A higher-order likelihood-based asymptotic method to obtain inference for the difference between two KS Sharpe ratios when gross returns of an investment are assumed to be lognormally distributed is proposed. Theoretically, our proposed method has distributional accuracy, whereas conventional methods for inference have distributional accuracy. Using an example, we show how discordant confidence interval results can be depending on the methodology used. We are able to demonstrate the accuracy of our proposed method through simulation studies.
{"title":"Inference for the Difference of Two Independent KS Sharpe Ratios under Lognormal Returns","authors":"J. Qi, M. Rekkas, A. Wong","doi":"10.1155/2020/6751574","DOIUrl":"https://doi.org/10.1155/2020/6751574","url":null,"abstract":"<jats:p>A higher-order likelihood-based asymptotic method to obtain inference for the difference between two KS Sharpe ratios when gross returns of an investment are assumed to be lognormally distributed is proposed. Theoretically, our proposed method has <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>O</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> distributional accuracy, whereas conventional methods for inference have <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>O</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> distributional accuracy. Using an example, we show how discordant confidence interval results can be depending on the methodology used. We are able to demonstrate the accuracy of our proposed method through simulation studies.</jats:p>","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/6751574","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45735295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Saddam Hussain, Mi Zichuan, S. Hussain, Anum Iftikhar, M. Asif, S. Akhtar, Sohaib Ahmad
In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.
{"title":"On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling","authors":"Saddam Hussain, Mi Zichuan, S. Hussain, Anum Iftikhar, M. Asif, S. Akhtar, Sohaib Ahmad","doi":"10.1155/2020/1693612","DOIUrl":"https://doi.org/10.1155/2020/1693612","url":null,"abstract":"In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/1693612","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41262746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.
{"title":"Comparative Analysis of Some Structural Equation Model Estimation Methods with Application to Coronary Heart Disease Risk","authors":"D. Adedia, A. Adebanji, S. Appiah","doi":"10.1155/2020/4181426","DOIUrl":"https://doi.org/10.1155/2020/4181426","url":null,"abstract":"This study compared a ridge maximum likelihood estimator to Yuan and Chan (2008) ridge maximum likelihood, maximum likelihood, unweighted least squares, generalized least squares, and asymptotic distribution-free estimators in fitting six models that show relationships in some noncommunicable diseases. Uncontrolled hypertension has been shown to be a leading cause of coronary heart disease, kidney dysfunction, and other negative health outcomes. It poses equal danger when asymptomatic and undetected. Research has also shown that it tends to coexist with diabetes mellitus (DM), with the presence of DM doubling the risk of hypertension. The study assessed the effect of obesity, type II diabetes, and hypertension on coronary risk and also the existence of converse relationship with structural equation modelling (SEM). The results showed that the two ridge estimators did better than other estimators. Nonconvergence occurred for most of the models for asymptotic distribution-free estimator and unweighted least squares estimator whilst generalized least squares estimator had one nonconvergence of results. Other estimators provided competing outputs, but unweighted least squares estimator reported unreliable parameter estimates such as large chi-square test statistic and root mean square error of approximation for Model 3. The maximum likelihood family of estimators did better than others like asymptotic distribution-free estimator in terms of overall model fit and parameter estimation. Also, the study found that increase in obesity could result in a significant increase in both hypertension and coronary risk. Diastolic blood pressure and diabetes have significant converse effects on each other. This implies those who are hypertensive can develop diabetes and vice versa.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4181426","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45747625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide a permutation invariant version of the strong law of large numbers for exchangeable sequences of random variables. The proof consists of a combination of the Komlós–Berkes theorem, the usual strong law of large numbers for exchangeable sequences, and de Finetti’s theorem.
{"title":"Permutation Invariant Strong Law of Large Numbers for Exchangeable Sequences","authors":"Stefan Tappe","doi":"10.1155/2021/3637837","DOIUrl":"https://doi.org/10.1155/2021/3637837","url":null,"abstract":"We provide a permutation invariant version of the strong law of large numbers for exchangeable sequences of random variables. The proof consists of a combination of the Komlós–Berkes theorem, the usual strong law of large numbers for exchangeable sequences, and de Finetti’s theorem.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44443745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Roshani W. Divisekara, Ruwan Dharshana Nawarathna, Lakshika S. Nawarathna
One of the easiest and fastest ways of building a healthy financial future is investing in the global market. However, the prices of the global market are highly volatile due to the impact of economic crises. Therefore, future prediction and comparison lead traders to make the low-risk decisions with price. The present study is based on time series modelling to forecast the daily close price values of financial instruments in the global market. The forecasting models were tested with two sample sizes, namely, 5-year close price values for correlation analysis and 3-year close price values for model building from 2013 January to 2018 January. The forecasting capabilities were compared for both ARIMA and GARCH class models, namely, TGARCH, APARCH, and EGARCH. The best-fitting model was selected based on the minimum value of the Akaike information criterion (AIC) and Bayesian information criteria (BIC). Finally, the comparison was carried out between ARIMA and GARCH class models using the measurement of forecast errors, based on the Root Mean Square Deviation (RMSE), Mean Absolute Error (MAE), and Mean absolute percentage error (MAPE). The GARCH model was the best-fitted model for Australian Dollar, Feeder cattle, and Coffee. The APARCH model provides the best out-of-sample performance for Corn and Crude Oil. EGARCH and TGARCH were the better-fitted models for Gold and Treasury bond, respectively. GARCH class models were selected as the better models for forecasting than the ARIMA model for daily close price values in global financial market instruments.
