scholarly journals Testing a Parametric Model Against a Semiparametric Alternative

1994 ◽  
Vol 10 (5) ◽  
pp. 821-848 ◽  
Author(s):  
Joel L. Horowitz ◽  
Wolfgang Härdle
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Random Variable ◽  
Parametric Model ◽  
Conditional Moment ◽  
Moment Conditions ◽  
Explanatory Variables ◽  
Conditional Moments ◽  
Monte Carlo Experiments ◽  
The Mean

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.

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 An Efficient Estimation of the Mean Residual Life Function with Length-Biased Right-Censored Data

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongping Wu ◽  
Yihui Luan
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Residual Life ◽  
Random Variable ◽  
Efficient Estimation ◽  
Mean Residual Life ◽  
Right Censored Data ◽  
Monte Carlo Simulation Study ◽  
The Mean ◽  
Model Setup

The mean residual life (MRL) function for a lifetime random variableT0is one of the basic parameters of interest in survival analysis. In this paper, we propose a new estimator of the MRL function with length-biased right-censored data and evaluate its performance through a small Monte Carlo simulation study. The results of the simulations show that the proposed estimator outperforms the existing one referred to in Data and Model Setup Section in terms of Monte Carlo bias and mean square error, especially when the censoring rate is heavy. We also show that the proposed estimator converges in distribution under some conditions.

On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity

1994 ◽  
Vol 10 (1) ◽  
pp. 70-90 ◽  
Author(s):  
R.M. de Jong ◽  
H.J. Bierens
Keyword(s):  
Infinite Number ◽  
Fixed Number ◽  
Model Specification ◽  
Test Statistic ◽  
Conditional Moment ◽  
Chi Square ◽  
Moment Conditions ◽  
Conditional Moments ◽  
Finite Samples ◽  
Consistent Model

In this paper, a consistent model specification test is proposed. Some consistent model specification tests have been discussed in econometrics literature. Those tests are consistent by randomization, display a discontinuity in sample size, or have an asymptotic distribution that depends on the data-generating process and on the model, whereas our test does not have one of those disadvantages. Our test can be viewed upon as a conditional moment test as proposed by Newey but instead of a fixed number of conditional moments, an asymptotically infinite number of moment conditions is employed. The use of an asymptotically infinite number of conditional moments will make it possible to obtain a consistent test. Computation of the test statistic is particularly simple, since in finite samples our statistic is equivalent to a chi-square conditional moment test of a finite number of conditional moments.

A Comment on Diagnostic Tools for Counterfactual Inference

2009 ◽  
Vol 17 (1) ◽  
pp. 89-106 ◽  
Author(s):  
Nicholas Sambanis ◽  
Alexander Michaelides
Keyword(s):  
Monte Carlo ◽  
Political Science ◽  
Diagnostic Tools ◽  
Counterfactual Analysis ◽  
Data Sets ◽  
Explanatory Variables ◽  
Monte Carlo Experiments ◽  
Data Points

We evaluate two diagnostic tools used to determine if counterfactual analysis requires extrapolation. Counterfactuals based on extrapolation are model dependent and might not support empirically valid inferences. The diagnostics help researchers identify those counterfactual “what if” questions that are empirically plausible. We show, through simple Monte Carlo experiments, that these diagnostics will often detect extrapolation, suggesting that there is a risk of biased counterfactual inference when there is no such risk of extrapolation bias in the data. This is because the diagnostics are affected by what we call the n/k problem: as the number of data points relative to the number of explanatory variables decreases, the diagnostics are more likely to detect the risk of extrapolation bias even when such risk does not exist. We conclude that the diagnostics provide too severe a test for many data sets used in political science.

Estimation of Random Variable Distribution Parameters by the Monte Carlo Method

2013 ◽  
Vol 20 (2) ◽  
pp. 249-262 ◽  
Author(s):  
Sergiusz Sienkowski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Variable ◽  
Statistical Parameters ◽  
The Monte Carlo Method ◽  
Variable Distribution ◽  
Distribution Parameters ◽  
The Subject ◽  
The Mean ◽  
Typical Measurement

Abstract The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.

