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## Tópicos em penalidades exatas diferenciáveis; Topics in differentiable exact penalties

## Time in the stair-climbing test as a predictor of thoracotomy postoperative complications

## The weak patch test for nonhomogeneous materials modeled with graded finite elements

## Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

## Méthodes d’inférence exactes pour un modèle de régression avec erreurs AR(2) gaussiennes

## Exact side effects for interprocedural dependence analysis

## Rank test of location optimal for hyperbolic secant distribution

## Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms

## Exact goodness-of-fit tests for censored dats

## Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

## Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

## Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

## Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

## Exact Tests for Contemporaneous Correlation of Disturbances in Seemingly Unrelated Regressions.

## Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

## Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

## Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics

## Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

## Spinning massive test particles in cosmological and general static spherically symmetric spacetimes

## Simulation Study on Exchangeability and Significant Test on Survey Data

The two years of Master of Science in Statistical and Economic Modeling program is the most rewarding time ever in my life. This thesis acts as a portfolio of project and applied experience while I am enrolled in the Master of Science in Statistical and Economic Modeling program. This thesis will summarize my graduate study in two parts: Simulation Study of Exchangeability for Binary Data, and Summary of Summer Internship at Center for Responsible Lending. The project of Simulation Study of Exchangeability for Binary Data contains materials from a team project, which jointly performed by Sheng Jiang, Xuan Sun and me. Abstracts for both projects are below in order.

(1) Simulation Study of Exchangeability for Binary Data

To investigate tractable Bayesian tests on exchangeability, this project considers special cases of nonexchangeable random sequences: Markov chains. Asymptotic results of Bayes factor (BF) are derived. When null hypothesis is true, Bayes Factor in favor of the null goes to infinity at geometric rate (true odds is not one half). When null hypothesis is not true, Bayes Factor in favor of the null goes to 0 faster than geometric rate. The results are robust under misspecifications. Simulation studies are employed to see the performance of the test when the sample size is small...