Pub Date : 2023-09-03DOI: 10.1080/02331888.2023.2253992
Swagata Nandi, D. Kundu
In this paper, we introduce a special multichannel model in the class of multichannel sinusoidal model. In multichannel sinusoidal model, the inherent frequencies from distinct channels are the same with different amplitudes. The underlying assumption here is that there is a fundamental frequency that is the same in each channel and the effective frequencies are harmonics of this fundamental frequency. We name this model as multichannel fundamental frequency with harmonics model. It is assumed that the errors in individual channel are independently and identically distributed whereas the signal from different channels are correlated. We propose generalized least squares estimators which become the maximum likelihood estimators also, when the error distribution of the different channels follows a multivariate Gaussian distribution. The proposed estimators are strongly consistent and asymptotically normally distributed. We have provided the implementation of the generalized least squares estimators in practice. Special attention has been taken when the number of channels is two and both have equal number of components. Simulation experiments have been carried out to observe the performances of the proposed estimators. Real data sets have been analysed using a two-channel fundamental frequency model.
{"title":"Estimating parameters in multichannel fundamental frequency with harmonics model","authors":"Swagata Nandi, D. Kundu","doi":"10.1080/02331888.2023.2253992","DOIUrl":"https://doi.org/10.1080/02331888.2023.2253992","url":null,"abstract":"In this paper, we introduce a special multichannel model in the class of multichannel sinusoidal model. In multichannel sinusoidal model, the inherent frequencies from distinct channels are the same with different amplitudes. The underlying assumption here is that there is a fundamental frequency that is the same in each channel and the effective frequencies are harmonics of this fundamental frequency. We name this model as multichannel fundamental frequency with harmonics model. It is assumed that the errors in individual channel are independently and identically distributed whereas the signal from different channels are correlated. We propose generalized least squares estimators which become the maximum likelihood estimators also, when the error distribution of the different channels follows a multivariate Gaussian distribution. The proposed estimators are strongly consistent and asymptotically normally distributed. We have provided the implementation of the generalized least squares estimators in practice. Special attention has been taken when the number of channels is two and both have equal number of components. Simulation experiments have been carried out to observe the performances of the proposed estimators. Real data sets have been analysed using a two-channel fundamental frequency model.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"14 1","pages":"1142 - 1164"},"PeriodicalIF":1.9,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80029696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-03DOI: 10.1080/02331888.2023.2260915
Shashi Bhushan, Anoop Kumar, Shivam Shukla
In survey sampling, several estimation procedures have been proffered by various prominent authors to compute the impact of measurement errors (ME) but the impact of correlated measurement errors (CME) has been computed only by Shalabh and Tsai [Ratio and product methods of estimation of population mean in the presence of correlated measurement errors. Commun Stat Simul Comput. 2016;46(7):5566–5593]. This study provides a novel approach to compute the impact of CME through some logarithmic-type estimators using simple random sampling (SRS). The properties of the proffered estimators have been studied and compared with the properties of the conventional estimators. A numerical study and a broad spectrum simulation study are accomplished over real and artificially generated populations to support the theoretical results.
{"title":"Impact assessment of correlated measurement errors using logarithmic-type estimators","authors":"Shashi Bhushan, Anoop Kumar, Shivam Shukla","doi":"10.1080/02331888.2023.2260915","DOIUrl":"https://doi.org/10.1080/02331888.2023.2260915","url":null,"abstract":"In survey sampling, several estimation procedures have been proffered by various prominent authors to compute the impact of measurement errors (ME) but the impact of correlated measurement errors (CME) has been computed only by Shalabh and Tsai [Ratio and product methods of estimation of population mean in the presence of correlated measurement errors. Commun Stat Simul Comput. 2016;46(7):5566–5593]. This study provides a novel approach to compute the impact of CME through some logarithmic-type estimators using simple random sampling (SRS). The properties of the proffered estimators have been studied and compared with the properties of the conventional estimators. A numerical study and a broad spectrum simulation study are accomplished over real and artificially generated populations to support the theoretical results.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134949282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-29DOI: 10.1080/02331888.2023.2248679
U. Amato, A. Antoniadis, I. De Feis, I. Gijbels
This paper concerns the study of a non-smooth logistic regression function. The focus is on a high-dimensional binary response case by penalizing the decomposition of the unknown logit regression function on a wavelet basis of functions evaluated on the sampling design. Sample sizes are arbitrary (not necessarily dyadic) and we consider general designs. We study separable wavelet estimators, exploiting sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, and using efficient iterative proximal gradient descent algorithms. We also discuss a level by level block wavelet penalization technique, leading to a type of regularization in multiple logistic regression with grouped predictors. Theoretical and numerical properties of the proposed estimators are investigated. A simulation study examines the empirical performance of the proposed procedures, and real data applications demonstrate their effectiveness.
