Pub Date : 2020-07-02DOI: 10.1080/07474946.2020.1823195
A. Walker
Abstract Postmarketing safety surveillance studies address two actionable questions: (1) Is the test product riskier than a standard? (2) Is the risk associated with the test product within some tolerable margin by comparison to the standard? Established techniques, not commonly applied to the setting of such complementary one-sided hypotheses, lead to useful conclusions in practice. For two-group studies, a search over possible one-sided binomial test results yields sample sizes that guarantee that the confidence bounds exclude one or the other of the hypotheses. With continuous monitoring, simple curtailment reduces the sample size. Point and interval estimates follow from the binomial distribution of events at the end of the study or from component negative binomials for crossing a bound of simple curtailment with continuous monitoring and earlier stopping. An asymptotic derivation corresponds to the problem of constructing a confidence interval that is smaller than the distance between the parameter values for tolerable excess and the absence of excess risk. Studies with guaranteed rejection of one of the pair of complementary hypotheses are somewhat larger than corresponding studies of a single hypothesis under usual power requirements, but the increase may be tolerable in return for certainty that there will be an actionable conclusion.
{"title":"Complementary hypotheses in safety surveillance","authors":"A. Walker","doi":"10.1080/07474946.2020.1823195","DOIUrl":"https://doi.org/10.1080/07474946.2020.1823195","url":null,"abstract":"Abstract Postmarketing safety surveillance studies address two actionable questions: (1) Is the test product riskier than a standard? (2) Is the risk associated with the test product within some tolerable margin by comparison to the standard? Established techniques, not commonly applied to the setting of such complementary one-sided hypotheses, lead to useful conclusions in practice. For two-group studies, a search over possible one-sided binomial test results yields sample sizes that guarantee that the confidence bounds exclude one or the other of the hypotheses. With continuous monitoring, simple curtailment reduces the sample size. Point and interval estimates follow from the binomial distribution of events at the end of the study or from component negative binomials for crossing a bound of simple curtailment with continuous monitoring and earlier stopping. An asymptotic derivation corresponds to the problem of constructing a confidence interval that is smaller than the distance between the parameter values for tolerable excess and the absence of excess risk. Studies with guaranteed rejection of one of the pair of complementary hypotheses are somewhat larger than corresponding studies of a single hypothesis under usual power requirements, but the increase may be tolerable in return for certainty that there will be an actionable conclusion.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1823195","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42325846","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 : 2020-07-02DOI: 10.1080/07474946.2020.1823196
S. Mingoti, G. A. Diniz
Abstract In this article Wald’s sequential probability ratio test (SPRT) is implemented for multivariate normal distribution, for independent and autocorrelated data and known covariance matrix. The methodology based on residuals from the vector autoregressive moving average (VARMA) class models is presented for autocorrelated data. In this approach the average sample size required to take a decision in the sequential test is based on the Mahalanobis distance between the vectors of the intercept constants with respect to the error covariance matrix. Monte Carlo simulations were performed considering different scenarios for bivariate normal distribution. For fixed probabilities of type I and II errors, the results showed that the estimated average sample sizes to stop the sequential test were a little larger than those expected by Wald’s theory for autocorrelated and independent data. Under independence assumption the SPRT estimated sample sizes were also smaller than the sample sizes required by Hotelling’s test. It was shown that the omission of the correlation structure of the data strongly affects the type I and II errors of the sequential test. An example in the quality control field is presented using real data from a pig iron production process and the multivariate VAR(1) model.
{"title":"On Wald’s sequential test for vector mean under multivariate normal distribution and correlated data","authors":"S. Mingoti, G. A. Diniz","doi":"10.1080/07474946.2020.1823196","DOIUrl":"https://doi.org/10.1080/07474946.2020.1823196","url":null,"abstract":"Abstract In this article Wald’s sequential probability ratio test (SPRT) is implemented for multivariate normal distribution, for independent and autocorrelated data and known covariance matrix. The methodology based on residuals from the vector autoregressive moving average (VARMA) class models is presented for autocorrelated data. In this approach the average sample size required to take a decision in the sequential test is based on the Mahalanobis distance between the vectors of the intercept constants with respect to the error covariance matrix. Monte Carlo simulations were performed considering different scenarios for bivariate normal distribution. For fixed probabilities of type I and II errors, the results showed that the estimated average sample sizes to stop the sequential test were a little larger than those expected by Wald’s theory for autocorrelated and independent data. Under independence assumption the SPRT estimated sample sizes were also smaller than the sample sizes required by Hotelling’s test. It was shown that the omission of the correlation structure of the data strongly affects the type I and II errors of the sequential test. An example in the quality control field is presented using real data from a pig iron production process and the multivariate VAR(1) model.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1823196","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44442567","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 : 2020-07-02DOI: 10.1080/07474946.2020.1823190
W. Rosenberger
Abstract Sequential analysis, as invented by Wald, was not targeted to clinical trials; in fact, the randomized clinical trial was being invented nearly simultaneously by Hill on the other side of the Atlantic. The connection to clinical trials was established by Bross and Armitage in the early 1950s and applied in a number of trials during that decade. Restrictions in its applicability in practice led to a dry spell until its resurgence with group sequential methods. This article reviews the historical context of the use of sequential analysis in actual randomized clinical trials. It does not review methodological developments, except as they relate to the historical and philosophical setting.
