Pub Date : 2020-02-26DOI: 10.5772/intechopen.86265
J. Hessling
Mathematical statistics has long been widely practiced in many fields of science [1]. Nevertheless, statistical methods have remained remarkably intact ever since the pioneering work [2] of R.A. Fisher and his contemporary scientists early in the twentieth century. Recently however, it has been claimed that most scientific results are wrong [3], due to malpractice of statistical methods. Errors of that kind are not caused by imperfect methodology but rather, reflect lack of understanding and proper interpretation. In this introductory chapter, a different cause of errors is addressed—the ubiquitous practice of willful ignorance (WI) [4]. Usually it is applied with intent to remedy lack of knowledge and simplify or merely enable application of established statistical methods. Virtually all statistical approaches require complete statistical knowledge at some stage. In practice though, that can hardly ever be established. For instance, Bayes estimation relies upon prior knowledge. Any equal a priori probability assumption (“uninformed prior”) does hardly disguise some facts are not known, which may be grossly deceiving. Uniform distribution is a specific assumption like any other. Willful ignorance of that kind must not be confused with knowledge to which we associate some degree of confidence. It may be better to explore rather than ignore consequences of what is not known at all. That will require novel perspectives on how mathematical statistics is practiced, which is the scope of this book.
{"title":"Introductory Chapter: Ramifications of Incomplete Knowledge","authors":"J. Hessling","doi":"10.5772/intechopen.86265","DOIUrl":"https://doi.org/10.5772/intechopen.86265","url":null,"abstract":"Mathematical statistics has long been widely practiced in many fields of science [1]. Nevertheless, statistical methods have remained remarkably intact ever since the pioneering work [2] of R.A. Fisher and his contemporary scientists early in the twentieth century. Recently however, it has been claimed that most scientific results are wrong [3], due to malpractice of statistical methods. Errors of that kind are not caused by imperfect methodology but rather, reflect lack of understanding and proper interpretation. In this introductory chapter, a different cause of errors is addressed—the ubiquitous practice of willful ignorance (WI) [4]. Usually it is applied with intent to remedy lack of knowledge and simplify or merely enable application of established statistical methods. Virtually all statistical approaches require complete statistical knowledge at some stage. In practice though, that can hardly ever be established. For instance, Bayes estimation relies upon prior knowledge. Any equal a priori probability assumption (“uninformed prior”) does hardly disguise some facts are not known, which may be grossly deceiving. Uniform distribution is a specific assumption like any other. Willful ignorance of that kind must not be confused with knowledge to which we associate some degree of confidence. It may be better to explore rather than ignore consequences of what is not known at all. That will require novel perspectives on how mathematical statistics is practiced, which is the scope of this book.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"51 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114135240","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}
Pub Date : 2020-02-26DOI: 10.5772/intechopen.84555
Y. Berkoun, K. Boualam
This note is devoted to the asymptotic normality of Hill's estimator when data are weakly dependent in the sense of Doukhan. The primary results on this setting rely on the observations being strong mixing. This assumption is often the key tool for establishing the asymptotic behavior of this estimator. A number of attempts have been made to relax the assumption of stationarity and mixing. Relaxing this condition, and assuming the weak dependence, we extend the results obtained by Rootzen and Starica. This approach requires less restrictive conditions than the previous results.
{"title":"Asymptotic Normality of Hill’s Estimator under Weak Dependence","authors":"Y. Berkoun, K. Boualam","doi":"10.5772/intechopen.84555","DOIUrl":"https://doi.org/10.5772/intechopen.84555","url":null,"abstract":"This note is devoted to the asymptotic normality of Hill's estimator when data are weakly dependent in the sense of Doukhan. The primary results on this setting rely on the observations being strong mixing. This assumption is often the key tool for establishing the asymptotic behavior of this estimator. A number of attempts have been made to relax the assumption of stationarity and mixing. Relaxing this condition, and assuming the weak dependence, we extend the results obtained by Rootzen and Starica. This approach requires less restrictive conditions than the previous results.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127444879","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}
Pub Date : 2020-02-26DOI: 10.5772/intechopen.90136
D. Korobkin, S. Vasiliev, S. Fomenkov, S. Kolesnikov
The article presents a method for extracting predicate-argument constructions characterizing the composition of the structural elements of the inventions and the relationships between them. The extracted structures are converted into a domain ontology and used in prior art patent search and information support of automated invention. The analysis of existing natural language processing (NLP) tools in relation to the processing of Russian-language patents has been carried out. A new method for extracting structured data from patents has been proposed taking into account the specificity of the text of patents and is based on the shallow parsing and segmentation of sentences. The value of the F1 metric for a rigorous estimate of data extraction is 63% and for a lax estimate is 79%. The results obtained suggest that the proposed method is promising.
