scholarly journals Shapley Value Confidence Intervals for Attributing Variance Explained

2020 ◽  
Vol 6 ◽  
Author(s):  
Daniel Fryer ◽  
Inga Strümke ◽  
Hien Nguyen
Keyword(s):  
Real Estate ◽  
Confidence Intervals ◽  
Shapley Value ◽  
Equal Treatment ◽  
Small Samples ◽  
Coefficient Of Determination ◽  
Computational Time ◽  
Monte Carlo Studies ◽  
Shapley Values ◽  
Variance Explained

The coefficient of determination, the R2, is often used to measure the variance explained by an affine combination of multiple explanatory covariates. An attribution of this explanatory contribution to each of the individual covariates is often sought in order to draw inference regarding the importance of each covariate with respect to the response phenomenon. A recent method for ascertaining such an attribution is via the game theoretic Shapley value decomposition of the coefficient of determination. Such a decomposition has the desirable efficiency, monotonicity, and equal treatment properties. Under a weak assumption that the joint distribution is pseudo-elliptical, we obtain the asymptotic normality of the Shapley values. We then utilize this result in order to construct confidence intervals and hypothesis tests for Shapley values. Monte Carlo studies regarding our results are provided. We found that our asymptotic confidence intervals required less computational time to competing bootstrap methods and are able to exhibit improved coverage, especially on small samples. In an expository application to Australian real estate price modeling, we employ Shapley value confidence intervals to identify significant differences between the explanatory contributions of covariates, between models, which otherwise share approximately the same R2 value. These different models are based on real estate data from the same periods in 2019 and 2020, the latter covering the early stages of the arrival of the novel coronavirus, COVID-19.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

An assessment of a daily rainfall erosivity model for New South Wales

Soil Research ◽  
1996 ◽  
Vol 34 (1) ◽  
pp. 139 ◽  
Author(s):  
B Yu ◽  
CJ Rosewell
Keyword(s):  
New South ◽  
New South Wales ◽  
Daily Rainfall ◽  
Climate Change Impacts ◽  
Seasonal Distribution ◽  
Coefficient Of Determination ◽  
Rainfall Erosivity ◽  
South Wales ◽  
Parameter Values ◽  
Variance Explained

A rainfall erosivity model using daily rainfall amounts to estimate rainfall erosivity was tested for 29 sites in New South Wales to see whether such a model could adequately describe the temporal variation and seasonal distribution of rainfall erosivity. The coefficient of determination varied from 0.57 to 0.97 and the average discrepancy between actual and estimated seasonal distribution was no more than 3%. A set of parameter values for sites without pluviograph data was recommended for New South Wales. With this set of recommended parameter values, the percentage of total variance explained was decreased to 44%–89% for the 29 sites. Large errors, however, can occur when estimating extreme storm erosivity with large return periods. The daily erosivity model could be used for determining the seasonal distribution of rainfall erosivity or for simulating changes to rainfall erosivity as part of climate change impacts assessment.

scholarly journals Maximin Efficiencies under Treatment-Dependent Costs and Outcome Variances for Parallel, AA/BB, and AB/BA Designs

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Math J. J. M. Candel
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Optimal Allocation ◽  
Power Level ◽  
Equal Treatment ◽  
Small Samples ◽  
Asymptotic Results ◽  
Crossover Designs ◽  
Mixed Model Analysis ◽  
Intraclass Correlations

If there are no carryover effects, AB/BA crossover designs are more efficient than parallel (A/B) and extended parallel (AA/BB) group designs. This study extends these results in that (a) optimal instead of equal treatment allocation is examined, (b) allowance for treatment-dependent outcome variances is made, and (c) next to treatment effects, also treatment by period interaction effects are examined. Starting from a linear mixed model analysis, the optimal allocation requires knowledge on intraclass correlations in A and B, which typically is rather vague. To solve this, maximin versions of the designs are derived, which guarantee a power level across plausible ranges of the intraclass correlations at the lowest research costs. For the treatment effect, an extensive numerical evaluation shows that if the treatment costs of A and B are equal, or if the sum of the costs of one treatment and measurement per person is less than the remaining subject-specific costs (e.g., recruitment costs), the maximin crossover design is most efficient for ranges of intraclass correlations starting at 0.15 or higher. For other cost scenarios, the maximin parallel or extended parallel design can also become most efficient. For the treatment by period interaction, the maximin AA/BB design can be proven to be the most efficient. A simulation study supports these asymptotic results for small samples.

