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Abstrak :
Suatu pengujian dibutuhkan untuk membandingkan mean dari dua populasi. Pada pengujian beda dua mean populasi ketika kedua variansi populasi tidak diketahui dan diasumsikan variansi sama, statistik ujinya dicari dengan menggunakan dalil limit pusat ketika ukuran sampel besar. Sedangkan ketika ukuran sampel kecil, digunakan uji likelihood rasio. Jika diasumsikan variansi populasi tidak sama, maka statistik ujinya didapat dari penurunan terhadap statistik Welch. Pada pengujian beda dua mean populasi ketika salah satu variansi populasi tidak diketahui, digunakan metode Satterthwaite untuk mencari aproksimasi dari derajat bebasnya. Penaksir dari derajat bebas yang diperoleh merupakan penaksir yang bias. Oleh karena itu, dicari penaksir dari derajat bebas yang tak bias dan memiliki variansi lebih kecil dari penaksir derajat bebas yang bias. Pada tugas akhir ini dibahas contoh pengujian untuk ketiga pengujian tersebut. ...... A test is required to compare the mean of two population. On the test of the difference between two population means when both of the population variances are unknown and with the assumption of the same variance, the test statistic is found using the central limit theorem in which the sample size is large. When the sample size is small, the likelihood ratio test is used. If both of the population variances aren’t assumed to be equal, then the test statistic is obtained from the derivation of the Welch’s statistic. On the test of the difference between two population means when one of the population variance is unknown, the Satterthwaite’s method is used to find the approximation of the degrees of freedom. The estimator of the degrees of freedom obtained is biased. Therefore, the unbiased estimator of degrees of freedom will be determined and it has smaller variance than the biased estimator of the degrees of freedom. This minithesis discussed about the example of the test for those three tests.

Abstrak :
This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used, the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.

Abstrak :
The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior).