Single‐index model is a very popular and powerful semiparametric model. As an improvement of the maximum rank correlation estimator, [[spiapacite]]bib1[[/spiapacite]] proposed the linearized maximum rank correlation estimator. We show that this estimator has some interesting connections with the distribution‐transformed least‐squares estimator for single‐index models. We also propose a rescaled distribution‐transformed least‐squares estimator, which is mathematically equivalent to the linearized maximum rank correlation estimator when the distribution of the response is absolutely continuous. Despite some nontrivial connections, the two estimation procedures are different in terms of motivations, interpretations, and applications. We discuss some of the differences between the two estimation procedures. This article is protected by copyright. All rights reserved.
{"title":"Connections between two classes of estimators for single‐index models","authors":"Weichao Yang, Xu Guo, Niwen Zhou, Changliang Zou","doi":"10.1111/stan.12329","DOIUrl":"https://doi.org/10.1111/stan.12329","url":null,"abstract":"Single‐index model is a very popular and powerful semiparametric model. As an improvement of the maximum rank correlation estimator, [[spiapacite]]bib1[[/spiapacite]] proposed the linearized maximum rank correlation estimator. We show that this estimator has some interesting connections with the distribution‐transformed least‐squares estimator for single‐index models. We also propose a rescaled distribution‐transformed least‐squares estimator, which is mathematically equivalent to the linearized maximum rank correlation estimator when the distribution of the response is absolutely continuous. Despite some nontrivial connections, the two estimation procedures are different in terms of motivations, interpretations, and applications. We discuss some of the differences between the two estimation procedures. This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose a new procedure to test conditional independence assumption in studying casual inference for time series data. The conditional independence assumption is transformed to a nonparametric conditional moment test with the help of auxiliary variables which are allowed to affect policy choice but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the conditional independence assumption conditional on policy propensity score. Under some regular conditions, we show that the proposed test statistics are asymptotically normal under the null hypotheses for time series data. In addition, the performances of the proposed methods are illustrated through Monte Carlo simulations and a real example considered in Angrist and Kuersteiner (2011).
{"title":"Testing Conditional Independence in Casual Inference for Time Series Data<sup>†</sup>","authors":"Zongwu Cai, Ying Fang, Ming Lin, Shengfang Tang","doi":"10.1111/stan.12323","DOIUrl":"https://doi.org/10.1111/stan.12323","url":null,"abstract":"In this paper, we propose a new procedure to test conditional independence assumption in studying casual inference for time series data. The conditional independence assumption is transformed to a nonparametric conditional moment test with the help of auxiliary variables which are allowed to affect policy choice but the dependence can be fully captured by potential outcomes and observable controls. When the policy choice is binary, a nonparametric statistic test is developed further for testing the conditional independence assumption conditional on policy propensity score. Under some regular conditions, we show that the proposed test statistics are asymptotically normal under the null hypotheses for time series data. In addition, the performances of the proposed methods are illustrated through Monte Carlo simulations and a real example considered in Angrist and Kuersteiner (2011).","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135477036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide a prior distribution for a functional parameter so that its trajectories are smooth and vanish on a given subset. This distribution can be interpreted as the distribution of an initial Gaussian process conditioned to be zero on a given subset. Precisely, we show that the initial Gaussian process is the sum of the conditioned process and an independent process with probability one and that all the processes have the same almost sure regularity. This prior distribution is use to provide an interpretable estimate of the coefficient function in the linear scalar‐on‐function regression; by interpretable, we mean a smooth function that may possibly be zero on some intervals. We apply our model in a simulation and real case studies with two different priors for the null region of the coefficient function. In one case, the null region is known to be an unknown single interval. In the other case, it can be any unknown unions of intervals.This article is protected by copyright. All rights reserved.