scholarly journals An Innovative Approach to Minimizing Uncertainty in Sediment Load Boundary Conditions for Modelling Sedimentation in Reservoirs

Water ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1411 ◽  
Author(s):  
Sardar Ateeq-Ur-Rehman ◽  
Minh Bui ◽  
Shabeh Hasson ◽  
Peter Rutschmann
Keyword(s):  
Boundary Conditions ◽  
Sediment Load ◽  
Sediment Supply ◽  
Coefficient Of Determination ◽  
Computational Time ◽  
Indus River ◽  
Sediment Deposits ◽  
Subsequent Decrease ◽  
Delta Formation ◽  
Near Future

A number of significant investigations have advanced our understanding of the parameters influencing reservoir sedimentation. However, a reliable modelling of sediment deposits and delta formation in reservoirs is still a challenging problem due to many uncertainties in the modelling process. Modelling performance can be improved by adjusting the uncertainty caused by sediment load boundary conditions. In our study, we diminished the uncertainty factor by setting more precise sediment load boundary conditions reconstructed using wavelet artificial neural networks for a morphodynamic model. The model was calibrated for hydrodynamics using a backward error propagation method. The proposed approach was applied to the Tarbela Reservoir located on the Indus River, in northern Pakistan. The results showed that the hydrodynamic calibration with coefficient of determination (R2) = 0.969 and Nash–Sutcliffe Efficiency (NSE) = 0.966 also facilitated good calibration in morphodynamic calculations with R2 = 0.97 and NSE = 0.96. The model was validated for the sediment deposits in the reservoir with R2 = 0.96 and NSE = 0.95. Due to desynchronization between the glacier melts and monsoon rain caused by warmer climate and subsequent decrease of 17% in sediment supply to the Tarbela dam, our modelling results showed a slight decrease in the sediment delta for the near future (until 2030). Based on the results, we conclude that our overall state-of-the-art modelling offers a significant improvement in computational time and accuracy, and could be used to estimate hydrodynamic and morphodynamic parameters more precisely for different events and poorly gauged rivers elsewhere in the world. The modelling concept could also be used for predicting sedimentation in the reservoirs under sediment load variability scenarios.

Axiomatization of Shapley Values of Fagle and Kern Type on Set Systems

2008 ◽  
Vol 12 (5) ◽  
pp. 409-415 ◽  
Author(s):  
Aoi Honda ◽  
◽  
Yoshiaki Okazaki
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Potential Application ◽  
Set Systems ◽  
Shapley Values

We propose axiomatizing a generalized Shapley value of games for potential application to games on set systems satisfying the condition of normality. This encompasses both the original Shapley value and Faigle and Kern's Shapley value, which is generalized for a cooperative game defined on a subcoalition.

Bootstrap confidence intervals for estimating audit value from skewed populations and small samples

SIMULATION ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Krishnamurty Muralidhar ◽  
Gary Adna Ames ◽  
Rathindra Sarathy
Keyword(s):  
Confidence Intervals ◽  
Small Samples ◽  
Bootstrap Confidence Intervals

scholarly journals NILAI PERUSAHAAN REAL ESTATE

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Kun Ismawati
Keyword(s):  
Linear Regression ◽  
Real Estate ◽  
Stock Exchange ◽  
Secondary Data ◽  
Financial Statements ◽  
Coefficient Of Determination ◽  
Investment Policies ◽  
Dividend Policies ◽  
Funding Policies ◽  
Regression Test

The purpose of the study is to determine the effect of investment policies, funding policies, and dividend policies on the value of real estate companies listed in the Indonesia Stock Exchange either partially or simultaneously. Data used in this research is secondary data obtained from the company's financial statements, as many as 42 companies from 2012-2014 period. There were 126 data obtained and analyzed with t test, F test, coefficient of determination test, and multiple linear regression test. The conclution of the research were investment policies, funding policies, and dividend policies affect the value of real estate companies listed in the Indonesia Stock Exchange either partially or simultaneously.

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