{"title":"Sequential design and analysis in the randomized clinical trial: A historical perspective","authors":"W. Rosenberger","doi":"10.1080/07474946.2020.1823190","DOIUrl":"https://doi.org/10.1080/07474946.2020.1823190","url":null,"abstract":"Abstract Sequential analysis, as invented by Wald, was not targeted to clinical trials; in fact, the randomized clinical trial was being invented nearly simultaneously by Hill on the other side of the Atlantic. The connection to clinical trials was established by Bross and Armitage in the early 1950s and applied in a number of trials during that decade. Restrictions in its applicability in practice led to a dry spell until its resurgence with group sequential methods. This article reviews the historical context of the use of sequential analysis in actual randomized clinical trials. It does not review methodological developments, except as they relate to the historical and philosophical setting.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1823190","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43368313","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 : 2020-07-02DOI: 10.1080/07474946.2020.1823193
N. Mukhopadhyay, Chen Zhang
Abstract In sequential analysis, an experimenter gathers information regarding an unknown functional (parameter) by observing random samples in successive steps. We discuss a number of distribution-free scenarios under a variety of loss functions. The number of observations gathered upon termination is a positive integer-valued random variable, customarily denoted by N. Often, a standardized version of N would follow an approximate normal distribution in the asymptotic sense. We provide exploratory data analysis (EDA) with the help of a number of interesting illustrations. We do so via large-scale simulation studies to demonstrate broad applicability of the purely sequential methodologies along with the appropriateness of asymptotic normality of the standardized stopping variables as a practical and useful guideline.
{"title":"EDA on the asymptotic normality of the standardized sequential stopping times, Part-II: Distribution-free models","authors":"N. Mukhopadhyay, Chen Zhang","doi":"10.1080/07474946.2020.1823193","DOIUrl":"https://doi.org/10.1080/07474946.2020.1823193","url":null,"abstract":"Abstract In sequential analysis, an experimenter gathers information regarding an unknown functional (parameter) by observing random samples in successive steps. We discuss a number of distribution-free scenarios under a variety of loss functions. The number of observations gathered upon termination is a positive integer-valued random variable, customarily denoted by N. Often, a standardized version of N would follow an approximate normal distribution in the asymptotic sense. We provide exploratory data analysis (EDA) with the help of a number of interesting illustrations. We do so via large-scale simulation studies to demonstrate broad applicability of the purely sequential methodologies along with the appropriateness of asymptotic normality of the standardized stopping variables as a practical and useful guideline.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1823193","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59425321","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 : 2020-04-02DOI: 10.1080/07474946.2020.1767406
J. Noonan, A. Zhigljavsky
Abstract In this article we discuss an online moving sum (MOSUM) test for detection of a transient change in the mean of a sequence of independent and identically distributed (i.i.d.) normal random variables. By using a well-developed theory for continuous time Gaussian processes and subsequently correcting the results for discrete time, we provide accurate approximations for the average run length (ARL) and power of the test. We check theoretical results against simulations, compare the power of the MOSUM test with that of the cumulative sum (CUSUM), and briefly consider the cases of nonnormal random variables and weighted sums.
