threat to sustainable urban development. To this end, this research examines the forecasting performance of functional time series [...] Read more.

Nowadays, short-term traffic flow forecasting has gained increasing attention from researchers due to traffic congestion in many large and medium-sized cities that pose a serious threat to sustainable urban development. To this end, this research examines the forecasting performance of functional time series modeling to forecast traffic flow in the ultra-short term. An appealing feature of the functional approach is that unlike other methods, it provides information over the whole day, and thus, forecasts can be obtained for any time within a day. Within this approach, a Functional AutoRegressive (FAR) model is used to forecast the next-day traffic flow. For empirical analysis, the traffic flow data of Dublin airport link road, Ireland, collected at a fifteen-minute interval from 1 January 2016 to 30 April 2017, are used. The first twelve months are used for model estimation, while the remaining four months are for the one-day-ahead out-of-sample forecast. For comparison purposes, a widely used model, namely AutoRegressive Integrated Moving Average (ARIMA), is also used to obtain the forecasts. Finally, the models’ performances are compared based on different accuracy statistics. The study results suggested that the functional time series model outperforms the traditional time series models. As the proposed method can produce traffic flow forecasts for the entire next day with satisfactory results, it can be used in decision making by transportation policymakers and city planners. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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19 pages, 4995 KiB

Open AccessArticle

Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

by Heba F. Nagy, Amer Ibrahim Al-Omari, Amal S. Hassan and Ghadah A. Alomani

Mathematics 2022, 10(21), 4102; https://doi.org/10.3390/math10214102 - 3 Nov 2022

Cited by 11 | Viewed by 1299

Abstract

The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of [...] Read more.

The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution parameters, which is extensively applied in life testing and reliability studies. Some estimation techniques are regarded, including the maximum likelihood, the maximum product of spacing’s, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling. We demonstrate a simulation investigation to assess the performance of the suggested RSS-based estimators via accuracy measures relative to simple random sampling. On the basis of actual data regarding the waiting times between 65 consecutive eruptions of Kiama Blowhole, additional conclusions have been drawn. The outcomes of simulation and real data application demonstrated that RSS-based estimators outperformed their simple random sampling counterparts significantly based on the same number of measured units. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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16 pages, 326 KiB

Open AccessArticle

Two-Sample Hypothesis Test for Functional Data

by Jing Zhao, Sanying Feng and Yuping Hu

Mathematics 2022, 10(21), 4060; https://doi.org/10.3390/math10214060 - 1 Nov 2022

Viewed by 1533

Abstract

In this paper, we develop and study a novel testing procedure that has more a powerful ability to detect mean difference for functional data. In general, it includes two stages: first, splitting the sample into two parts and selecting principle components adaptively based [...] Read more.

In this paper, we develop and study a novel testing procedure that has more a powerful ability to detect mean difference for functional data. In general, it includes two stages: first, splitting the sample into two parts and selecting principle components adaptively based on the first half-sample; then, constructing a test statistic based on another half-sample. An extensive simulation study is presented, which shows that the proposed test works very well in comparison with several other methods in a variety of alternative settings. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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17 pages, 359 KiB

Open AccessArticle

Functional Ergodic Time Series Analysis Using Expectile Regression

by Fatimah Alshahrani, Ibrahim M. Almanjahie, Zouaoui Chikr Elmezouar, Zoulikha Kaid, Ali Laksaci and Mustapha Rachdi

Mathematics 2022, 10(20), 3919; https://doi.org/10.3390/math10203919 - 21 Oct 2022

Cited by 4 | Viewed by 1409

Abstract

In this article, we study the problem of the recursive estimator of the expectile regression of a scalar variable Y given a random variable X that belongs in functional space. We construct a new estimator and study the asymptotic properties over a general [...] Read more.

In this article, we study the problem of the recursive estimator of the expectile regression of a scalar variable Y given a random variable X that belongs in functional space. We construct a new estimator and study the asymptotic properties over a general functional time structure. Precisely, the strong consistency of this estimator is established, considering that the sampled observations are taken from an ergodic functional process. Next, a simulation experiment is conducted to highlight the great impact of the constructed estimator as well as the ergodic functional time series data. Finally, a real data analysis is used to demonstrate the superiority of the constructed estimator. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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33 pages, 431 KiB

Open AccessArticle

Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

by Sultana DIDI, Ahoud AL HARBY and Salim BOUZEBDA

Mathematics 2022, 10(19), 3433; https://doi.org/10.3390/math10193433 - 21 Sep 2022

Cited by 8 | Viewed by 1117

Abstract

The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of [...] Read more.

The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of wavelet density and regression estimators, the Martingale method is used. These results are obtained under some mild conditions on the model; aside from ergodicity, no other assumptions are imposed on the data. This paper extends the scope of some previous results for wavelet density and regression estimators by relaxing the independence or the mixing condition to the ergodicity. Potential applications include the conditional distribution, curve discrimination, and time series prediction from a continuous set of past values. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

32 pages, 1263 KiB

Open AccessArticle

On Some Improved Class of Estimators by Using Stratified Ranked Set Sampling

by Shashi Bhushan, Anoop Kumar, Usman Shahzad, Amer Ibrahim Al-Omari and Ibrahim Mufrah Almanjahie

Mathematics 2022, 10(18), 3283; https://doi.org/10.3390/math10183283 - 9 Sep 2022

Cited by 10 | Viewed by 1146

Abstract

In this manuscript, we propose the combined and separate difference and ratio type estimators of population mean using stratified ranked set sampling. Additionally, several well-known estimators are identified as the sub-class of the suggested estimators. The characteristics of the suggested estimators have been [...] Read more.

In this manuscript, we propose the combined and separate difference and ratio type estimators of population mean using stratified ranked set sampling. Additionally, several well-known estimators are identified as the sub-class of the suggested estimators. The characteristics of the suggested estimators have been analyzed and their effective performances are compared with the prominent estimators existing till date. Moreover, to prove the credibility of the theoretical findings, an extensive empirical study is administered over some real and hypothetically yielded symmetric and asymmetric populations. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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18 pages, 870 KiB

Open AccessArticle

Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design

by Amer Ibrahim Al-Omari, SidAhmed Benchiha and Ibrahim M. Almanjahie

Mathematics 2022, 10(17), 3170; https://doi.org/10.3390/math10173170 - 2 Sep 2022

Cited by 7 | Viewed by 1351

Abstract

An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set [...] Read more.

An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study. Full article

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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