{"title":"Forecasting of Global Market Prices of Major Financial Instruments","authors":"Roshani W. Divisekara, Ruwan Dharshana Nawarathna, Lakshika S. Nawarathna","doi":"10.1155/2020/1258463","DOIUrl":"https://doi.org/10.1155/2020/1258463","url":null,"abstract":"One of the easiest and fastest ways of building a healthy financial future is investing in the global market. However, the prices of the global market are highly volatile due to the impact of economic crises. Therefore, future prediction and comparison lead traders to make the low-risk decisions with price. The present study is based on time series modelling to forecast the daily close price values of financial instruments in the global market. The forecasting models were tested with two sample sizes, namely, 5-year close price values for correlation analysis and 3-year close price values for model building from 2013 January to 2018 January. The forecasting capabilities were compared for both ARIMA and GARCH class models, namely, TGARCH, APARCH, and EGARCH. The best-fitting model was selected based on the minimum value of the Akaike information criterion (AIC) and Bayesian information criteria (BIC). Finally, the comparison was carried out between ARIMA and GARCH class models using the measurement of forecast errors, based on the Root Mean Square Deviation (RMSE), Mean Absolute Error (MAE), and Mean absolute percentage error (MAPE). The GARCH model was the best-fitted model for Australian Dollar, Feeder cattle, and Coffee. The APARCH model provides the best out-of-sample performance for Corn and Crude Oil. EGARCH and TGARCH were the better-fitted models for Gold and Treasury bond, respectively. GARCH class models were selected as the better models for forecasting than the ARIMA model for daily close price values in global financial market instruments.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/1258463","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45652924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.
{"title":"Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme","authors":"Kyeongjun Lee, J. Seo","doi":"10.1155/2020/3541946","DOIUrl":"https://doi.org/10.1155/2020/3541946","url":null,"abstract":"This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/3541946","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42309293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.
{"title":"Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling","authors":"Mohammed Obeidat, Amjad D. Al-Nasser, A. Al-Omari","doi":"10.1155/2020/7362657","DOIUrl":"https://doi.org/10.1155/2020/7362657","url":null,"abstract":"This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/7362657","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48203760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multivariate noises in the learning process are most of the time supposed to follow a standard multivariate normal distribution. This hypothesis does not often hold in many real-world situations. In this paper, we consider an approach based on multivariate skew-normal distribution. It allows for a multiple continuous variation from normality to nonnormality. We give an extension of the generalized least squares error function in a context of multivariate nonlinear regression to learn imprecise data. The simulation study and application case on real datasets conducted and based on multilayer perceptron neural networks (MLP) with bivariate continuous response and asymmetric revealed a significant gain in precision using the new quadratic error function for these types of data rather than using a classical generalized least squares error function having any covariance matrix.
{"title":"An Extension of the Quadratic Error Function for Learning Imprecise Data in Multivariate Nonlinear Regression","authors":"C. Hounmenou, K. Gneyou, R. G. Glèlè Kakaï","doi":"10.1155/2020/9187503","DOIUrl":"https://doi.org/10.1155/2020/9187503","url":null,"abstract":"Multivariate noises in the learning process are most of the time supposed to follow a standard multivariate normal distribution. This hypothesis does not often hold in many real-world situations. In this paper, we consider an approach based on multivariate skew-normal distribution. It allows for a multiple continuous variation from normality to nonnormality. We give an extension of the generalized least squares error function in a context of multivariate nonlinear regression to learn imprecise data. The simulation study and application case on real datasets conducted and based on multilayer perceptron neural networks (MLP) with bivariate continuous response and asymmetric revealed a significant gain in precision using the new quadratic error function for these types of data rather than using a classical generalized least squares error function having any covariance matrix.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/9187503","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41498335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a new definition of the number of observations near the th order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions . Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.
在本文中，提出了一个新的定义，接近于一阶统计量的观测次数。然后根据质量概率函数、这些新的计数随机变量的一阶矩以及函数序列的完备性，建立了Pareto和一些相关分布的一些表征结果。最后，基于帕累托分布的这些新特征，提出了新的拟合优度检验。通过蒙特卡洛模拟，将所提出的测试的功率值与著名测试的功率值相比较，如Kolmogorov“Smirnov”和Cramer von Mises测试。
{"title":"Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics","authors":"M. Akbari","doi":"10.1155/2020/4262574","DOIUrl":"https://doi.org/10.1155/2020/4262574","url":null,"abstract":"In this paper, a new definition of the number of observations near the th order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions . Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4262574","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41483646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on - record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of - record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.
本文研究了基于非记录值的极值指标的极大似然估计的存在性和相合性。根据Drees et al.(2004)和Zhou(2009)的方法，我们证明了在不受极值指标限制的情况下，就-记录值而言，似然方程最终存在强一致解，而上述研究并非如此。
{"title":"On the Maximum Likelihood Estimation of Extreme Value Index Based on k-Record Values","authors":"Abderrahim Louzaoui, Mohamed El Arrouchi","doi":"10.1155/2020/5497413","DOIUrl":"https://doi.org/10.1155/2020/5497413","url":null,"abstract":"In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on - record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of - record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/5497413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46497295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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