Smaller Mean Square Error Research Articles

Comparison of Model Performance for Basic and Advanced Modeling Approaches to Crime Prediction

A good machine learning model would greatly contribute to an accurate crime prediction. Thus, researchers select advanced models more frequently than basic models. To find out whether advanced models have a prominent advantage, this study focuses shift from obtaining crime prediction to on comparing model performance between these two types of models on crime prediction. In this study, we aimed to predict burglary occurrence in Los Angeles City, and compared a basic model just using prior year burglary occurrence with advanced models including linear regressor and random forest regressor. In addition, American Community Survey data was used to provide neighborhood level socio-economic features. After finishing data preprocessing steps that regularize the dataset, recursive feature elimination was utilized to determine the final features and the parameters of the two advanced models. Finally, to find out the best fit model, three metrics were used to evaluate model performance: R squared, adjusted R squared and mean squared error. The results indicate that linear regressor is the most suitable model among three models applied in the study with a slightly smaller mean squared error than that of basic model, whereas random forest model performed worse than the basic model. With a much more complex learning steps, advanced models did not show prominent advantages, and further research to extend the current study were discussed.

An Improved Family of Estimators of Finite Population Mean Using Information on an Auxiliary Variable in Sample Surveys

AbstractIn this paper we have suggested a family of estimators of the population mean using auxiliary information in sample surveys. The bias and mean squared error of the proposed class of estimators have been obtained under large sample approximation. We have derived the conditions for the parameters under which the proposed class of estimators has smaller mean squared error than the sample mean, ratio, product, regression estimator and the two parameter ratio-product-ratio estimators envisaged by Chami et al (2012). An empirical study is carried out to demonstrate the performance of the proposed class of estimators over other existing estimators.

Best linear estimation via minimization of relative mean squared error

We propose methods to construct a biased linear estimator for linear regression which optimizes the relative mean squared error (MSE). Although there have been proposed biased estimators which are shown to have smaller MSE than the ordinary least squares estimator, our construction is based on the minimization of relative MSE directly. The performance of the proposed methods is illustrated by a simulation study and a real data example. The results show that our methods can improve on MSE, particularly when there exists correlation among the predictors.

An Instrumental Variable Tree Approach for Detecting Heterogeneous Treatment Effects in Observational Studies

This study addresses the ubiquitous challenge of using big observational data to identify heterogeneous treatment effects. This problem arises in precision medicine, targeted marketing, personalized education, and many other environments. Identifying heterogeneous treatment effects presents several analytical challenges including high-dimensionality and endogeneity issues. We develop a new instrumental variable tree (IVT) approach that incorporates the instrumental variable (IV) method into a causal tree (CT) to correct for potential endogeneity biases that may exist in observational data. Our IVT approach partitions subjects into subgroups with similar treatment effects within subgroups and different treatment effects across subgroups. The estimated treatment effects are asymptotically consistent under a set of mild assumptions. Using simulated data, we show our approach has a better coverage rate and smaller mean-squared error than the conventional CT approach. We also demonstrate that an instrumental variable forest (IVF) constructed using IVTs has better accuracy and stratification than a generalized random forest (GRF). Finally, by applying the IVF approach to an empirical assessment of laparoscopic colectomy, we demonstrate the importance of accounting for endogeneity to make accurate comparisons of the heterogeneous effects of the treatment (teaching hospitals) and control (non-teaching hospitals) on different types of patients.

MSE performance of the weighted average estimators consisting of shrinkage estimators

ABSTRACTIn this paper, we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators; the Stein-rule (SR), the minimum mean squared error (MMSE), and the adjusted minimum mean-squared error (AMMSE) estimators. It is shown that one of the proposed estimators has smaller mean-squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3), and its MSE performance is comparable to the PSR estimator even when the number of the regression coefficients is not so small.

