scholarly journals Confidence Distributions for FIC Scores

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 27
Author(s):  
Céline Cunen ◽  
Nils Lid Hjort
Keyword(s):  
Mean Squared Error ◽  
Information Criterion ◽  
Second Development ◽  
Focused Information Criterion ◽  
Estimation Uncertainty ◽  
Squared Error ◽  
Point Estimates ◽  
Form Model ◽  
Careful Assessment ◽  
Better Than

When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the y-axis and the root-FIC scores on the x-axis, these being the estimated root-mean-square scores. In this paper we address the estimation uncertainty involved in each of the points of such a FIC plot. This needs careful assessment of each of the estimators from the candidate models, taking also modelling bias into account, along with the relative precision of the associated estimated mean squared error quantities. We use confidence distributions for these tasks. This leads to fruitful CD–FIC plots, helping the statistician to judge to what extent the seemingly best models really are better than other models, etc. These efforts also lead to two further developments. The first is a new tool for model selection, which we call the quantile-FIC, which helps overcome certain difficulties associated with the usual FIC procedures, related to somewhat arbitrary schemes for handling estimated squared biases. A particular case is the median-FIC. The second development is to form model averaged estimators with weights determined by the relative sizes of the median- and quantile-FIC scores.

Combining two soil property rasters using an adaptive gating approach

Soil Research ◽  
2015 ◽  
Vol 53 (8) ◽  
pp. 907 ◽  
Author(s):  
David Clifford ◽  
Yi Guo
Keyword(s):  
Confidence Intervals ◽  
Soil Property ◽  
Mean Squared Error ◽  
Geographic Space ◽  
Covariate Information ◽  
Squared Error ◽  
Inverse Variance ◽  
Machine Learning Approach ◽  
Further Development ◽  
Better Than

Given the wide variety of ways one can measure and record soil properties, it is not uncommon to have multiple overlapping predictive maps for a particular soil property. One is then faced with the challenge of choosing the best prediction at a particular point, either by selecting one of the maps, or by combining them together in some optimal manner. This question was recently examined in detail when Malone et al. (2014) compared four different methods for combining a digital soil mapping product with a disaggregation product based on legacy data. These authors also examined the issue of how to compute confidence intervals for the resulting map based on confidence intervals associated with the original input products. In this paper, we propose a new method to combine models called adaptive gating, which is inspired by the use of gating functions in mixture of experts, a machine learning approach to forming hierarchical classifiers. We compare it here with two standard approaches – inverse-variance weights and a regression based approach. One of the benefits of the adaptive gating approach is that it allows weights to vary based on covariate information or across geographic space. As such, this presents a method that explicitly takes full advantage of the spatial nature of the maps we are trying to blend. We also suggest a conservative method for combining confidence intervals. We show that the root mean-squared error of predictions from the adaptive gating approach is similar to that of other standard approaches under cross-validation. However under independent validation the adaptive gating approach works better than the alternatives and as such it warrants further study in other areas of application and further development to reduce its computational complexity.

scholarly journals Day-Ahead Forecasting of Hourly Photovoltaic Power Based on Robust Multilayer Perception

2018 ◽  
Vol 10 (12) ◽  
pp. 4863 ◽  
Author(s):  
Chao Huang ◽  
Longpeng Cao ◽  
Nanxin Peng ◽  
Sijia Li ◽  
Jing Zhang ◽  
...  
Keyword(s):  
Power Plants ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Multilayer Perception ◽  
Squared Error ◽  
The Mean ◽  
Effectiveness And Efficiency ◽  
Mlp Network ◽  
Grid Operation ◽  
Better Than