{"title":"Penalized wavelet nonparametric univariate logistic regression for irregular spaced data","authors":"U. Amato, A. Antoniadis, I. De Feis, I. Gijbels","doi":"10.1080/02331888.2023.2248679","DOIUrl":"https://doi.org/10.1080/02331888.2023.2248679","url":null,"abstract":"This paper concerns the study of a non-smooth logistic regression function. The focus is on a high-dimensional binary response case by penalizing the decomposition of the unknown logit regression function on a wavelet basis of functions evaluated on the sampling design. Sample sizes are arbitrary (not necessarily dyadic) and we consider general designs. We study separable wavelet estimators, exploiting sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, and using efficient iterative proximal gradient descent algorithms. We also discuss a level by level block wavelet penalization technique, leading to a type of regularization in multiple logistic regression with grouped predictors. Theoretical and numerical properties of the proposed estimators are investigated. A simulation study examines the empirical performance of the proposed procedures, and real data applications demonstrate their effectiveness.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"3 1","pages":"1037 - 1060"},"PeriodicalIF":1.9,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82703068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-27DOI: 10.1080/02331888.2023.2249572
N. Balakrishnan, R. Mukerjee
In this paper, we discuss the joint estimation and prediction of unobserved order statistics based on a Type-II censored sample from a location-scale family. Using the concept of Loewner order, we simplify the derivations made earlier, and also strengthen in the process some of the existing results. We then study the efficiency of the methods and finally examine the determination of optimal number of order statistics to be observed as well as the performance of non-linear predictors.
{"title":"On optimal joint prediction of order statistics","authors":"N. Balakrishnan, R. Mukerjee","doi":"10.1080/02331888.2023.2249572","DOIUrl":"https://doi.org/10.1080/02331888.2023.2249572","url":null,"abstract":"In this paper, we discuss the joint estimation and prediction of unobserved order statistics based on a Type-II censored sample from a location-scale family. Using the concept of Loewner order, we simplify the derivations made earlier, and also strengthen in the process some of the existing results. We then study the efficiency of the methods and finally examine the determination of optimal number of order statistics to be observed as well as the performance of non-linear predictors.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"13 1","pages":"1239 - 1250"},"PeriodicalIF":1.9,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75575584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1080/02331888.2023.2242549
A. Melnikov, A. Pak
The paper is devoted to the problem of parameter estimation in a multivariate optional semimartingale regression model. The family of optional semimartingales is a rich class of stochastic processes that contains càdlàg semimartingales. In general, such processes do not admit càdlàg modifications, i.e. right-continuous with finite left-limits. The weighted least squares estimator is derived, and its strong consistency is proved under general conditions on regressors. Furthermore, sequential least squares estimates are systematically studied. It is shown that such estimates have a nice statistical property called fixed accuracy. Sequential estimation procedure developed in the paper works without restrictions on dimensions of unknown parameter and of observation process. The paper contains several examples of multivariate regressions to demonstrate our results and proposed techniques.
{"title":"Parameter estimation in optional semimartingale regression models","authors":"A. Melnikov, A. Pak","doi":"10.1080/02331888.2023.2242549","DOIUrl":"https://doi.org/10.1080/02331888.2023.2242549","url":null,"abstract":"The paper is devoted to the problem of parameter estimation in a multivariate optional semimartingale regression model. The family of optional semimartingales is a rich class of stochastic processes that contains càdlàg semimartingales. In general, such processes do not admit càdlàg modifications, i.e. right-continuous with finite left-limits. The weighted least squares estimator is derived, and its strong consistency is proved under general conditions on regressors. Furthermore, sequential least squares estimates are systematically studied. It is shown that such estimates have a nice statistical property called fixed accuracy. Sequential estimation procedure developed in the paper works without restrictions on dimensions of unknown parameter and of observation process. The paper contains several examples of multivariate regressions to demonstrate our results and proposed techniques.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"27 1","pages":"1165 - 1201"},"PeriodicalIF":1.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83477021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-31DOI: 10.1080/02331888.2023.2234061
S. Nkurunziza
{"title":"Corrigendum: a note on Liu-type shrinkage estimations in linear models (Statistics 56, 396–420)","authors":"S. Nkurunziza","doi":"10.1080/02331888.2023.2234061","DOIUrl":"https://doi.org/10.1080/02331888.2023.2234061","url":null,"abstract":"","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87358751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-24DOI: 10.1080/02331888.2023.2238236
Žikica Lukić, B. Milošević
The Lévy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the Lévy distribution. In this paper, two novel classes of goodness-of-fit tests for the Lévy distribution are proposed. Both tests are based on V-empirical Laplace transforms. New tests are scale free under the null hypothesis, which makes them suitable for testing the composite hypothesis. The finite sample and limiting properties of test statistics are obtained. In addition, a generalization of the recent Bhati–Kattumannil goodness-of-fit test to the Lévy distribution is considered. For assessing the quality of novel and competitor tests, the local Bahadur efficiencies are computed, and a wide power study is conducted. Both criteria clearly demonstrate the quality of the new tests. The applicability of the novel tests is demonstrated with two real-data examples.