Pengujian Metode Fuzzy Time Series Chen dan Hsu Untuk Meramalkan Nilai Indeks Bursa Saham Syariah Di Jakarta Islamic Index (JII)

This research is an empirical study to tested the accuracy of Chen and Hsu’s Fuzzy Time Series Method used to forecast sharia market stock index in Jakarta Islamic Index. The data used in this research are secondary data consists of daily stock market indexes during 23 November 2016 to 14 July 2017. Chen dan Hsu’s Fuzzied Series Method used in this research has the smallest MSE (Mean Square Error) and AFER (Average Forecasting Error Rate) value rather than others method such as Song and Chrissom (1993). Song and Chrissom (1994), Chen (1996), Hwang, Chen and Lee (1998), Huarng (2001) and Chen (2002). To tested the accuracy of the Chen’s dan Hsu’s Fuzzied Series. Method researcher has to do 5 (five) steps such as (1) Determine lag between historical data, interval and The Universe Data (U), (2) Distributing Data into The Unniverse, (3) Define The Fuzzy Set, (4) Determine The Fuzzy Logical Relationship (FLR), and (5) Analyse the Difference between data. There are 3 (three) rules in Chen’s dan Hsu’s Fuzzied Series Method based on the Difference and FLR. The result of this research is Chen dan Hsu’s Fuzzied Series Method has MSE = 1.88 and AFER =0.006% and it can be used to make forecasting on value and trend sharia stock market in Jakarta Islamic index.

A Generalised Semiparametric Bayesian Fay–Herriot Model for Small Area Estimation Shrinking Both Means and Variances

In survey sampling, interest often lies in unplanned domains (or small areas), whose sample sizes may be too small to allow for accurate design-based inference. To improve the direct estimates by borrowing strength from similar domains, most small area methods rely on mixed effects regression models. This contribution extends the well known Fay–Herriot model (Fay and Herriot, 1979) within a Bayesian approach in two directions. First, the default normality assumption for the random effects is replaced by a nonparametric specification using a Dirichlet process. Second, uncertainty on variances is explicitly introduced, recognizing the fact that they are actually estimated from survey data. The proposed approach shrinks variances as well as means, and accounts for all sources of uncertainty. Adopting a flexible model for the random effects allows to accommodate outliers and vary the borrowing of strength by identifying local neighbourhoods where the exchangeability assumption holds. Through application to real and simulated data, we investigate the performance of the proposed model in predicting the domain means under different distributional assumptions. We also focus on the construction of credible intervals for the area means, a topic that has received less attention in the literature. Frequentist properties such as mean squared prediction error (MSPE), coverage and interval length are investigated. The experiments performed seem to indicate that inferences under the proposed model are characterised by smaller mean squared error than competing approaches; frequentist coverage of the credible intervals is close to nominal.

New modified moment estimators for the two-parameter weighted Lindley distribution

ABSTRACTWe propose a modification of the moment estimators for the two-parameter weighted Lindley distribution. The modification replaces the second sample moment (or equivalently the sample variance) by a certain sample average which is bounded on the unit interval for all values in the sample space. In this method, the estimates always exist uniquely over the entire parameter space and have consistency and asymptotic normality over the entire parameter space. The bias and mean squared error of the estimators are also examined by means of a Monte Carlo simulation study, and the empirical results show the small-sample superiority in addition to the desirable large sample properties. Monte Carlo simulation study showed that the proposed modified moment estimators have smaller biases and smaller mean-square errors than the existing moment estimators and are compared favourably with the maximum likelihood estimators in terms of bias and mean-square error. Three illustrative examples are finally presented.

