A bootstrap calculation of confidence regions for proportions of sediment contributed by different source areas in a ‘fingerprinting’ model

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

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Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

Discrete Dynamics in Nature and Society ◽

10.1155/2020/8893594 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Hanji He ◽

Guangming Deng

Keyword(s):

Empirical Likelihood ◽

Missing At Random ◽

Confidence Regions ◽

Likelihood Inference ◽

High Dimensional ◽

Finite Sample ◽

The Mean ◽

Data Missing ◽

Consistency And Asymptotic Normality ◽

The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

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Presumed Trade and Aberrant Pottery

Memoirs of the Society for American Archaeology ◽

10.1017/s0081130000004901 ◽

1949 ◽

Vol 5 ◽

pp. 130-145

Author(s):

Alex D. Krieger

Keyword(s):

Mississippi Valley ◽

Lower Mississippi Valley ◽

Great Range ◽

Source Areas ◽

Site Occupation ◽

Foreign Origin ◽

Pronounced Deviation

The pottery in the following sections is not considered to belong to the Alto Focus complex, but to occur with it at different points in the Davis site occupation by trade or other means. If the writer appears to vacillate over what is and what is not trade pottery here, it is due in part to the problem of separating what could have been produced at the site (as extreme variations of resident styles) from what probably was not (because of some distinctive attribute which would mark it as foreign). In certain cases of pronounced deviation, a foreign origin is obvious enough, particularly when the source areas are well known. But where the whole tradition is similar as in the clay-tempered pottery of the lower Mississippi Valley region, and a great range of decorative techniques was employed for long periods of time, the problem is not easy.

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