Bayesian Estimation of the Number of Change Points in Simple Linear Regression Models

A Bayesian approach is considered to detect the number of change points in simple linear regression models. A normal-gamma empirical prior for the regression parameters based on maximum likelihood estimator (MLE) is employed in the analysis. Under mild conditions, consistency for the number of change points and boundedness between the estimated location and the true location of the change points are established. The Bayesian approach to the detection of the number of change points is suitable whether the switching simple regression is continuous or discontinuous. Some simulation results are given to confirm the accuracy of the proposed estimator.     

Some Properties of Semi-Folding Designs

Suppose that some information is available for the particular factor. The experimenter may apply the technique of foldover to isolate the factor and the two-factor interactions involving this factor. In fact, under some situations this can be done by the method of semi-folding. We will discuss this property in detail in this article. Furthermore, we use the computer to search the corresponding optimal semi-folding design for the given 2 ^k?p designs that are tabulated in Chen et al. (1993 Chen , J. , Sun , D. X. , Wu , C. F. J. ( 1993 ). A catalogue of two-level and three-level fractional factorial designs with small runs . International Statistical Review 61 : 131 – 145 .[Crossref], [Web of Science ®] , [Google Scholar]) research.     

Asymptotic Optimal Estimation of Poisson Mean Under LINEX Loss Function

In this article, we consider the problem of sequentially estimating the mean of a Poisson distribution under LINEX (linear exponential) loss function and fixed cost per observation within a Bayesian framework. An asymptotically pointwise optimal rule with a prior distribution is proposed and shown to be asymptotically optimal for arbitrary priors. The proposed asymptotically pointwise optimal rule is illustrated using a real data set.     

Is Each NPMLE of a Continuous Bivariate Distribution Function with Singly Right-Censored Data Really Inconsistent?

We consider non-parametric estimation of a continuous cdf of a random vector (X ₁, X ₂). With bivariate RC data, it is stated in van der Laan (1996 Van der Laan , M. J. ( 1996 ) Efficient estimation in the bivariate censoring model and repairing NPMLE . Ann. Statist. 24 : 596 – 627 .[Crossref], [Web of Science ®] , [Google Scholar], p. 598¹⁰, Ann. Statist.), Quale et al. (2006 Quale , C. M. , van der Laan , M. J. , Robins , J. R. ( 2006 ). Locally efficient estimation with bivariate right-censored data . JASA. 101 : 1076 – 1084 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], JASA) etc. that “it is well known that the NPMLE for continuous data is inconsistent (Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar])).” The claim is based on a result in Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], p.1352, Ann. Statist.) that if X ₁ is right censored but not X ₂, then common ways for defining one NPMLE lead to inconsistency. If X ₁ is right censored and X ₂ is type I right-censored (which includes the case in Tsai et al.), we present a consistent NPMLE. The result corrects a common misinterpretation of Tsai's example (Tsai et al., 1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], Ann. Statist.).     

New Confidence Intervals for the Proportion of Interest in One-Sample Correlated Binary Data

Correlated binary data is obtained in many fields of biomedical research. When constructing a confidence interval for the proportion of interest, asymptotic confidence intervals have already been developed. However, such asymptotic confidence intervals are unreliable in small samples. To improve the performance of asymptotic confidence intervals in small samples, we obtain the Edgeworth expansion of the distribution of the studentized mean of beta-binomial random variables. Then, we propose new asymptotic confidence intervals by correcting the skewness in the Edgeworth expansion in one direct and two indirect ways. New confidence intervals are compared with the existing confidence intervals in simulation studies.     

Dependence Models Arising from the Lagrangian Probability Distributions

In this article, we propose a method based on the Lagrangian probability distributions for developing new dependence models. Specifically, a generalized Poisson–gamma dependence model is derived. The maximum likelihood estimation (MLE) technique is proposed for estimating the dependence model parameters. Application of the generalized Poisson–gamma dependence model is illustrated by using an operational risks dataset.     

The Yule–Walker equations as a weighted least-squares problem and the association with tapering

ABSTRACT

A common method for estimating the time-domain parameters of an autoregressive process is to use the Yule–Walker equations. Tapering has been shown intuitively and proven theoretically to reduce the bias of the periodogram in the frequency domain, but the intuition for the similar bias reduction in the time-domain estimates has been lacking. We provide insightful reasoning for why tapering reduces the bias in the Yule–Walker estimates by showing them to be equivalent to a weighted least-squares problem. This leads to the derivation of an optimal taper which behaves similarly to commonly used tapers.     

Probability of correct selection of weibull versus gamma based on livelihood ratio

This paper proposes the use of tne likelihood ratio statistic in choosing between a Neibull or gamma model, values of the probability of correct seeiection are obtained by Monte Carlo simulation. This method provides some basis for decision even when the sample size is small. The technique is applied to four sets of data from the literature.