{"title":"An Informative Prior distribution on Functions with Application to Functional Regression","authors":"C. Abraham","doi":"10.1111/stan.12322","DOIUrl":"https://doi.org/10.1111/stan.12322","url":null,"abstract":"We provide a prior distribution for a functional parameter so that its trajectories are smooth and vanish on a given subset. This distribution can be interpreted as the distribution of an initial Gaussian process conditioned to be zero on a given subset. Precisely, we show that the initial Gaussian process is the sum of the conditioned process and an independent process with probability one and that all the processes have the same almost sure regularity. This prior distribution is use to provide an interpretable estimate of the coefficient function in the linear scalar‐on‐function regression; by interpretable, we mean a smooth function that may possibly be zero on some intervals. We apply our model in a simulation and real case studies with two different priors for the null region of the coefficient function. In one case, the null region is known to be an unknown single interval. In the other case, it can be any unknown unions of intervals.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"21 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90644063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sufficient dimension reduction (SDR) methods are effective tools for handling high dimensional data. Classical SDR methods are developed under the assumption that the data are completely observed. When the data are incomplete due to missing values, SDR has only been considered when the data are randomly missing, but not when they are non‐ignorably missing, which is arguably more difficult to handle due to the missing values' dependence on the reasons they are missing. The purpose of this paper is to fill this void. We propose an intuitive, easy‐to‐implement SDR estimator based on a semiparametric propensity score function for response data with non‐ignorable missing values. We refer to it as the dimension reduction‐based imputed estimator. We establish the theoretical properties of this estimator and examine its empirical performance via an extensive numerical study on real and simulated data. As well, we compare the performance of our proposed dimension reduction‐based imputed estimator with two competing estimators, including the fusion refined estimator and cumulative slicing estimator. A distinguishing feature of our method is that it requires no validation sample. The SDR theory developed in this paper is a non‐trivial extension of the existing literature, due to the technical challenges posed by non‐ignorable missingness. All the technical proofs of the theorems are given in the Online Supplementary Material.This article is protected by copyright. All rights reserved.
{"title":"Semiparametric Recovery of Central Dimension Reduction Space with Nonignorable Nonresponse","authors":"Siming Zheng, Alan T.K. Wan, Yong Zhou","doi":"10.1111/stan.12321","DOIUrl":"https://doi.org/10.1111/stan.12321","url":null,"abstract":"Sufficient dimension reduction (SDR) methods are effective tools for handling high dimensional data. Classical SDR methods are developed under the assumption that the data are completely observed. When the data are incomplete due to missing values, SDR has only been considered when the data are randomly missing, but not when they are non‐ignorably missing, which is arguably more difficult to handle due to the missing values' dependence on the reasons they are missing. The purpose of this paper is to fill this void. We propose an intuitive, easy‐to‐implement SDR estimator based on a semiparametric propensity score function for response data with non‐ignorable missing values. We refer to it as the dimension reduction‐based imputed estimator. We establish the theoretical properties of this estimator and examine its empirical performance via an extensive numerical study on real and simulated data. As well, we compare the performance of our proposed dimension reduction‐based imputed estimator with two competing estimators, including the fusion refined estimator and cumulative slicing estimator. A distinguishing feature of our method is that it requires no validation sample. The SDR theory developed in this paper is a non‐trivial extension of the existing literature, due to the technical challenges posed by non‐ignorable missingness. All the technical proofs of the theorems are given in the Online Supplementary Material.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89912126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Martín Andrés, Álvarez Hernández M, Gayá Moreno F
Asymptotic inferences about the difference, ratio or odds‐ratio of two independent proportions are very common in diverse fields. This article defines for each parameter eight conditional inference methods. These methods depend on: (1) using a chi‐squared type statistic or a z type one; (2) using the classic Yates continuity correction or the less well‐known Conover one; and (3) whether the p‐value of the test is determined by doubling the one‐tailed p‐value or by the Mantel method (asymmetrical approach). In all cases, the conclusions are: (i) the methods based on the chi‐squared statistic should not be used, as they are too liberal; (ii) for those in favour of using the criterion of doubling the p‐value, the best method is using the z statistic with Conover continuity correction; and (iii) for those in favour of the asymmetrical approach, the best method is based on the z statistic with Conover continuity correction and the Mantel p‐value.This article is protected by copyright. All rights reserved.