On Monte Carlo Estimates in Network Reliability

1994 ◽  
Vol 8 (2) ◽  
pp. 245-264 ◽  
Author(s):  
M. Lomonosov
Keyword(s):  
Monte Carlo ◽  
Markov Process ◽  
Critical Point ◽  
Natural Condition ◽  
Network Reliability ◽  
Random Variable ◽  
Mean Value ◽  
Reliability Measures ◽  
The Mean ◽  
Edge Failure

The paper considers representations of network reliability measures as the mean value of a random variable defined on the trajectories of a certain Markov process and investigates utility of such formulae for Monte Carlo (MC) estimating. Such an MC estimator is called (ε,δ)-polynomial if its relative error is less than ε with probability >1 – δ, for any sample size equal to or greater than a polynomial of ε-1, δ-1, and the size of the network. One of the main results: The suggested MC estimator for the disconnectedness probability of a multiterminal network is (ε,δ)-polynomial, under a certain natural condition on the edge failure probabilities. The method applies also to estimating the percolation critical point and certain equilibrium characteristics of renewal networks.

scholarly journals NONPARAMETRIC SIGNIFICANCE TESTING

2000 ◽  
Vol 16 (4) ◽  
pp. 576-601 ◽  
Author(s):  
Pascal Lavergne ◽  
Quang Vuong
Keyword(s):  
Monte Carlo ◽  
Null Hypothesis ◽  
Kernel Method ◽  
Significance Testing ◽  
Local Alternatives ◽  
Test Statistic ◽  
Explanatory Variables ◽  
Monte Carlo Experiments ◽  
Standard Normal ◽  
Complete Set

A procedure for testing the significance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has an nhp2/2 standard normal limiting distribution, where p2 is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detects local alternatives approaching the null at rate slower than n−1/2h−p2/4. Our Monte-Carlo experiments indicate that it outperforms the test proposed by Fan and Li (1996, Econometrica 64, 865–890).

scholarly journals Estimation of Stochastic Frontier Models with Fixed Effects through Monte Carlo Maximum Likelihood

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Grigorios Emvalomatis ◽  
Spiro E. Stefanou ◽  
Alfons Oude Lansink
Keyword(s):  
Monte Carlo ◽  
Random Effects ◽  
Fixed Effects ◽  
Likelihood Function ◽  
Stochastic Frontier ◽  
General Context ◽  
Explanatory Variables ◽  
Monte Carlo Experiments ◽  
Incidental Parameters ◽  
Stochastic Frontier Models

Estimation of nonlinear fixed-effects models is plagued by the incidental parameters problem. This paper proposes a procedure for choosing appropriate densities for integrating the incidental parameters from the likelihood function in a general context. The densities are based on priors that are updated using information from the data and are robust to possible correlation of the group-specific constant terms with the explanatory variables. Monte Carlo experiments are performed in the specific context of stochastic frontier models to examine and compare the sampling properties of the proposed estimator with those of the random-effects and correlated random-effects estimators. The results suggest that the estimator is unbiased even in short panels. An application to a cross-country panel of EU manufacturing industries is presented as well. The proposed estimator produces a distribution of efficiency scores suggesting that these industries are highly efficient, while the other estimators suggest much poorer performance.

scholarly journals Risk Assessment of Power Generated from a Wind Turbine in Different Climate Cities in Indonesia.

2019 ◽  
Vol 2 (1) ◽  
pp. 97-102
Author(s):  
Irvan Lumban Gaol ◽  
Charles O. P. Marpaung
Keyword(s):  
Risk Assessment ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Wind Speed ◽  
Wind Turbine ◽  
Power Density ◽  
Upper Bound ◽  
Random Variable ◽  
The Mean ◽  
Software Risk

In this paper, a risk analysis based on Monte Carlo Simulation has been used to examine the power generated from a wind turbine. There are five cities are selected based on the wind speed to be examined the power density generated from the wind turbine. The cities are Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak. Among the five cities, Kupang has the highest wind speed, while Pontianak has the lowest wind speed. In this study, the wind speed is assumed to be an unspecified parameter or a random variable. The Monte Carlo Simulation is run by using a software @RISK. The results show that the mean of power density generated from the wind turbine is found 171.23, 113.97, 71.28, 28.67, and 12.49 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively. The width of the confidence interval with the level of probability 90% is 110.30, 75.00, 69.10, 19.64, and 7.34 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively. The upper bound of the confidence intervals are 230.1, 154.7, 113.3, 39.27, and 16.30 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively, while the lower bounds are 119.8, 79.7, 44.2, and 19.63 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively. The probability of the power density will exceed the upper bound or will below the lower bound is 5%.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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