Predictive Models for Photovoltaic Electricity Production in Hot Weather Conditions

The process of finding a correct forecast equation for photovoltaic electricity production from renewable sources is an important matter, since knowing the factors affecting the increase in the proportion of renewable energy production and reducing the cost of the product has economic and scientific benefits. This paper proposes a mathematical model for forecasting energy production in photovoltaic (PV) panels based on a self-organizing feature map (SOFM) model. The proposed model is compared with other models, including the multi-layer perceptron (MLP) and support vector machine (SVM) models. Moreover, a mathematical model based on a polynomial function for fitting the desired output is proposed. Different practical measurement methods are used to validate the findings of the proposed neural and mathematical models such as mean square error (MSE), mean absolute error (MAE), correlation (R), and coefficient of determination (R2). The proposed SOFM model achieved a final MSE of 0.0007 in the training phase and 0.0005 in the cross-validation phase. In contrast, the SVM model resulted in a small MSE value equal to 0.0058, while the MLP model achieved a final MSE of 0.026 with a correlation coefficient of 0.9989, which indicates a strong relationship between input and output variables. The proposed SOFM model closely fits the desired results based on the R2 value, which is equal to 0.9555. Finally, the comparison results of MAE for the three models show that the SOFM model achieved a best result of 0.36156, whereas the SVM and MLP models yielded 4.53761 and 3.63927, respectively. A small MAE value indicates that the output of the SOFM model closely fits the actual results and predicts the desired output.

Robust Adaptive Control for Temperature Regulation of Glycerin Bleaching Process

This paper present the performance evaluation on several modification approaches for robust Model reference adaptive control (MRAC) in regulating temperature of glycerin bleaching process. Three approaches which are MRAC without integral, MRAC with σ-modification and MRAC with e-modification are used and compared. The design of MRAC is based on first order system. Both of simulation study and real time implementation will be analyzed based on 2% band transient analysis and for steady state error analysis, Mean Square Error (MSE) is used. Results indicate that, MRAC without integral and MRAC with σ-modification provide better performance as compared with MRAC with e-modification. Also, MRAC without integral provides slightly better performance compared to MRAC with σ-modification especially in providing less overshoot and small MSE. In addition, results also reveal that MRAC without integral provide less tuning parameter as compared with MRAC with σ-modification and MRAC with e-modification.

Extrapolation techniques in U-statistic variance estimation

ABSTRACTThis article considers the problem of variance estimation of a U-statistic. Following the proposal of a linearly extrapolated variance estimator in Wang and Chen (2015), we consider a second-order extrapolation technique and devise a variance estimator that is nearly second-order unbiased. Simulation studies confirm that the second-order extrapolated variance estimator has smaller bias than the linearly extrapolated variance estimator and the jackknife variance estimator across a wide selection of distributions. In addition, the proposal also yields a smaller mean squared error than its counterparts. In the end, we discuss the advantages of the proposed variance estimator in regression analysis and model selection.

Autoregressive and cross-lagged model for bivariate non-commensurate outcomes.

Autoregressive and cross-lagged models have been widely used to understand the relationship between bivariate commensurate outcomes in social and behavioral sciences, but not much work has been carried out in modeling bivariate non-commensurate (e.g., mixed binary and continuous) outcomes simultaneously. We develop a likelihood-based methodology combining ordinary autoregressive and cross-lagged models with a shared subject-specific random effect in the mixed-model framework to model two correlated longitudinal non-commensurate outcomes. The estimates of the cross-lagged and the autoregressive effects from our model are shown to be consistent with smaller mean-squared error than the estimates from the univariate generalized linear models. Inclusion of the subject-specific random effects in the proposed model accounts for between-subject variability arising from the omitted and/or unobservable, but possibly explanatory, subject-level predictors. Our model is not restricted to the case with equal number of events per subject, and it can be extended to different types of bivariate outcomes. We apply our model to an ecological momentary assessment study with complex dependence and sampling data structures. Specifically, we study the dependence between the condom use and sexual satisfaction based on the data reported in a longitudinal study of sexually transmitted infections. We find negative cross-lagged effect between these two outcomes and positive autoregressive effect within each outcome. Copyright © 2017 John Wiley & Sons, Ltd.

