Fisher’s “Nile” example is a classic which involves a bivariate random variable ( X, Y ) having a joint probability density function given by f ( x, y ; θ ) = exp( − θx − θ − 1 y ), 0 < x, y < ∞ , where θ > 0 is a single unknown parameter. We develop bounded-length confidence interval estimations for P θ ( X > a ) with a preassigned confidence coefficient using both purely sequential and two-stage methodologies. We show: (i) Both methodologies enjoy asymptotic first-order efficiency and asymptotic consistency properties; (ii) Both methodologies enjoy second-order efficiency properties. After presenting substantial theoretical investigations, we have also imple-mented extensive sets of computer simulations to empirically validate the theoretical properties.
{"title":"Purely Sequential and Two-Stage Bounded-Length Confidence Interval Estimation Problems in Fisher’s “Nile” Example","authors":"N. Mukhopadhyay, Y. Zhuang","doi":"10.14490/JJSS.47.237","DOIUrl":"https://doi.org/10.14490/JJSS.47.237","url":null,"abstract":"Fisher’s “Nile” example is a classic which involves a bivariate random variable ( X, Y ) having a joint probability density function given by f ( x, y ; θ ) = exp( − θx − θ − 1 y ), 0 < x, y < ∞ , where θ > 0 is a single unknown parameter. We develop bounded-length confidence interval estimations for P θ ( X > a ) with a preassigned confidence coefficient using both purely sequential and two-stage methodologies. We show: (i) Both methodologies enjoy asymptotic first-order efficiency and asymptotic consistency properties; (ii) Both methodologies enjoy second-order efficiency properties. After presenting substantial theoretical investigations, we have also imple-mented extensive sets of computer simulations to empirically validate the theoretical properties.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121834361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, two estimation approaches based on age-specific parametric model have been proposed and a comparative study between them has been studied. We assume that outcome variable follows a parametric model, but the parameters are smooth function of time (age). Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the parameters at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. We derived asymptotic properties such as asymptotic biases, variances and mean squared error (MSE) for the local polynomial smoothed estimator and kernel smoothing estimator for the parameter of the time-variant parametric model. A mathematical relationship is established between two asymptotic MSEs. Mathematical relationship between two smoothing estimators has also been established. Applications of our two-step estimation method have been demonstrated through a large demographic study to estimate fecundability. Theoretical results on coverage of bootstrap confidence intervals for these smoothing estimators have been derived. Finite sample properties of our procedures are investigated by a simulation study.
{"title":"Nonparametric Estimation of Time-Variant Parametric Models with Application to Cross-Sectional Data","authors":"M. Chowdhury","doi":"10.14490/JJSS.47.197","DOIUrl":"https://doi.org/10.14490/JJSS.47.197","url":null,"abstract":"In this article, two estimation approaches based on age-specific parametric model have been proposed and a comparative study between them has been studied. We assume that outcome variable follows a parametric model, but the parameters are smooth function of time (age). Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the parameters at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. We derived asymptotic properties such as asymptotic biases, variances and mean squared error (MSE) for the local polynomial smoothed estimator and kernel smoothing estimator for the parameter of the time-variant parametric model. A mathematical relationship is established between two asymptotic MSEs. Mathematical relationship between two smoothing estimators has also been established. Applications of our two-step estimation method have been demonstrated through a large demographic study to estimate fecundability. Theoretical results on coverage of bootstrap confidence intervals for these smoothing estimators have been derived. Finite sample properties of our procedures are investigated by a simulation study.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132606927","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}
The Ewens sampling formula is well-known as a distribution of a random partition of the set of integers {1, 2, . . . , n}. We give the condition that the number Kn of distinct components of the formula converges to the shifted Poisson distribution. Based on this convergence, we give the new approximations to the distribution of Kn, which are different from the approximations by Arratia et al. (2000, 2003). The formers are better than the latters. This is shown by comparing the bounds for the total variation distances between the distributions of the approximations and the distribution of Kn. Several examples are given to illustrate the results.
{"title":"Poisson Approximations for Sum of Bernoulli Random Variables and its Application to Ewens Sampling Formula","authors":"Hajime Yamato","doi":"10.14490/JJSS.47.187","DOIUrl":"https://doi.org/10.14490/JJSS.47.187","url":null,"abstract":"The Ewens sampling formula is well-known as a distribution of a random partition of the set of integers {1, 2, . . . , n}. We give the condition that the number Kn of distinct components of the formula converges to the shifted Poisson distribution. Based on this convergence, we give the new approximations to the distribution of Kn, which are different from the approximations by Arratia et al. (2000, 2003). The formers are better than the latters. This is shown by comparing the bounds for the total variation distances between the distributions of the approximations and the distribution of Kn. Several examples are given to illustrate the results.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126267048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider selecting of the linear and the quadratic discriminant functions in two normal populations. We do not know which of two discriminant functions lowers the expected probability of misclassification. When difference of the covariance matrices is large, it is known that the expected probability of misclassification of the quadratic discriminant functions is smaller than that of linear discriminant function. Therefore, we should consider only the selection when the difference between covariance matrices is small. In this paper we suggest a selection method using asymptotic expansion for the linear and the quadratic discriminant functions when the difference between the covariance matrices is small.