{"title":"The Yates, Conover and Mantel statistics in 2×2 tables revisited (and extended)","authors":"A. Martín Andrés, Álvarez Hernández M, Gayá Moreno F","doi":"10.1111/stan.12320","DOIUrl":"https://doi.org/10.1111/stan.12320","url":null,"abstract":"Asymptotic inferences about the difference, ratio or odds‐ratio of two independent proportions are very common in diverse fields. This article defines for each parameter eight conditional inference methods. These methods depend on: (1) using a chi‐squared type statistic or a z type one; (2) using the classic Yates continuity correction or the less well‐known Conover one; and (3) whether the p‐value of the test is determined by doubling the one‐tailed p‐value or by the Mantel method (asymmetrical approach). In all cases, the conclusions are: (i) the methods based on the chi‐squared statistic should not be used, as they are too liberal; (ii) for those in favour of using the criterion of doubling the p‐value, the best method is using the z statistic with Conover continuity correction; and (iii) for those in favour of the asymmetrical approach, the best method is based on the z statistic with Conover continuity correction and the Mantel p‐value.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"55 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84502447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Estimation of the average treatment effect is one of the crucial problems in clinical trials for two or multiple treatments. The covariate‐adaptive randomization methods are often applied to balance treatment assignments across prognostic factors in clinical trials, such as the minimization and stratified permuted blocks method. We propose a model‐free estimator of average treatment effects under covariate‐adaptive randomization methods, which is least square adjustment for the estimator of outcome models. The proposed estimator is not only applicable to the case of binary treatment, but also can be extended to the case of multiple treatment. The proposed estimator is consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator and Ye's estimator are comparable, and it performs better than Bugni's estimator when the outcome model is linear. The proposed estimator has some advantages over targeted maximum likelihood estimator, Bugni's estimator and Ye's estimator in terms of the standard error and root mean squared error when the outcome model is nonlinear. The proposed estimator is stable for the from of outcome model. Finally, we apply the proposed methodology to a data set that studies the causal effect promotional videos mode on the school‐age children's educational attainment in Peru.This article is protected by copyright. All rights reserved.
{"title":"Improved estimation of average treatment effects under covariate‐adaptive randomization methods","authors":"Jun Wang, Yahe Yu","doi":"10.1111/stan.12319","DOIUrl":"https://doi.org/10.1111/stan.12319","url":null,"abstract":"Estimation of the average treatment effect is one of the crucial problems in clinical trials for two or multiple treatments. The covariate‐adaptive randomization methods are often applied to balance treatment assignments across prognostic factors in clinical trials, such as the minimization and stratified permuted blocks method. We propose a model‐free estimator of average treatment effects under covariate‐adaptive randomization methods, which is least square adjustment for the estimator of outcome models. The proposed estimator is not only applicable to the case of binary treatment, but also can be extended to the case of multiple treatment. The proposed estimator is consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator and Ye's estimator are comparable, and it performs better than Bugni's estimator when the outcome model is linear. The proposed estimator has some advantages over targeted maximum likelihood estimator, Bugni's estimator and Ye's estimator in terms of the standard error and root mean squared error when the outcome model is nonlinear. The proposed estimator is stable for the from of outcome model. Finally, we apply the proposed methodology to a data set that studies the causal effect promotional videos mode on the school‐age children's educational attainment in Peru.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"5 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90073386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christopher Aguirre‐Hamilton, Stephen A. Sedory, Sarjinder Singh
We propose two types of estimators that are analogous to Franklin's model. One estimator is derived by concentrating on the row averages of the responses, and another is obtained by concentrating on the column averages of the observed responses. In the latter case we have two responses per respondent from a bi‐variate normal distribution. The proposed estimator based on row averages, by making use of negatively correlated random numbers from a multivariate density, is always more efficient than the corresponding Franklin's estimator. In the case of the proposed estimator based on column averages, we found that the use of positively correlated random numbers from a bivariate density can lead to the most efficient estimator. We also discuss results which are observed by making use of three responses per respondent. When the three responses are recorded, three independent normal densities are derived from three correlated variables. The findings are supported based on analytical, numerical and simulation studies. A simulation study was done to determine the minimum sample size required to produce non‐negative estimates of the population proportion of a sensitive characteristic, and to investigate the 95% nominal coverage by the interval estimates. Ultimately at the end, one best estimator is suggested. A very neat and clean derivations of theoretical results and discussion of numerical and simulation studies are documented in online supplementary material.This article is protected by copyright. All rights reserved.
