Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Applied Probability and Queues.

We consider fixed-size estimation for a linear function of means from independent and normally distributed populations having unknown and respective variances We construct a fixed-width confidence interval with required accuracy about the magnitude of the length and the confidence coefficient We propose a two-stage estimation methodology having the asymptotic second-order consistency with the required accuracy The key is the asymptotic second-order analysis about the risk function We give a variety of asymptotic characteristics about the estimation methodology, such as asymptotic sample size and asymptotic Fisher-information With the help of the asymptotic second-order analysis, we also explore a number of generalizations and extensions of the two-stage methodology to such as bounded risk point estimation, multiple comparisons among components between the populations, and power analysis in equivalence tests to plan the appropriate sample size for a study

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Asymptotic second-order consistency for two-stage estimation methodologies and its applications

In this study, a renewal-reward process with a discrete interference of chance is constructed and considered. Under weak conditions, the ergodicity of the process X(t) is proved and exact formulas for the ergodic distribution and its moments are found. Within some assumptions for the discrete interference of chance in general form, two-term asymptotic expansions for all moments of the ergodic distribution are obtained. Additionally, kurtosis coefficient, skewness coefficient, and coefficient of variation of the ergodic distribution are computed. As a special case, a semi-Markovian inventory model of type (s, S) is investigated.

Asymptotic approach for a renewal-reward process with a general interference of chance

We consider equivalence tests that control both size and power for a difference of means from , i = 1,2. We give equivalence test procedures in two-stage sampling for both the cases and . The test procedures control both size and power with second-order accuracy. We also consider some related problems in clinical trials. Two examples are given to illustrate how the methodologies should be used.

Two-Stage Equivalence Tests That Control Both Size and Power

Aras and Woodroofe (1993) provide asymptotic expansions of the first four moments of ¯ Xt := St/t where t = ta =i nf{n ≥ 1: Zn >a }, Zn = n + YT. Martinsek (1983) obtained the second order expansion of the risk of this sequential estimation procedure, assuming the initial sample size m →∞ at a certain rate (but without specifying the form of distribution). If the initial sample size m is assumed to be prefixed, the second order expansion of the risk has been established by Woodroofe (1977) but only for normally distributed Yi .T he present paper provides the second order expansion of the risk under assumptions that m is prefixed and that the Yi is continuous with a bounded probability density function.

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Asymptotic expansions for the moments of a randomly stopped average: extension and applications of a result of aras and woodroofe

A note on Hall's triple sampling procedure: A multiple sample second order sequential analogue of the Behrens–Fisher problem

It is important to classify academic papers in a fine-grained manner to uncover deeper implicit themes and semantics in papers for better semantic retrieval, paper recommendation, research trend prediction, topic analysis, and a series of other functions. Based on the ontology of the climate change domain, this study used an unsupervised approach to combine two methods, syntactic structure and semantic modeling, to build a framework of subject-indexing techniques for academic papers in the climate change domain. The framework automatically indexes a set of conceptual terms as research topics from the domain ontology by inputting the titles, abstracts and keywords of the papers using natural language processing techniques such as syntactic dependencies, text similarity calculation, pre-trained language models, semantic similarity calculation, and weighting factors such as word frequency statistics and graph path calculation. Finally, we evaluated the proposed method using the gold standard of manually annotated articles and demonstrated significant improvements over the other five alternative methods in terms of precision, recall and F1-score. Overall, the method proposed in this study is able to identify the research topics of academic papers more accurately, and also provides useful references for the application of domain ontologies and unsupervised data annotation.

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Research on the Automatic Subject-Indexing Method of Academic Papers Based on Climate Change Domain Ontology

The central limit theorem for a normalized summation of random number of i.i.d. random variables is well known. In this paper we improve the central limit theorem by providing a two-term expansion for the distribution when the random number is the first time that a simple random walk exceeds a given level. Some numerical evidences are provided to show that this expansion is more accurate than the simple normality approximation for a specific problem considered.

Nan Wang

Papers

Asymptotic expansions for the moments of a randomly stopped average: extension and applications of a result of aras and woodroofe

A note on Hall's triple sampling procedure: A multiple sample second order sequential analogue of the Behrens–Fisher problem

Research on the Automatic Subject-Indexing Method of Academic Papers Based on Climate Change Domain Ontology

Expansions for the distributions of some normalized summations of random numbers of I.I.D. random variables

Pyrolysis mechanism of R601a/R245fa mixture: A ReaxFF-MD and DFT study