Photovoltaic (PV) modules convert renewable and sustainable solar energy into electricity. However, the uncertainty of PV power production brings challenges for the grid operation. To facilitate the management and scheduling of PV power plants, forecasting is an essential technique. In this paper, a robust multilayer perception (MLP) neural network was developed for day-ahead forecasting of hourly PV power. A generic MLP is usually trained by minimizing the mean squared loss. The mean squared error is sensitive to a few particularly large errors that can lead to a poor estimator. To tackle the problem, the pseudo-Huber loss function, which combines the best properties of squared loss and absolute loss, was adopted in this paper. The effectiveness and efficiency of the proposed method was verified by benchmarking against a generic MLP network with real PV data. Numerical experiments illustrated that the proposed method performed better than the generic MLP network in terms of root mean squared error (RMSE) and mean absolute error (MAE).

scholarly journals Target and Equalizer Design for High-Density Bit-Patterned Media Recording

1970 ◽  
Vol 6 (2) ◽  
pp. 128-135
Author(s):  
Santi Koonkarnkhai ◽  
Phongsak Keeratiwintakorn ◽  
Piya Kovintavewat
Keyword(s):  
Partial Response ◽  
Mean Squared Error ◽  
Bit Patterned Media ◽  
Patterned Media ◽  
Media Noise ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Cross Track ◽  
Partial Response Maximum Likelihood ◽  
Better Than

In bit-patterned media recording (BPMR) channels, the inter-track interference (ITI) is extremely severe at ultra high areal densities, which significantly degrades the system performance. The partial-response maximum-likelihood (PRML) technique that uses an one-dimensional (1D) partial response target might not be able to cope with this severe ITI, especially in the presence of media noise and track mis-registration (TMR). This paper describes the target and equalizer design for highdensity BPMR channels. Specifically, we proposes a two-dimensional (2D) cross-track asymmetric target, based on a minimum mean-squared error (MMSE) approach, to combat media noise and TMR. Results indicate that the proposed 2D target performs better than the previously proposed 2D targets, especially when media noise and TMR is severe.

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

2022 ◽  
pp. 62-85
Author(s):  
Carlos N. Bouza-Herrera ◽  
Jose M. Sautto ◽  
Khalid Ul Islam Rather
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Auxiliary Variables ◽  
Mild Conditions ◽  
Squared Error ◽  
The Mean ◽  
Better Than

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

scholarly journals Modelling the growth of rearing cattle

2021 ◽  
Author(s):  
Hanna Unterauer ◽  
Norbert Brunner ◽  
Manfred Kühleitner
Keyword(s):  
Goodness Of Fit ◽  
Linear Growth ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Information Criterion ◽  
Squared Error ◽  
Akaike Criterion ◽  
Linear Growth Model ◽  
Bp Model ◽  
Scientific Growth

Scientific growth literature often uses the models of Brody, Gompertz, Verhulst, and von Bertalanffy. The versatile five-parameter Bertalanffy-Pütter (BP) model generalizes them. Using the least-squares method, we fitted the BP model to mass-at-age data of 161 calves, cows, bulls, and oxen of cattle breeds that are common in Austria and Southern Germany. We used three measures to assess the goodness of fit: R-squared, normalized root-mean squared error, and the Akaike information criterion together with a correction for sample size. Although the BP model improved the fit of the linear growth model considerably in terms of R-squared, the better fit did not, in general, justify the use of its additional parameters, because most of the data had a non-sigmoidal character. In terms of the Akaike criterion, we could identify only a small core of data (15%) where sigmoidal models were indispensable.    

scholarly journals On the Use of Entropy to Improve Model Selection Criteria

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 394 ◽  
Author(s):  
Andrea Murari ◽  
Emmanuele Peluso ◽  
Francesco Cianfrani ◽  
Pasquale Gaudio ◽  
Michele Lungaroni
Keyword(s):  
Model Selection ◽  
Shannon Entropy ◽  
Selection Criteria ◽  
Mean Squared Error ◽  
Geodesic Distance ◽  
Information Criterion ◽  
Residual Distribution ◽  
Model Selection Criteria ◽  
Synthetic Indicators ◽  
Squared Error

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

scholarly journals A Class of Modified Ratio Estimators for Estimation of Population Variance

