scholarly journals Conditional Monte Carlo randomization tests for regression models

2014 ◽  
Vol 33 (18) ◽  
pp. 3078-3088 ◽  
Author(s):  
Parwen Parhat ◽  
William F. Rosenberger ◽  
Guoqing Diao
Keyword(s):  
Monte Carlo ◽  
Regression Models ◽  
Randomization Tests ◽  
Conditional Monte Carlo ◽  
Monte Carlo Randomization

scholarly journals Interactions in Fixed Effects Regression Models

2020 ◽  
pp. 004912412091493
Author(s):  
Marco Giesselmann ◽  
Alexander W. Schmidt-Catran
Keyword(s):  
Monte Carlo ◽  
Time Constant ◽  
Fixed Effects ◽  
Regression Models ◽  
Time Varying ◽  
Unit Level ◽  
Monte Carlo Experiments ◽  
Product Term ◽  
Fixed Effects Regression ◽  
Effect Heterogeneity

An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, algebraic transformations reveal that this strategy does not yield a within-unit estimator. Instead, the standard FE interaction estimator reflects unit-level differences of the interacted variables. This property allows interactions of a time-constant variable and a time-varying variable in FE to be estimated but may yield unwanted results if both variables vary within units. In such cases, Monte Carlo experiments confirm that the standard FE estimator of x ⋅ z is biased if x is correlated with an unobserved unit-specific moderator of z (or vice versa). A within estimator of an interaction can be obtained by first demeaning each variable and then demeaning their product. This “double-demeaned” estimator is not subject to bias caused by unobserved effect heterogeneity. It is, however, less efficient than standard FE and only works with T > 2.

Evaluating the Statistical Significance of Models Developed by Stepwise Regression

1983 ◽  
Vol 20 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Shelby H. McIntyre ◽  
David B. Montgomery ◽  
V. Srinivasan ◽  
Barton A. Weitz
Keyword(s):  
Monte Carlo ◽  
Null Hypothesis ◽  
Regression Models ◽  
Stepwise Regression ◽  
Statistical Significance ◽  
Selection Procedure ◽  
Coefficient Of Determination ◽  
Forward Selection ◽  
Monte Carlo Simulation Study ◽  
Independent Variables

Information for evaluating the statistical significance of stepwise regression models developed with a forward selection procedure is presented. Cumulative distributions of the adjusted coefficient of determination ([Formula: see text]) under the null hypothesis of no relationship between the dependent variable and m potential independent variables are derived from a Monté Carlo simulation study. The study design included sample sizes of 25, 50, and 100, available independent variables of 10, 20, and 40, and three criteria for including variables in the regression model. The results reveal that the biases involved in testing statistical significance by two well-known rules are very large, thus demonstrating the desirability of using the Monté Carlo cumulative [Formula: see text] distributions developed by the authors. Although the results were derived under the assumption of uncorrelated predictors, the authors show that the results continue to be useful for the correlated predictor case.

scholarly journals Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

2019 ◽  
Vol 11 (3) ◽  
pp. 815 ◽  
Author(s):  
Yijuan Liang ◽  
Xiuchuan Xu
Keyword(s):  
Monte Carlo ◽  
Variance Reduction ◽  
Convergence Rates ◽  
Option Price ◽  
Correlation Coefficients ◽  
Control Variate ◽  
Stochastic Volatilities ◽  
Conditional Monte Carlo ◽  
Mc Simulation ◽  
Martingale Representation Theorem

Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.

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