{"title":"Characterization-based approach for construction of goodness-of-fit test for Lévy distribution","authors":"Žikica Lukić, B. Milošević","doi":"10.1080/02331888.2023.2238236","DOIUrl":"https://doi.org/10.1080/02331888.2023.2238236","url":null,"abstract":"The Lévy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the Lévy distribution. In this paper, two novel classes of goodness-of-fit tests for the Lévy distribution are proposed. Both tests are based on V-empirical Laplace transforms. New tests are scale free under the null hypothesis, which makes them suitable for testing the composite hypothesis. The finite sample and limiting properties of test statistics are obtained. In addition, a generalization of the recent Bhati–Kattumannil goodness-of-fit test to the Lévy distribution is considered. For assessing the quality of novel and competitor tests, the local Bahadur efficiencies are computed, and a wide power study is conducted. Both criteria clearly demonstrate the quality of the new tests. The applicability of the novel tests is demonstrated with two real-data examples.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"13 1","pages":"1087 - 1116"},"PeriodicalIF":1.9,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87231153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-04DOI: 10.1080/02331888.2023.2239507
Jun Jin, Shuangzhe Liu, Tiefeng Ma
Massive datasets have gained increasing prominence across various fields, but their analysis is often impeded by computational limitations. In response, Wang and Ma (Optimal subsampling for quantile regression in big data. Biometrika. 2021;108:99–112) have proposed an optimal subsampling method for quantile regression in massive datasets. Composite quantile regression, as a robust and efficient alternative to ordinary least squares regression and quantile regression in linear models, presents further complexities due to its distinct loss function. This paper extends the optimal subsampling method to accommodate composite quantile regression problems. We begin by deriving two new optimal subsampling probabilities for composite quantile regression, considering both the L- and A-optimality criteria Subsequently, we develop an adaptive two-step method based on these probabilities. The resulting estimators exhibit desirable asymptotic properties. In addition, to estimate the variance-covariance matrix without explicitly estimating the densities of the responses, we propose a combining subsamples method. Numerical studies on simulated and real data are conducted to assess and showcase the practical performance of our proposed methods.
{"title":"Optimal subsampling algorithms for composite quantile regression in massive data","authors":"Jun Jin, Shuangzhe Liu, Tiefeng Ma","doi":"10.1080/02331888.2023.2239507","DOIUrl":"https://doi.org/10.1080/02331888.2023.2239507","url":null,"abstract":"Massive datasets have gained increasing prominence across various fields, but their analysis is often impeded by computational limitations. In response, Wang and Ma (Optimal subsampling for quantile regression in big data. Biometrika. 2021;108:99–112) have proposed an optimal subsampling method for quantile regression in massive datasets. Composite quantile regression, as a robust and efficient alternative to ordinary least squares regression and quantile regression in linear models, presents further complexities due to its distinct loss function. This paper extends the optimal subsampling method to accommodate composite quantile regression problems. We begin by deriving two new optimal subsampling probabilities for composite quantile regression, considering both the L- and A-optimality criteria Subsequently, we develop an adaptive two-step method based on these probabilities. The resulting estimators exhibit desirable asymptotic properties. In addition, to estimate the variance-covariance matrix without explicitly estimating the densities of the responses, we propose a combining subsamples method. Numerical studies on simulated and real data are conducted to assess and showcase the practical performance of our proposed methods.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"29 1","pages":"811 - 843"},"PeriodicalIF":1.9,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79520910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-04DOI: 10.1080/02331888.2023.2236745
Eliana Christou
Marginalizing the importance of characterizing tail events can lead to catastrophic repercussions. Look no further than examples from meteorology and climatology (polar reversals, natural disasters), economics (2008 subprime mortgage crisis), or even medical-diagnostics (low/high risk patients in survival analysis). Investigating these events can become even more challenging when working with high-dimensional data, making it necessary to use dimension reduction techniques. Although research has recently turned to dimension reduction techniques that use conditional quantiles, there is a surprisingly limited amount of research dedicated to the underexplored research area of expectile regression (ER). Therefore, we present the first comprehensive work about dimension reduction techniques for conditional expectiles. Specifically, we introduce the central expectile subspace, i.e., the space that spans the fewest linear combinations of the predictors that contain all the information about the response that is available from the conditional expectile. We then introduce a nonlinear extension of the proposed methodology that extracts nonlinear features. The performance of the algorithms are demonstrated through extensive simulation examples and a real data application. The results suggest that ER is an effective tool for describing tail events and is a competitive alternative to quantile regression.