{"title":"Selection of the Linear and the Quadratic Discriminant Functions when the Difference between Two Covariance Matrices is Small","authors":"Tomoyuki Nakagawa, H. Wakaki","doi":"10.14490/JJSS.47.145","DOIUrl":"https://doi.org/10.14490/JJSS.47.145","url":null,"abstract":"We consider selecting of the linear and the quadratic discriminant functions in two normal populations. We do not know which of two discriminant functions lowers the expected probability of misclassification. When difference of the covariance matrices is large, it is known that the expected probability of misclassification of the quadratic discriminant functions is smaller than that of linear discriminant function. Therefore, we should consider only the selection when the difference between covariance matrices is small. In this paper we suggest a selection method using asymptotic expansion for the linear and the quadratic discriminant functions when the difference between the covariance matrices is small.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131677944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to use historical data in the design of sample surveys with a Bayesian approach, the information from the historical data must be expressed as a prior distribution. Then, the best prior distribution for the parameter of interest is a predictive distribution. The density function of the predictive distribution generally is not available in an analytical form. From the perspective of practical use, Schmidli et al. (2014) proposed an approximation for the predictive distribution using a mixture of conjugate prior distributions. Their method relies on random numbers drawn from the predictive distribution. However, if the population distribution includes a nuisance parameter, their method becomes impractical. We propose a new approximation method that does not rely on these simulated numbers. Our approximation instead minimizes the mean squared error between the exact Bayes estimator and the one corresponding to the approximated predictive distribution.
为了在贝叶斯方法的抽样调查设计中使用历史数据，来自历史数据的信息必须表示为先验分布。然后，感兴趣参数的最佳先验分布是预测分布。预测分布的密度函数通常不能用解析形式表示。从实际应用的角度来看，Schmidli et al.(2014)提出了一种使用共轭先验分布混合的预测分布近似。他们的方法依赖于从预测分布中抽取的随机数。但是，如果总体分布包含了一个干扰参数，那么他们的方法就变得不切实际了。我们提出了一种新的不依赖于这些模拟数字的近似方法。相反，我们的近似最小化了精确贝叶斯估计量与近似预测分布对应的估计量之间的均方误差。
{"title":"Approximation of the Meta-Analytic-Predictive Prior Distribution in the One-Way Random Effects Model with Unknown Variance","authors":"Harunori Mori","doi":"10.14490/JJSS.47.167","DOIUrl":"https://doi.org/10.14490/JJSS.47.167","url":null,"abstract":"In order to use historical data in the design of sample surveys with a Bayesian approach, the information from the historical data must be expressed as a prior distribution. Then, the best prior distribution for the parameter of interest is a predictive distribution. The density function of the predictive distribution generally is not available in an analytical form. From the perspective of practical use, Schmidli et al. (2014) proposed an approximation for the predictive distribution using a mixture of conjugate prior distributions. Their method relies on random numbers drawn from the predictive distribution. However, if the population distribution includes a nuisance parameter, their method becomes impractical. We propose a new approximation method that does not rely on these simulated numbers. Our approximation instead minimizes the mean squared error between the exact Bayes estimator and the one corresponding to the approximated predictive distribution.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130184011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we discuss two-sample tests for high-dimension, non-Gaussian data. We suppose that two classes have a strongly spiked eigenvalue model. First, we investigate the noise space for high-dimension, non-Gaussian data. A two-sample test is proposed by using the cross-data-matrix (CDM) methodology and its power is derived under some regularity conditions when the dimension is very large. We discuss the validity of assumptions. We check the performance of the proposed two-sample test procedure by simulations. Finally, we demonstrate the proposed two-sample test in actual data analyses.
{"title":"A High-Dimensional Two-Sample Test for Non-Gaussian Data under a Strongly Spiked Eigenvalue Model","authors":"Aki Ishii","doi":"10.14490/JJSS.47.273","DOIUrl":"https://doi.org/10.14490/JJSS.47.273","url":null,"abstract":"In this paper, we discuss two-sample tests for high-dimension, non-Gaussian data. We suppose that two classes have a strongly spiked eigenvalue model. First, we investigate the noise space for high-dimension, non-Gaussian data. A two-sample test is proposed by using the cross-data-matrix (CDM) methodology and its power is derived under some regularity conditions when the dimension is very large. We discuss the validity of assumptions. We check the performance of the proposed two-sample test procedure by simulations. Finally, we demonstrate the proposed two-sample test in actual data analyses.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128477619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes nonparametric tests for the null hypothesis that a treatment has a zero effect on conditional variance for all subpopulations defined by covariates. Rather than the mean of outcome, which measures to what extent treatment changes the level of outcome, researchers are also interested in how the treatment affects the dispersion of outcome. We use variance to measure the dispersion and estimate the conditional variances by series method. We give a test rule comparing a Wald-type test statistic with the critical value from chi-squared distribution. We also construct a normalized test statistic that is asymptotically standard normal under the null hypothesis. We illustrate the usefulness of the proposed test by Monte Carlo simulations and an empirical example that investigates the effect of unionism on wage dispersion.