{"title":"Franklin's Randomized Response Model With Correlated Scrambled Variables","authors":"Christopher Aguirre‐Hamilton, Stephen A. Sedory, Sarjinder Singh","doi":"10.1111/stan.12318","DOIUrl":"https://doi.org/10.1111/stan.12318","url":null,"abstract":"We propose two types of estimators that are analogous to Franklin's model. One estimator is derived by concentrating on the row averages of the responses, and another is obtained by concentrating on the column averages of the observed responses. In the latter case we have two responses per respondent from a bi‐variate normal distribution. The proposed estimator based on row averages, by making use of negatively correlated random numbers from a multivariate density, is always more efficient than the corresponding Franklin's estimator. In the case of the proposed estimator based on column averages, we found that the use of positively correlated random numbers from a bivariate density can lead to the most efficient estimator. We also discuss results which are observed by making use of three responses per respondent. When the three responses are recorded, three independent normal densities are derived from three correlated variables. The findings are supported based on analytical, numerical and simulation studies. A simulation study was done to determine the minimum sample size required to produce non‐negative estimates of the population proportion of a sensitive characteristic, and to investigate the 95% nominal coverage by the interval estimates. Ultimately at the end, one best estimator is suggested. A very neat and clean derivations of theoretical results and discussion of numerical and simulation studies are documented in online supplementary material.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"29 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89826934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Clustering is a technique used to partition a dataset into groups of similar elements. In addition to traditional clustering methods, clustering for probability density functions (CDF) has been studied to capture data uncertainty. In CDF, automatic clustering is a clever technique that can determine the number of clusters automatically. However, current automatic clustering algorithms update the new probability density function (pdf) fi(t) based on the weighted mean of all previous pdfs fj(t − 1), j = 1, 2, …, N, resulting in slow convergence. This paper proposes an efficient automatic clustering algorithm for pdfs. In the proposed approach, the update of fi(t) is based on the weighted mean of {f1(t), f2(t),…, fi − 1(t), fi(t − 1), fi+1(t − 1),…,fN(t − 1)}, where N is the number of pdfs and i = 1,2,…, N. This technique allows for the incorporation of recently updated pdfs, leading to faster convergence. This paper also pioneers the applications of certain CDF algorithms in the field of surface image recognition. The numerical examples demonstrate that the proposed method can result in a rapid convergence at some early iterations. It also outperforms other state‐of‐the‐art automatic clustering methods in terms of the Adjusted Rand Index (ARI) and the Normalized Mutual Information (NMI). Additionally, the proposed algorithm proves to be competitive when clustering material images contaminated by noise. These results highlight the applicability of the proposed method in the problem of surface image recognition.This article is protected by copyright. All rights reserved.
{"title":"An efficient automatic clustering algorithm for probability density functions and its applications in surface material classification","authors":"Thao Nguyen-Trang, Tai Vo-Van, Ha Che-Ngoc","doi":"10.1111/stan.12315","DOIUrl":"https://doi.org/10.1111/stan.12315","url":null,"abstract":"Clustering is a technique used to partition a dataset into groups of similar elements. In addition to traditional clustering methods, clustering for probability density functions (CDF) has been studied to capture data uncertainty. In CDF, automatic clustering is a clever technique that can determine the number of clusters automatically. However, current automatic clustering algorithms update the new probability density function (pdf) fi(t) based on the weighted mean of all previous pdfs fj(t − 1), j = 1, 2, …, N, resulting in slow convergence. This paper proposes an efficient automatic clustering algorithm for pdfs. In the proposed approach, the update of fi(t) is based on the weighted mean of {f1(t), f2(t),…, fi − 1(t), fi(t − 1), fi+1(t − 1),…,fN(t − 1)}, where N is the number of pdfs and i = 1,2,…, N. This technique allows for the incorporation of recently updated pdfs, leading to faster convergence. This paper also pioneers the applications of certain CDF algorithms in the field of surface image recognition. The numerical examples demonstrate that the proposed method can result in a rapid convergence at some early iterations. It also outperforms other state‐of‐the‐art automatic clustering methods in terms of the Adjusted Rand Index (ARI) and the Normalized Mutual Information (NMI). Additionally, the proposed algorithm proves to be competitive when clustering material images contaminated by noise. These results highlight the applicability of the proposed method in the problem of surface image recognition.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"26 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83291722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sheng Li, Wen Wang, Menghan Yao, Junyu Wang, Qianqian Du, Xuelin Li, Xinyue Tian, Jing Zeng, Ying Deng, Zhang Tao, F. Yin, Yue Ma
The Poisson ridge estimator (PRE) is a commonly used parameter estimation method to address multicollinearity in Poisson regression (PR). However, PRE shrinks the parameters toward zero, contradicting the real association. In such cases, PRE tends to become an insufficient solution for multicollinearity. In this work, we proposed a new estimator called the Poisson average maximum likelihood‐centered penalized estimator (PAMLPE), which shrinks the parameters toward the weighted average of the maximum likelihood estimators. We conducted a simulation study and case study to compare PAMLPE with existing estimators in terms of mean squared error (MSE) and predictive mean squared error (PMSE). These results suggest that PAMLPE can obtain smaller MSE and PMSE (i.e., more accurate estimates) than the Poisson ridge estimator, Poisson Liu estimator, and Poisson K‐L estimator when the true β$$ beta $$ s have the same sign and small variation. Therefore, we recommend using PAMLPE to address multicollinearity in PR when the signs of the true β$$ beta $$ s are known to be identical in advance.
