scholarly journals The CUSUM statistic of change point under NA sequences

2021 ◽  
Vol 36 (4) ◽  
pp. 512-520
Author(s):  
Jin Ling ◽  
Xiao-qin Li ◽  
Wen-zhi Yang ◽  
Jian-ling Jiao
Keyword(s):  
Change Point ◽  
Brownian Bridge ◽  
Moving Average ◽  
Real Data ◽  
Normal Sample ◽  
Finite Sample ◽  
Covariance Functions ◽  
Finite Sample Properties ◽  
Moving Average Processes ◽  
Na Sequences

AbstractIn this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes. Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

scholarly journals Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 394-417
Author(s):  
Aboubacrène Ag Ahmad ◽  
El Hadji Deme ◽  
Aliou Diop ◽  
Stéphane Girard
Keyword(s):  
Asymptotic Properties ◽  
Real Data ◽  
Scale Model ◽  
Extreme Value Index ◽  
Finite Sample ◽  
Scale Functions ◽  
Nonparametric Estimators ◽  
Heavy Tailed Distributions ◽  
Finite Sample Properties ◽  
Heavy Tailed

AbstractWe introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

scholarly journals ASYMPTOTIC INFERENCE FOR NONSTATIONARY FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING-AVERAGE MODELS

2001 ◽  
Vol 17 (4) ◽  
pp. 738-764 ◽  
Author(s):  
Shiqing Ling ◽  
W.K. Li
Keyword(s):  
Moving Average ◽  
Unit Roots ◽  
Asymptotic Distributions ◽  
Autoregressive Moving Average ◽  
Finite Sample ◽  
Asymptotic Inference ◽  
Moving Average Models ◽  
Special Cases ◽  
Finite Sample Properties ◽  
Memory Time

This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ∈ (− 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ∈ (− 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations.

scholarly journals STRUCTURAL CHANGE IN NONSTATIONARY AR(1) MODELS

2017 ◽  
Vol 34 (5) ◽  
pp. 985-1017 ◽  
Author(s):  
Tianxiao Pang ◽  
Terence Tai-Leung Chong ◽  
Danna Zhang ◽  
Yanling Liang
Keyword(s):  
Monte Carlo ◽  
Structural Change ◽  
Monte Carlo Simulations ◽  
Change Point ◽  
Indicator Function ◽  
The Other ◽  
Finite Sample ◽  
Mild Conditions ◽  
Finite Sample Properties ◽  
Image Position

This article revisits the asymptotic inference for nonstationary AR(1) models of Phillips and Magdalinos (2007a) by incorporating a structural change in the AR parameter at an unknown time k0. Consider the model ${y_t} = {\beta _1}{y_{t - 1}}I\{ t \le {k_0}\} + {\beta _2}{y_{t - 1}}I\{ t > {k_0}\} + {\varepsilon _t},t = 1,2, \ldots ,T$, where I{·} denotes the indicator function, one of ${\beta _1}$ and ${\beta _2}$ depends on the sample size T, and the other is equal to one. We examine four cases: Case (I): ${\beta _1} = {\beta _{1T}} = 1 - c/{k_T}$, ${\beta _2} = 1$; (II): ${\beta _1} = 1$, ${\beta _2} = {\beta _{2T}} = 1 - c/{k_T}$; (III): ${\beta _1} = 1$, ${\beta _2} = {\beta _{2T}} = 1 + c/{k_T}$; and case (IV): ${\beta _1} = {\beta _{1T}} = 1 + c/{k_T}$, ${\beta _2} = 1$, where c is a fixed positive constant, and kT is a sequence of positive constants increasing to ∞ such that kT = o(T). We derive the limiting distributions of the t-ratios of ${\beta _1}$ and ${\beta _2}$ and the least squares estimator of the change point for the cases above under some mild conditions. Monte Carlo simulations are conducted to examine the finite-sample properties of the estimators. Our theoretical findings are supported by the Monte Carlo simulations.

scholarly journals Two-sample Tests for Functional Data Using Characteristic Functions

2021 ◽  
Vol 50 (4) ◽  
pp. 53-64
Author(s):  
Mirosław Krzyśko ◽  
Łukasz Smaga
Keyword(s):  
Functional Data ◽  
Real Data ◽  
Characteristic Functions ◽  
Weight Functions ◽  
Test Statistics ◽  
Finite Sample ◽  
Testing Procedures ◽  
Two Sample Problem ◽  
Finite Sample Properties ◽  
Multivariate Functional Data

In this paper, we consider the two-sample problem for univariate and multivariate functional data. To solve this problem, we use tool of characteristic function and a basis function representation of functional data. We construct test statistics for conformity of distributions based on a weighted distance between characteristic functions of random vectors obtained in basis representation. Different weight functions result in different test statistics, whose distributions are approximated by permutation method. Testing procedures are implemented in the R program and the code is available. Simulation study shows good finite sample properties of proposed methods, while real data example illustrates the application of them.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

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