{"title":"Nonparametric tests for the effect of treatment on conditional variance","authors":"Yanchun Jin","doi":"10.14490/JJSS.47.107","DOIUrl":"https://doi.org/10.14490/JJSS.47.107","url":null,"abstract":"This paper proposes nonparametric tests for the null hypothesis that a treatment has a zero effect on conditional variance for all subpopulations defined by covariates. Rather than the mean of outcome, which measures to what extent treatment changes the level of outcome, researchers are also interested in how the treatment affects the dispersion of outcome. We use variance to measure the dispersion and estimate the conditional variances by series method. We give a test rule comparing a Wald-type test statistic with the critical value from chi-squared distribution. We also construct a normalized test statistic that is asymptotically standard normal under the null hypothesis. We illustrate the usefulness of the proposed test by Monte Carlo simulations and an empirical example that investigates the effect of unionism on wage dispersion.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115860600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study proposes a spatial extension of time series autoregressive conditional heteroskedasticity (ARCH) models to those for areal data. We call the spatially extended ARCH models as spatial ARCH (S-ARCH) models. S-ARCH models specify conditional variances given surrounding observations, which constitutes a good contrast with time series ARCH models that specify conditional variances given past observations. We estimate the parameters of S-ARCH models by a two-step procedure of least squares and the quasi maximum likelihood estimation, which are validated to be consistent and asymptotically normal. We demonstrate the empirical properties by simulation studies and real data analysis of land price data in Tokyo areas.
{"title":"Spatial Autoregressive Conditional Heteroskedasticity Models","authors":"Takaki Sato, Y. Matsuda","doi":"10.14490/JJSS.47.221","DOIUrl":"https://doi.org/10.14490/JJSS.47.221","url":null,"abstract":"This study proposes a spatial extension of time series autoregressive conditional heteroskedasticity (ARCH) models to those for areal data. We call the spatially extended ARCH models as spatial ARCH (S-ARCH) models. S-ARCH models specify conditional variances given surrounding observations, which constitutes a good contrast with time series ARCH models that specify conditional variances given past observations. We estimate the parameters of S-ARCH models by a two-step procedure of least squares and the quasi maximum likelihood estimation, which are validated to be consistent and asymptotically normal. We demonstrate the empirical properties by simulation studies and real data analysis of land price data in Tokyo areas.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131187204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we develop a method for estimating varying coefficients on effects of covariates without modeling the shape of the spatial-temporal baseline trend. We consider the situation where primary interest is in the effects of covariates and the spatial-temporal baseline trend, though non-negligible, is of secondary interest. This is similar to the situation with the Cox proportional hazards model in survival analysis. Basis functions are used to model the shapes of the varying coefficients, but no particular shape is assumed for the spatial-temporal baseline trend. After the effects of covariates are evaluated, estimates of the spatial-temporal baseline trend can be obtained nonparametrically.
{"title":"Estimating Varying Coefficients for Longitudinal Data without Specifying Spatial-Temporal Baseline Trend","authors":"T. Tonda, K. Satoh","doi":"10.14490/JJSS.47.1","DOIUrl":"https://doi.org/10.14490/JJSS.47.1","url":null,"abstract":"In this paper we develop a method for estimating varying coefficients on effects of covariates without modeling the shape of the spatial-temporal baseline trend. We consider the situation where primary interest is in the effects of covariates and the spatial-temporal baseline trend, though non-negligible, is of secondary interest. This is similar to the situation with the Cox proportional hazards model in survival analysis. Basis functions are used to model the shapes of the varying coefficients, but no particular shape is assumed for the spatial-temporal baseline trend. After the effects of covariates are evaluated, estimates of the spatial-temporal baseline trend can be obtained nonparametrically.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133142378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study adaptive Bayes type estimation and hybrid type estimation of both drift and volatility parameters for small diffusion processes from discrete observations. By applying adaptive maximum likelihood type estimation for small diffusion processes to the Bayesian method and by using the polynomial type large deviation inequality for the statistical random field and Ibragimov-Has’minskiiKutoyants program, the adaptive Bayes type estimators and hybrid type estimators are obtained and we show that they have asymptotic normality and convergence of moments.
{"title":"Adaptive Bayes Estimators and Hybrid Estimators for Small Diffusion Processes Based on Sampled Data","authors":"Ryo Nomura, Masayuki Uchida","doi":"10.14490/JJSS.46.129","DOIUrl":"https://doi.org/10.14490/JJSS.46.129","url":null,"abstract":"We study adaptive Bayes type estimation and hybrid type estimation of both drift and volatility parameters for small diffusion processes from discrete observations. By applying adaptive maximum likelihood type estimation for small diffusion processes to the Bayesian method and by using the polynomial type large deviation inequality for the statistical random field and Ibragimov-Has’minskiiKutoyants program, the adaptive Bayes type estimators and hybrid type estimators are obtained and we show that they have asymptotic normality and convergence of moments.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123889119","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：