scholarly journals Symmetry, Regression Design, and Sampling Distributions

1994 ◽  
Vol 10 (1) ◽  
pp. 116-129 ◽  
Author(s):  
Andrew Chesher ◽  
Simon Peters
Keyword(s):  
Monte Carlo ◽  
Sampling Distribution ◽  
Small Samples ◽  
Monte Carlo Experiment ◽  
Conditional Distributions ◽  
Monte Carlo Experiments ◽  
Least Squares Estimators ◽  
Sampling Distributions ◽  
Regression Design ◽  
Require Response

When values of regressors are symmetrically disposed, many M-estimators in a wide class of models have a reflection property, namely, that as the signs of the coefficients on regressors are reversed, their estimators' sampling distribution is reflected about the origin. When the coefficients are zero, sign reversal can have no effect. So in this case, the sampling distribution of regression coefficient estimators is symmetric about zero, the estimators are median unbiased and, when moments exist, the estimators are exactly uncorrelated with estimators of other parameters. The result is unusual in that it does not require response variates to have symmetric conditional distributions. It demonstrates the potential importance of covariate design in determining the distributions of estimators, and it is useful in designing and interpreting Monte Carlo experiments. The result is illustrated by a Monte Carlo experiment in which maximum likelihood and symmetrically censored least-squares estimators are calculated for small samples from a censored normal linear regression, Tobit, model.

scholarly journals Real-virtual Monte Carlo simulation on impulse-momentum and collisions

2019 ◽  
Vol 13 (1) ◽  
pp. 7
Author(s):  
Wartono Wartono ◽  
Dwi Hartoyo ◽  
Nilasari Nilasari ◽  
John Rafafy Batlolona
Keyword(s):  
Monte Carlo ◽  
Scientific Literacy ◽  
Inquiry Learning ◽  
Monte Carlo Experiment ◽  
Control Group ◽  
Learning Models ◽  
Monte Carlo Experiments ◽  
Quasi Experimental ◽  
Conventional Models ◽  
Literacy Scores

<p>This study aims to determine the differences in scientific literacy of students who were given inquiry learning through a real-virtual Monte Carlo experiment with students who were given conventional learning. This study used quasi experimental design with pretest-posttest control group. The results showed that the ability of students who were taught by inquiry learning models through real-virtual Monte Carlo experiments had higher scientific literacy than those taught with conventional models, it also applied well to students with high and low initial abilities. The results of the average gain in scientific literacy scores also showed a higher value between students who studied with the inquiry model through a real-virtual Monte Carlo experiment with students who studied with conventional models. The novelty of this research is combining real and virtual activities become real-virtual Monte Carlo by using the inquiry learning model to improve students' scientific literacy.</p>

The distribution of the geometric mean

2006 ◽  
Vol 90 (517) ◽  
pp. 40-49 ◽  
Author(s):  
David A. L. Wilson ◽  
Barry Martin
Keyword(s):  
Sample Size ◽  
Observational Data ◽  
Geometric Mean ◽  
Sampling Distribution ◽  
Small Samples ◽  
General Description ◽  
Mathematical Study ◽  
New Techniques ◽  
Sampling Distributions ◽  
Large Sample Theory

Although a number of earlier researchers had used the geometric mean as a convenient statistic to summarise observational data, Gallon is usually credited with being the first to consider its sampling distribution. At Gallon’s request, in 1879 McAlister undertook a pioneering mathematical study, which eventually led to the modern large-sample theory. However, some sixty years elapsed before much attention was paid to small samples from particular parent distributions. Since about 1960, new techniques have made it possible to derive exact sampling distributions for a much wider class of parent distributions. Some work has been done on producing approximate general relationships between the moments of the parent distribution and those of the sample geometric mean but they are of very limited value for small samples and even now it is difficult to find any general description of how the distribution from which a sample is drawn will affect the distribution of its geometric mean and how this will vary with sample size.

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

scholarly journals Closed-Form Asymptotic Sampling Distributions under the Coalescent with Recombination for an Arbitrary Number of Loci

2012 ◽  
Vol 44 (2) ◽  
pp. 391-407 ◽  
Author(s):  
Anand Bhaskar ◽  
Yun S. Song
Keyword(s):  
Asymptotic Expansion ◽  
Closed Form ◽  
Recombination Rate ◽  
Functional Form ◽  
Asymptotic Series ◽  
Sampling Distribution ◽  
Challenging Problem ◽  
Sampling Distributions ◽  
Asymptotic Sampling ◽  
New Framework

Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on an asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.

PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS

2006 ◽  
Vol 17 (11) ◽  
pp. 1527-1549 ◽  
Author(s):  
J. N. CORCORAN ◽  
U. SCHNEIDER ◽  
H.-B. SCHÜTTLER
Keyword(s):  
Monte Carlo ◽  
Feynman Graph ◽  
Sampling Technique ◽  
Small Samples ◽  
Brute Force ◽  
Perfect Sampling ◽  
Self Energy ◽  
Graph Expansions ◽  
Low Dimensional ◽  
True Values

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

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