{"title":"Power of the MOSUM test for online detection of a transient change in mean","authors":"J. Noonan, A. Zhigljavsky","doi":"10.1080/07474946.2020.1767406","DOIUrl":"https://doi.org/10.1080/07474946.2020.1767406","url":null,"abstract":"Abstract In this article we discuss an online moving sum (MOSUM) test for detection of a transient change in the mean of a sequence of independent and identically distributed (i.i.d.) normal random variables. By using a well-developed theory for continuous time Gaussian processes and subsequently correcting the results for discrete time, we provide accurate approximations for the average run length (ARL) and power of the test. We check theoretical results against simulations, compare the power of the MOSUM test with that of the cumulative sum (CUSUM), and briefly consider the cases of nonnormal random variables and weighted sums.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1767406","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42087429","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 : 2020-04-02DOI: 10.1080/07474946.2020.1766875
A. Novikov, Juan Luis Palacios-Soto
Abstract We consider a problem of sequential testing a simple hypothesis against a simple alternative, based on observations of a discrete-time stochastic process in the presence of a random horizon H. At any time n of the experiment, the statistician is only informed whether H > n or not. In this latter case, the experiment should be terminated and the final decision on the acceptance or rejection of the hypothesis should be taken on the basis of the available observations ( ). H is assumed to be independent of the observations, and its distribution is known to the statistician. Under the random horizon, we consider a variant of the modified Kiefer-Weiss problem: given restrictions on the probabilities of errors, minimize the average sample size calculated under the assumption that the observations follow a fixed distribution, not necessarily one of those hypothesized. Under suitable conditions on the process and/or the horizon, we characterize the structure of all optimal sequential tests in this problem. Then, we apply these results to characterize optimal tests in the case of independent observations. On the basis of the general theory, more specific results are obtained for independent and identically distributed (i.i.d.) observations with a geometrically distributed horizon. In a simple sampling model, we solve the Kiefer-Weiss problem under the random horizon model. We also discuss the questions of Wald-Wolfowitz optimality in the presence of the random horizon. In particular, we show that the stopping rules of the optimal tests, minimizing the average sample size under one of the hypotheses, are randomized versions of those of Wald’s sequential probability ratio tests.
{"title":"Sequential hypothesis tests under random horizon","authors":"A. Novikov, Juan Luis Palacios-Soto","doi":"10.1080/07474946.2020.1766875","DOIUrl":"https://doi.org/10.1080/07474946.2020.1766875","url":null,"abstract":"Abstract We consider a problem of sequential testing a simple hypothesis against a simple alternative, based on observations of a discrete-time stochastic process in the presence of a random horizon H. At any time n of the experiment, the statistician is only informed whether H > n or not. In this latter case, the experiment should be terminated and the final decision on the acceptance or rejection of the hypothesis should be taken on the basis of the available observations ( ). H is assumed to be independent of the observations, and its distribution is known to the statistician. Under the random horizon, we consider a variant of the modified Kiefer-Weiss problem: given restrictions on the probabilities of errors, minimize the average sample size calculated under the assumption that the observations follow a fixed distribution, not necessarily one of those hypothesized. Under suitable conditions on the process and/or the horizon, we characterize the structure of all optimal sequential tests in this problem. Then, we apply these results to characterize optimal tests in the case of independent observations. On the basis of the general theory, more specific results are obtained for independent and identically distributed (i.i.d.) observations with a geometrically distributed horizon. In a simple sampling model, we solve the Kiefer-Weiss problem under the random horizon model. We also discuss the questions of Wald-Wolfowitz optimality in the presence of the random horizon. In particular, we show that the stopping rules of the optimal tests, minimizing the average sample size under one of the hypotheses, are randomized versions of those of Wald’s sequential probability ratio tests.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766875","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45262977","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 : 2020-04-02DOI: 10.1080/07474946.2020.1766887
P. Meyvisch
Abstract Bioequivalence (BE) trials are sometimes preceded by a pilot relative bioavailability (BA) trial to investigate whether the test formulation is sufficiently similar to the reference. The geometric mean ratio and its confidence bounds provide guidance as to how the BE trial can be appropriately sized to attain sufficient power. The aim of this work is to optimize the sample size of a pilot BA trial in order to minimize the overall sample size for the combination of pilot and pivotal trials. This is done through specification of a gain function associated with any of two possible outcomes of the trial; that is, abandon further development of the test formulation or proceed to a pivotal BE trial. The gain functions will be constructed on the basis of sample size considerations only, because subject numbers are indicative of both the cost and the feasibility of a clinical trial. Using simulations, it is demonstrated that for drugs with high intrasubject variability, the BA trial should be sufficiently sized to avoid erroneous decision making and to control the overall cost. In contrast, when the intrasubject variability of the pharmacokinetic (PK) parameters is low, not conducting the BA trial should be considered. It is concluded that the rather typical practice of conducting small pilot trials is unlikely to be a cost-effective approach.