{"title":"Methods of Russian Patent Analysis","authors":"D. Korobkin, S. Vasiliev, S. Fomenkov, S. Kolesnikov","doi":"10.5772/intechopen.90136","DOIUrl":"https://doi.org/10.5772/intechopen.90136","url":null,"abstract":"The article presents a method for extracting predicate-argument constructions characterizing the composition of the structural elements of the inventions and the relationships between them. The extracted structures are converted into a domain ontology and used in prior art patent search and information support of automated invention. The analysis of existing natural language processing (NLP) tools in relation to the processing of Russian-language patents has been carried out. A new method for extracting structured data from patents has been proposed taking into account the specificity of the text of patents and is based on the shallow parsing and segmentation of sentences. The value of the F1 metric for a rigorous estimate of data extraction is 63% and for a lax estimate is 79%. The results obtained suggest that the proposed method is promising.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129877290","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}
Pub Date : 2019-09-27DOI: 10.5772/intechopen.82850
P. Parichha, K. Basu, A. Bandyopadhyay
This article describes the problem of estimation of finite population mean in two-phase stratified random sampling. Using information on two auxiliary variables, a class of product to regression chain type estimators has been proposed and its characteristic is discussed. The unbiased version of the proposed class of estimators has been constructed and the optimality condition for the proposed class of estimators is derived. The efficacy of the proposed methodology has been justified through empirical investigations carried over the data set of natural population as well as the data set of artificially generated population. The survey statistician may be suggested to use it.
{"title":"Development of Estimation Procedure of Population Mean in Two-Phase Stratified Sampling","authors":"P. Parichha, K. Basu, A. Bandyopadhyay","doi":"10.5772/intechopen.82850","DOIUrl":"https://doi.org/10.5772/intechopen.82850","url":null,"abstract":"This article describes the problem of estimation of finite population mean in two-phase stratified random sampling. Using information on two auxiliary variables, a class of product to regression chain type estimators has been proposed and its characteristic is discussed. The unbiased version of the proposed class of estimators has been constructed and the optimality condition for the proposed class of estimators is derived. The efficacy of the proposed methodology has been justified through empirical investigations carried over the data set of natural population as well as the data set of artificially generated population. The survey statistician may be suggested to use it.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115075119","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}
Pub Date : 2019-09-27DOI: 10.5772/intechopen.85627
Kaisar Ahmad, Sheikh Parvaiz Ahmad
In this chapter, Erlang distribution is considered. For parameter estimation, maximum likelihood method of estimation, method of moments and Bayesian method of estimation are applied. In Bayesian methodology, different prior distributions are employed under various loss functions to estimate the rate parameter of Erlang distribution. At the end the simulation study is conducted in R-Software to compare these methods by using mean square error with varying sample sizes. Also the real life applications are examined in order to compare the behavior of the data sets in the parametric estimation. The comparison is also done among the different loss functions.
{"title":"A Comparative Study of Maximum Likelihood Estimation and Bayesian Estimation for Erlang Distribution and Its Applications","authors":"Kaisar Ahmad, Sheikh Parvaiz Ahmad","doi":"10.5772/intechopen.85627","DOIUrl":"https://doi.org/10.5772/intechopen.85627","url":null,"abstract":"In this chapter, Erlang distribution is considered. For parameter estimation, maximum likelihood method of estimation, method of moments and Bayesian method of estimation are applied. In Bayesian methodology, different prior distributions are employed under various loss functions to estimate the rate parameter of Erlang distribution. At the end the simulation study is conducted in R-Software to compare these methods by using mean square error with varying sample sizes. Also the real life applications are examined in order to compare the behavior of the data sets in the parametric estimation. The comparison is also done among the different loss functions.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"37 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132365567","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}
Pub Date : 2019-08-07DOI: 10.5772/INTECHOPEN.88392
J. Minjárez‐Sosa
This chapter deals with a class of discrete-time inventory control systems where the demand process D t is formed by independent and identically distributed random variables with unknown density. Our objective is to introduce a suitable density estimation method which, combined with optimal control schemes, defines a procedure to construct optimal policies under a discounted optimality criterion.