Modelling Diagnostic Validity Estimates from Administrative Health Data

ABSTRACT
 ObjectivesValidation studies compare diagnostic information in linked administrative and reference (i.e., gold standard) data; they are an essential tool to develop accurate case definitions, the rules used to identify individuals in administrative data with a specific health condition. Validation studies often estimate the accuracy of multiple case definitions, in order to identify the data features (e.g., diagnosis codes, type of data source) that influence accuracy estimates. Descriptive analyses are commonly used to select a case definition(s) with the greatest accuracy estimates, but fail to account for uncertainty in accuracy estimates. The objectives were to: (1) compare the performance of regression-based approaches to test for differences in diagnostic accuracy estimates, and (2) demonstrate how to apply and use these models.
 ApproachComputer simulation was used to compare three regression models: (a) univariate fixed-effects models applied to estimates of sensitivity and specificity; (b) univariate fixed-effects model for Youden's index, the average of sensitivity and the complement of specificity; and (c) bivariate random-effects joint model of sensitivity and specificity. The simulations varied the means and variances of sensitivity and specificity, the correlation between these parameters, and the number of case definitions. Performance was compared using: (a) bias (i.e., difference between estimated and observed mean), (b) mean squared error (MSE), the sum of the estimated variance and bias squared, and (c) 95% confidence interval (CI) coverage, the proportion of times the population mean is contained in the 95% CI. For objective 2, we applied the models to estimates of diagnostic accuracy from a published rheumatoid arthritis (RA) validation study with 61 case definitions.
 ResultsUnivariate models of sensitivity and specificity had lower bias than the bivariate model (e.g., univariate=1.8%, bivariate=2.2%). The bivariate model had a smaller MSE than the univariate models when sample size was large and there was a small correlation between sensitivity and specificity (e.g., univariate=3.4%, bivariate=2.6%). Across all scenarios, the univariate model for Youden’s index showed small bias (average=2.4%) and MSE (average=2.1%). For objective 2, the univariate models of sensitivity, specificity, and Youden’s index revealed multiple case definition features that were associated with estimates of RA diagnostic accuracy: 1+ diagnosis in hospital records, >1 diagnosis in physician claims, and 1+ diagnoses by a specialist physician.
 ConclusionsWe recommend the bivariate model when a validation study contains a large number of case definitions. When the data contain a small number of case definitions, univariate models are recommended.

A New Two-Parameter Estimator for the Poisson Regression Model

It is known that multicollinearity affects the maximum likelihood estimator (MLE) negatively when estimating the coefficients in Poisson regression. Namely, the variance of MLE inflates and the estimations become instable. Therefore, in this article we propose a new two-parameter estimator (TPE) and some methods to estimate these two parameters for the Poisson regression model when there is multicollinearity problem. Moreover, we conduct a Monte Carlo simulation to evaluate the performance of the estimators using mean squared error (MSE) criterion. We finally consider a real data application. The simulations results show that TPE outperforms MLE in almost all the situations considered in the simulation and it has a smaller MSE and smaller standard errors than MLE in the application.

Statistical estimation in the presence of possibly incorrect model assumptions

ABSTRACTThe estimation problem of a parameter of interest when some model assumptions may be incorrect is considered. The parameter of interest is defined in a model-independent manner and the estimating procedure selects a model with the smallest mean square error (MSE) as estimated by a proposed MSE estimator. This proposed MSE estimator combines both a nonparametric bootstrap and plug-in estimation in its structure. It requires at least one consistent estimator with a quickly disappearing systematic bias ( mean convergence). This estimator is not tied up to a single set of model assumptions (e.g., a class of parametric models), and thus it works across various sets of possibly nonnested classes of statistical models. The derived large sample properties constitute theoretical justification of its use and allow the estimation of the probability of how likely this estimator will have the smallest MSE in a pool of candidate estimators. Multiple simulation studies illustrate the performance of the proposed ...