{"title":"Optimizing sample size in relative bioavailability trials using a Bayesian decision-theoretic framework","authors":"P. Meyvisch","doi":"10.1080/07474946.2020.1766887","DOIUrl":"https://doi.org/10.1080/07474946.2020.1766887","url":null,"abstract":"Abstract Bioequivalence (BE) trials are sometimes preceded by a pilot relative bioavailability (BA) trial to investigate whether the test formulation is sufficiently similar to the reference. The geometric mean ratio and its confidence bounds provide guidance as to how the BE trial can be appropriately sized to attain sufficient power. The aim of this work is to optimize the sample size of a pilot BA trial in order to minimize the overall sample size for the combination of pilot and pivotal trials. This is done through specification of a gain function associated with any of two possible outcomes of the trial; that is, abandon further development of the test formulation or proceed to a pivotal BE trial. The gain functions will be constructed on the basis of sample size considerations only, because subject numbers are indicative of both the cost and the feasibility of a clinical trial. Using simulations, it is demonstrated that for drugs with high intrasubject variability, the BA trial should be sufficiently sized to avoid erroneous decision making and to control the overall cost. In contrast, when the intrasubject variability of the pharmacokinetic (PK) parameters is low, not conducting the BA trial should be considered. It is concluded that the rather typical practice of conducting small pilot trials is unlikely to be a cost-effective approach.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766887","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44155228","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 : 2020-04-02DOI: 10.1080/07474946.2020.1766928
Liang Cai
Abstract Motivated by the practical investigation of a state-dependent quickest detection problem in continuous time, especially for Brownian observations, we propose an asymptotic scheme in discrete time called a quickest detection scheme of an accumulated state-dependent change point. Here the state-dependent means that the priori probability of the change point depends on the current state. We reduce the problem to finding an optimal stopping time of a vector-valued Markov process. We illustrate the scheme via a numerical example.
{"title":"Quickest detection of an accumulated state-dependent change point","authors":"Liang Cai","doi":"10.1080/07474946.2020.1766928","DOIUrl":"https://doi.org/10.1080/07474946.2020.1766928","url":null,"abstract":"Abstract Motivated by the practical investigation of a state-dependent quickest detection problem in continuous time, especially for Brownian observations, we propose an asymptotic scheme in discrete time called a quickest detection scheme of an accumulated state-dependent change point. Here the state-dependent means that the priori probability of the change point depends on the current state. We reduce the problem to finding an optimal stopping time of a vector-valued Markov process. We illustrate the scheme via a numerical example.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766928","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42782977","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 : 2020-04-02DOI: 10.1080/07474946.2020.1766893
N. Mukhopadhyay, Zhe Wang
Abstract Two fundamental problems on purely sequential estimation are revisited—(i) the fixed-width confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem—in the context of estimating an unknown mean (μ) in a normal population having an unknown variance ( ). We begin by laying down general frameworks for the second-order asymptotic analyses, in both problems, under sequential sampling of one observation at a time. Then, instead of gathering one observation at a time, we consider sequentially sampling k observations at a time in defining our proposed estimation strategies. We replace the customary sample standard deviation as an estimator for σ with a number of other pertinent estimators to come up with new and more appropriate stopping rules to suit the occasion. We do so because in real life we know that packaged items purchased in bulk often cost less per unit sample than the cost of an individual item. This article builds the whole array of estimation methodologies in order to address both FWCI and MRPE problems with appropriate first-order and second-order asymptotic analyses. These are followed by extensive sets of carefully laid out data analyses assisted via large-scale computer simulations. These are wrapped up with illustrations using breast cancer data.
{"title":"Purely sequential FWCI and MRPE problems for the mean of a normal population by sampling in groups with illustrations using breast cancer data","authors":"N. Mukhopadhyay, Zhe Wang","doi":"10.1080/07474946.2020.1766893","DOIUrl":"https://doi.org/10.1080/07474946.2020.1766893","url":null,"abstract":"Abstract Two fundamental problems on purely sequential estimation are revisited—(i) the fixed-width confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem—in the context of estimating an unknown mean (μ) in a normal population having an unknown variance ( ). We begin by laying down general frameworks for the second-order asymptotic analyses, in both problems, under sequential sampling of one observation at a time. Then, instead of gathering one observation at a time, we consider sequentially sampling k observations at a time in defining our proposed estimation strategies. We replace the customary sample standard deviation as an estimator for σ with a number of other pertinent estimators to come up with new and more appropriate stopping rules to suit the occasion. We do so because in real life we know that packaged items purchased in bulk often cost less per unit sample than the cost of an individual item. This article builds the whole array of estimation methodologies in order to address both FWCI and MRPE problems with appropriate first-order and second-order asymptotic analyses. These are followed by extensive sets of carefully laid out data analyses assisted via large-scale computer simulations. These are wrapped up with illustrations using breast cancer data.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766893","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42921311","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 : 2020-04-02DOI: 10.1080/07474946.2020.1766930
N. Mukhopadhyay, Ya. G. Khariton
Abstract We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.
{"title":"Minimum risk point estimation (MRPE) of the mean in an exponential distribution under powered absolute error loss (PAEL) due to estimation plus cost of sampling","authors":"N. Mukhopadhyay, Ya. G. Khariton","doi":"10.1080/07474946.2020.1766930","DOIUrl":"https://doi.org/10.1080/07474946.2020.1766930","url":null,"abstract":"Abstract We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766930","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48288940","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}