{"title":"Dimension reduction techniques for conditional expectiles","authors":"Eliana Christou","doi":"10.1080/02331888.2023.2236745","DOIUrl":"https://doi.org/10.1080/02331888.2023.2236745","url":null,"abstract":"Marginalizing the importance of characterizing tail events can lead to catastrophic repercussions. Look no further than examples from meteorology and climatology (polar reversals, natural disasters), economics (2008 subprime mortgage crisis), or even medical-diagnostics (low/high risk patients in survival analysis). Investigating these events can become even more challenging when working with high-dimensional data, making it necessary to use dimension reduction techniques. Although research has recently turned to dimension reduction techniques that use conditional quantiles, there is a surprisingly limited amount of research dedicated to the underexplored research area of expectile regression (ER). Therefore, we present the first comprehensive work about dimension reduction techniques for conditional expectiles. Specifically, we introduce the central expectile subspace, i.e., the space that spans the fewest linear combinations of the predictors that contain all the information about the response that is available from the conditional expectile. We then introduce a nonlinear extension of the proposed methodology that extracts nonlinear features. The performance of the algorithms are demonstrated through extensive simulation examples and a real data application. The results suggest that ER is an effective tool for describing tail events and is a competitive alternative to quantile regression.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"28 1","pages":"960 - 985"},"PeriodicalIF":1.9,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81780238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-04DOI: 10.1080/02331888.2023.2232912
D. Bickel
One remedy to the misuse of p-values transforms them to bounds on Bayes factors. With a prior probability of the null hypothesis, such a bound gives a lower bound on the posterior probability. Unfortunately, knowing a posterior probability is above some number cannot ensure that the null hypothesis is improbable enough to warrant its rejection. For example, if the lower bound is 0.0001, that implies that the posterior probability is at least 0.0001 but does not imply it is lower than 0.05 or even 0.9. A fiducial argument suggests an alternative estimate of the posterior probability that the null hypothesis is true. In the case that the prior probability of the null hypothesis is 50%, the estimated posterior probability is about for low p. In other cases, each occurrence of in the formula is the p-value calibrated by multiplying it by the prior odds of the null hypothesis. In the absence of a prior, also serves as an asymptotic Bayes factor. Since the fiducial estimate of the posterior probability is greater than the lower bounds, its use in place of a bound leads to more stringent hypothesis testing. Making that replacement in a rationale for 0.005 as the significance level reduces the level to 0.001.
{"title":"Fiducialize statistical significance: transforming p-values into conservative posterior probabilities and Bayes factors","authors":"D. Bickel","doi":"10.1080/02331888.2023.2232912","DOIUrl":"https://doi.org/10.1080/02331888.2023.2232912","url":null,"abstract":"One remedy to the misuse of p-values transforms them to bounds on Bayes factors. With a prior probability of the null hypothesis, such a bound gives a lower bound on the posterior probability. Unfortunately, knowing a posterior probability is above some number cannot ensure that the null hypothesis is improbable enough to warrant its rejection. For example, if the lower bound is 0.0001, that implies that the posterior probability is at least 0.0001 but does not imply it is lower than 0.05 or even 0.9. A fiducial argument suggests an alternative estimate of the posterior probability that the null hypothesis is true. In the case that the prior probability of the null hypothesis is 50%, the estimated posterior probability is about for low p. In other cases, each occurrence of in the formula is the p-value calibrated by multiplying it by the prior odds of the null hypothesis. In the absence of a prior, also serves as an asymptotic Bayes factor. Since the fiducial estimate of the posterior probability is greater than the lower bounds, its use in place of a bound leads to more stringent hypothesis testing. Making that replacement in a rationale for 0.005 as the significance level reduces the level to 0.001.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"114 1","pages":"941 - 959"},"PeriodicalIF":1.9,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79420770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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