{"title":"Density Estimation in Inventory Control Systems under a Discounted Optimality Criterion","authors":"J. Minjárez‐Sosa","doi":"10.5772/INTECHOPEN.88392","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.88392","url":null,"abstract":"This chapter deals with a class of discrete-time inventory control systems where the demand process D t is formed by independent and identically distributed random variables with unknown density. Our objective is to introduce a suitable density estimation method which, combined with optimal control schemes, defines a procedure to construct optimal policies under a discounted optimality criterion.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122689910","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}
Pub Date : 2019-02-25DOI: 10.5772/INTECHOPEN.84524
E. Oral
Data reliability is a common concern especially when asking about sensitive topics such as sexual misconduct, domestic violence, or drug and alcohol abuse. Sensitive topics might cause refusals in surveys due to privacy concerns of the subjects. Unit nonresponse occurs when sampled subjects fail to participate in a study; item nonresponse occurs when sampled subjects do not respond to certain survey questions. Unit nonresponse reduces sample size and study power; it might also increase bias. Respondents, on the other hand, might answer the sensitive questions in a manner that will be viewed favorably by others instead of answering truthfully. Social desirability bias (SDB) has long been recognized as a serious problem in surveying sensitive topics. Various indirect questioning methods have been developed to reduce SDB and increase data reliability, one of them being the randomized response technique (RRT). In this chapter, we will review some of the important indirect questioning techniques proposed for binary responses, with a special focus on RRTs. We will discuss the advantages and disadvantages of some of the indirect questioning techniques and describe some of the recent novel methods.
{"title":"Surveying Sensitive Topics with Indirect Questioning","authors":"E. Oral","doi":"10.5772/INTECHOPEN.84524","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.84524","url":null,"abstract":"Data reliability is a common concern especially when asking about sensitive topics such as sexual misconduct, domestic violence, or drug and alcohol abuse. Sensitive topics might cause refusals in surveys due to privacy concerns of the subjects. Unit nonresponse occurs when sampled subjects fail to participate in a study; item nonresponse occurs when sampled subjects do not respond to certain survey questions. Unit nonresponse reduces sample size and study power; it might also increase bias. Respondents, on the other hand, might answer the sensitive questions in a manner that will be viewed favorably by others instead of answering truthfully. Social desirability bias (SDB) has long been recognized as a serious problem in surveying sensitive topics. Various indirect questioning methods have been developed to reduce SDB and increase data reliability, one of them being the randomized response technique (RRT). In this chapter, we will review some of the important indirect questioning techniques proposed for binary responses, with a special focus on RRTs. We will discuss the advantages and disadvantages of some of the indirect questioning techniques and describe some of the recent novel methods.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116688858","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}
Pub Date : 2018-12-18DOI: 10.5772/INTECHOPEN.82366
N. Yıldız
In this study, we proposed an alternative biased estimator. The linear regression model might lead to ill-conditioned design matrices because of the multicollinearity and thus result in inadequacy of the ordinary least squares estimator (OLS). Scientists have developed alternative estimation techniques that would eradicate the instability in the estimates. Several biased estimators such as Stein estimator, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator. Liu developed a Liu estimator (LE) by combining the Stein estimator with the ORR estimator. Since both ORR and LE depend on OLS estimator, multicollinearity affects them both. Therefore, the ORR and LE may give misleading information in the presence of multicollinearity. To overcome this problem, Liu introduced a new estimator, which is based on k and d biasing parameters, the authors worked on developing an estimator that would still have the valuable characteristics of the Liu-type estimator (LTE) but have a smaller bias. We are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the LTE and JLTE. Under mean square error matrix criteria, the MJLTE is superior to Liu-type estimator (LTE) and jackknifed Liu-type estimator (JLTE). Finally, a real data example and a Monte Carlo simulation are also given to illustrate theoretical results.
{"title":"A Study on the Comparison of the Effectiveness of the Jackknife Method in the Biased Estimators","authors":"N. Yıldız","doi":"10.5772/INTECHOPEN.82366","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.82366","url":null,"abstract":"In this study, we proposed an alternative biased estimator. The linear regression model might lead to ill-conditioned design matrices because of the multicollinearity and thus result in inadequacy of the ordinary least squares estimator (OLS). Scientists have developed alternative estimation techniques that would eradicate the instability in the estimates. Several biased estimators such as Stein estimator, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator. Liu developed a Liu estimator (LE) by combining the Stein estimator with the ORR estimator. Since both ORR and LE depend on OLS estimator, multicollinearity affects them both. Therefore, the ORR and LE may give misleading information in the presence of multicollinearity. To overcome this problem, Liu introduced a new estimator, which is based on k and d biasing parameters, the authors worked on developing an estimator that would still have the valuable characteristics of the Liu-type estimator (LTE) but have a smaller bias. We are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the LTE and JLTE. Under mean square error matrix criteria, the MJLTE is superior to Liu-type estimator (LTE) and jackknifed Liu-type estimator (JLTE). Finally, a real data example and a Monte Carlo simulation are also given to illustrate theoretical results.","PeriodicalId":381809,"journal":{"name":"Statistical Methodologies","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115115464","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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