{"title":"Poisson average maximum likelihood‐centred penalized estimator: A new estimator to better address multicollinearity in Poisson regression","authors":"Sheng Li, Wen Wang, Menghan Yao, Junyu Wang, Qianqian Du, Xuelin Li, Xinyue Tian, Jing Zeng, Ying Deng, Zhang Tao, F. Yin, Yue Ma","doi":"10.1111/stan.12313","DOIUrl":"https://doi.org/10.1111/stan.12313","url":null,"abstract":"The Poisson ridge estimator (PRE) is a commonly used parameter estimation method to address multicollinearity in Poisson regression (PR). However, PRE shrinks the parameters toward zero, contradicting the real association. In such cases, PRE tends to become an insufficient solution for multicollinearity. In this work, we proposed a new estimator called the Poisson average maximum likelihood‐centered penalized estimator (PAMLPE), which shrinks the parameters toward the weighted average of the maximum likelihood estimators. We conducted a simulation study and case study to compare PAMLPE with existing estimators in terms of mean squared error (MSE) and predictive mean squared error (PMSE). These results suggest that PAMLPE can obtain smaller MSE and PMSE (i.e., more accurate estimates) than the Poisson ridge estimator, Poisson Liu estimator, and Poisson K‐L estimator when the true β$$ beta $$ s have the same sign and small variation. Therefore, we recommend using PAMLPE to address multicollinearity in PR when the signs of the true β$$ beta $$ s are known to be identical in advance.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"57 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79135996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Various researches have been conducted on forecasting stock prices. Several tools ranging from statistical techniques to quantitative methods have been used by researchers to forecast the market. But so far, very little research has been done on forecasting the stock markets of the Gulf countries such as Saudi Arabia, United Arab Emirates, Oman, Kuwait, Bahrain, and Qatar. Our approach is to predict the market indices of the Gulf countries using Long Short‐Term Memory (LSTM) techniques. Thereafter, we optimized the hyperparameters of the LSTM technique using various optimization methods such as Grid Search and Bayesian Optimization with Gaussian Process and found out the best‐suited hyperparameter for the LSTM model. We tried the LSTM method for predicting the indices using data from the last twenty years.
{"title":"A case study of Gulf Securities Market in the last 20 years: A Long Short‐Term Memory approach","authors":"Abhibasu Sen, Karabi Dutta Choudhury","doi":"10.1111/stan.12309","DOIUrl":"https://doi.org/10.1111/stan.12309","url":null,"abstract":"Various researches have been conducted on forecasting stock prices. Several tools ranging from statistical techniques to quantitative methods have been used by researchers to forecast the market. But so far, very little research has been done on forecasting the stock markets of the Gulf countries such as Saudi Arabia, United Arab Emirates, Oman, Kuwait, Bahrain, and Qatar. Our approach is to predict the market indices of the Gulf countries using Long Short‐Term Memory (LSTM) techniques. Thereafter, we optimized the hyperparameters of the LSTM technique using various optimization methods such as Grid Search and Bayesian Optimization with Gaussian Process and found out the best‐suited hyperparameter for the LSTM model. We tried the LSTM method for predicting the indices using data from the last twenty years.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"42 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91252395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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