2015 ◽  
Vol 11 (1) ◽  
pp. 91-114 ◽  
Author(s):  
J. Subramani ◽  
G. Kumarapandiyan
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Variance Estimators ◽  
Squared Error ◽  
Ratio Estimators ◽  
Better Than

Abstract In this paper we have proposed a class of modified ratio type variance estimators for estimation of population variance of the study variable using the known parameters of the auxiliary variable. The bias and mean squared error of the proposed estimators are obtained and also derived the conditions for which the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators. Further we have compared the proposed estimators with that of the traditional ratio type variance estimator and existing modified ratio type variance estimators for certain natural populations.

scholarly journals A new estimator for the multicollinear Poisson regression model: simulation and application

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adewale F. Lukman ◽  
Emmanuel Adewuyi ◽  
Kristofer Månsson ◽  
B. M. Golam Kibria
Keyword(s):  
Regression Model ◽  
Poisson Regression ◽  
Mean Squared Error ◽  
Model Simulation ◽  
Real Life ◽  
Poisson Regression Model ◽  
Squared Error ◽  
Damage Data ◽  
The Mean ◽  
Better Than

AbstractThe maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

scholarly journals Soft Computing Techniques for Appraisal of Potentially Toxic Elements from Jalandhar (Punjab), India

2021 ◽  
Vol 11 (18) ◽  
pp. 8362
Author(s):  
Vinod Kumar ◽  
Parveen Sihag ◽  
Ali Keshavarzi ◽  
Shevita Pandita ◽  
Andrés Rodríguez-Seijo
Keyword(s):  
Toxic Elements ◽  
Mean Squared Error ◽  
Agricultural Soils ◽  
Potentially Toxic Elements ◽  
Performance Estimation ◽  
Boosted Regression Trees ◽  
Squared Error ◽  
Soft Computing Techniques ◽  
Models Comparison ◽  
Better Than

The contamination of potentially toxic elements (PTEs) in agricultural soils is a serious concern around the globe, and modelling approaches is imperative in order to determine the possible hazards linked with PTEs. These techniques accurately assess the PTEs in soil, which play a pivotal role in eliminating the weaknesses in determining PTEs in soils. This paper aims to predict the concentration of Cu, Co and Pb using neural networks (NNs) based on multilayer perceptron (MLP) and boosted regression trees (BT). Statistical performance estimation factors were rummage-sale to measure the performance of developed models. Comparison of the coefficient of correlation and root mean squared error suggest that MLP-established models perform better than BT-based models for predicting the concentration of Cu and Pb, whereas BT models perform better than MLP established models at predicting the concentration of Co.

scholarly journals COVID-19 Infection Forecasting based on Deep Learning in Iran

2020 ◽  
Author(s):  
Mehdi Azarafza ◽  
Mohammad Azarafza ◽  
Jafar Tanha
Keyword(s):  
Short Term Memory ◽  
Mean Squared Error ◽  
Moving Average ◽  
National Level ◽  
Absolute Error ◽  
Percentage Error ◽  
Autoregressive Integrated Moving Average ◽  
Error Metrics ◽  
Squared Error ◽  
Better Than

Since December 2019 coronavirus disease (COVID-19) is outbreak from China and infected more than 4,666,000 people and caused thousands of deaths. Unfortunately, the infection numbers and deaths are still increasing rapidly which has put the world on the catastrophic abyss edge. Application of artificial intelligence and spatiotemporal distribution techniques can play a key role to infection forecasting in national and province levels in many countries. As methodology, the presented study employs long short-term memory-based deep for time series forecasting, the confirmed cases in both national and province levels, in Iran. The data were collected from February 19, to March 22, 2020 in provincial level and from February 19, to May 13, 2020 in national level by nationally recognised sources. For justification, we use the recurrent neural network, seasonal autoregressive integrated moving average, Holt winter's exponential smoothing, and moving averages approaches. Furthermore, the mean absolute error, mean squared error, and mean absolute percentage error metrics are used as evaluation factors with associate the trend analysis. The results of our experiments show that the LSTM model is performed better than the other methods on the collected COVID-19 dataset in Iran

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