A double-DD blind equalizer for PolMux QAM optical coherent systems

In polarization-multiplexed (PolMux) coherent system, adaptive blind equalization is efficient in demultiplexing and mitigating inter-symbol interference (ISI). We propose a double decision-directed (double-DD) blind algorithm which combines the output of soft decision-directed (SDD) algorithm with that of the equalizer in variable step size decision-directed (VSS-DD) mode. In our scheme, two equalizers can softly switch when the mean-square error (MSE) is sufficiently low and it can achieve fast convergence rate and small steady MSE in steady state. By simulation in PolMux-16QAM/64QAM coherent systems, we show that the double-DD algorithm outperforms existing blind equalizers.

A generalized pivotal quantity approach to portfolio selection

ABSTRACTThe major problem of mean–variance portfolio optimization is parameter uncertainty. Many methods have been proposed to tackle this problem, including shrinkage methods, resampling techniques, and imposing constraints on the portfolio weights, etc. This paper suggests a new estimation method for mean–variance portfolio weights based on the concept of generalized pivotal quantity (GPQ) in the case when asset returns are multivariate normally distributed and serially independent. Both point and interval estimations of the portfolio weights are considered. Comparing with Markowitz's mean–variance model, resampling and shrinkage methods, we find that the proposed GPQ method typically yields the smallest mean-squared error for the point estimate of the portfolio weights and obtains a satisfactory coverage rate for their simultaneous confidence intervals. Finally, we apply the proposed methodology to address a portfolio rebalancing problem.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7 T.

To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Fitting Proportional Odds Model to Case-Control data with Incorporating Hardy-Weinberg Equilibrium.

Genetic association studies have been proved to be an efficient tool to reveal the aetiology of many human complex diseases and traits. When the phenotype is binary, the logistic regression model is commonly employed to evaluate the association strength of the genetic variants predispose to human diseases because the maximum likelihood estimator of the odds ratio based on case-control data is equivalent to that from the same model by taking the data as being arisen prospectively. This equivalence does not hold for the proportional odds model and using it to analyze the case-control data directly often results in a substantial bias. Through putting a parameter of the minor allele frequency in the modified likelihood function under the condition that the Hardy-Weinberg equilibrium law holds within controls, a consistent estimator is obtained. On the basis of it, we construct a score test statistic to test whether the genetic variant is associated with the diseases. Simulation studies show that the proposed estimator has smaller mean squared error than the existing methods when the genetic effect size is away from zero and the proposed test statistic has a good control of type I error rate and is more powerful than the existing procedures. Application to 45 single nucleotide polymorphisms located in the region of TRAF1-C5 genes for the association with four-level anticyclic citrullinated protein antibody from Genetic Analysis Workshop 16 further demonstrates its performance.

An Area- and Energy-Efficient FIFO Design Using Error-Reduced Data Compression and Near-Threshold Operation for Image/Video Applications

Many image/video processing algorithms require FIFO for filtering. The FIFO size is proportional to the length of the filters and input data width, causing large area and power consumption. We have proposed an energy- and area-efficient FIFO design for image/video applications through FIFO with error-reduced data compression (FERDC) and near-threshold operation. On architecture level, FERDC technique is proposed to reduce the size and power consumption of the FIFO by utilizing the spatial correlation between neighboring pixels and performing error-reduced data compression together with quantization to minimize the mean square error (MSE). On circuit level, near-threshold operation is adopted to achieve further power reduction while maintaining the required performance. To demonstrate the proposed FIFO, it has been implemented using a 0.18- $\mu $ m CMOS process technology. The implementation covers different FIFO length, including 128, 256, 512, and 1024. The experimental results show that the proposed FIFO operating at 0.5 V and 28.57 MHz achieves up to 99%, 65%, and 34.91% reduction in dynamic power, leakage power, and area, respectively, with a small MSE of 2.76, compared with the conventional FIFO design. The proposed FIFO can be applied to a wide range of image/video signal processing applications to achieve high area and energy efficiency.