Search

Researchers in statistical shape analysis often analyze outlines of objects. Even though these contours are infinite-dimensional in theory, they must be discretized in practice. When discretizing, it is important to reduce the number of sampling points considerably to reduce computational costs, but to not use too few points so as to result in too much approximation error. Unfortunately, determining the minimum number of points needed to achieve sufficiently approximate the contours is computationally expensive. In this paper, we fit regression models to predict these lower bounds using characteristics of the contours that are computationally cheap as predictor variables. However, least squares regression is inadequate for this task because it treats overestimation and underestimation equally, but underestimation of lower bounds is far more serious. Instead, to fit the models, we use the LINEX loss function, which allows us to penalize underestimation at an exponential rate while penalizing overestimation only linearly. We present a novel approach to select the shape parameter of the loss function and tools for analyzing how well the model fits the data. Through validation methods, we show that the LINEX models work well for reducing the underestimation for the lower bounds. [ABSTRACT FROM AUTHOR]

In the presence of non-normally distributed asset returns, an optimal portfolio selection should consider higher-order (co-)moments when no sampling errors exist. However, the curse of dimensionality has already been a serious concern in mean-variance analyses; higher-order (co-)moments also face the same dilemma. This study uses mixed-frequency (MF) data under the assumption that stock returns are generated by a mixed-data sampling (MIDAS) regression model, which shows to provide well-improved estimates for the covariance, co-skewness, and co-kurtosis matrices for higher dimension. We discover that the new, improved estimates used in higher-order (co-)moment portfolio selections can dominate the other existing structured estimates from an out-of-sample perspective in most instances. [ABSTRACT FROM AUTHOR]

Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large datasets due to computational limitations. A critical step in big data analysis is data reduction. Existing investigations in the context of linear regression focus on subsampling-based methods. However, not only is this approach prone to sampling errors, it also leads to a covariance matrix of the estimators that is typically bounded from below by a term that is of the order of the inverse of the subdata size. We propose a novel approach, termed information-based optimal subdata selection (IBOSS). Compared to leading existing subdata methods, the IBOSS approach has the following advantages: (i) it is significantly faster; (ii) it is suitable for distributed parallel computing; (iii) the variances of the slope parameter estimators converge to 0 as the full data size increases even if the subdata size is fixed, that is, the convergence rate depends on the full data size; (iv) data analysis for IBOSS subdata is straightforward and the sampling distribution of an IBOSS estimator is easy to assess. Theoretical results and extensive simulations demonstrate that the IBOSS approach is superior to subsampling-based methods, sometimes by orders of magnitude. The advantages of the new approach are also illustrated through analysis of real data. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, an admittance control scheme for a user-in-charge exoskeleton is presented. The controller basically consists of a composite adaptive controller implementing a feedback law to estimate the structured uncertainties and to modify the apparent dynamics of the robot, and an LWPR estimator which tries to give an appropriate approximation of unmodeled uncertainty along with a robust term aiming to overcome the approximation residue. The control scheme offers a unified general control structure that explains the effect of each control component on the others. It is proved that based on the developed controller, the tracking and estimation errors converge to small boundaries with ultimate boundedness property due to the presence of the unstructured uncertainty. Based on simulations of a 2-DOF leg, the effectiveness of the controller is investigated. The results show the effectiveness of employing a universal approximator alongside a robust adaptive control and the success of the recommended approach in estimating model parameters and unmodeled dynamics simultaneously. [ABSTRACT FROM AUTHOR]

Among other types of non sampling errors, non response error (NRE) is an inherent component of any sample survey, which is supposed to be given much attention during the designing and execution stages. With increasing awareness of these estimators, therefore, there is an urge for the development of suitable techniques for controlling them. This article proposes two families of estimators for population mean in the presence of non response and discuses various properties under model approach, namely polynomial regression model. The families include some existing estimators. Comparison of efficiencies along with the robustness of the estimators under misspecification of models has been empirically discussed. [ABSTRACT FROM AUTHOR]

This article compares the mean-squared error (or ℓ2risk) of ordinary least squares (OLS), James–Stein, and least absolute shrinkage and selection operator (Lasso) shrinkage estimators in simple linear regression where the number of regressors is smaller than the sample size. We compare and contrast the known risk bounds for these estimators, which shows that neither James–Stein nor Lasso uniformly dominates the other. We investigate the finite sample risk using a simple simulation experiment. We find that the risk of Lasso estimation is particularly sensitive to coefficient parameterization, and for a significant portion of the parameter space Lasso has higher mean-squared error than OLS. This investigation suggests that there are potential pitfalls arising with Lasso estimation, and simulation studies need to be more attentive to careful exploration of the parameter space. [ABSTRACT FROM AUTHOR]

Background:The use of the borderline regression method (BRM) is a widely accepted standard setting method for OSCEs. However, it is unclear whether this method is appropriate for use with small cohorts (e.g. specialist post-graduate examinations). Aims and methods:This work uses an innovative application of resampling methods applied to four pre-existing OSCE data sets (number of stations between 17 and 21) from two institutions to investigate how the robustness of the BRM changes as the cohort size varies. Using a variety of metrics, the ‘quality’ of an OSCE is evaluated for cohorts of approximatelyn = 300 down ton = 15. Estimates of the standard error in station-level and overall pass marks,R2coefficient, and Cronbach’s alpha are all calculated as cohort size varies. Results and conclusion: For larger cohorts (n > 200), the standard error in the overall pass mark is small (less than 0.5%), and for individual stations is of the order of 1–2%. These errors grow as the sample size reduces, with cohorts of less than 50 candidates showing unacceptably large standard error. Alpha andR2also become unstable for small cohorts. The resampling methodology is shown to be robust and has the potential to be more widely applied in standard setting and medical assessment quality assurance and research. [ABSTRACT FROM PUBLISHER]

A number of alternative mean-variance portfolio strategies have been recently proposed to improve the empirical performance of the classic Markowitz mean-variance framework. Designed as remedies for parameter uncertainty and estimation errors in portfolio selection problems, these alternative portfolio strategies deliver substantially better out-of-sample performance. In this article, we first show how to solve a general portfolio selection problem in a linear regression framework. Then we propose to reduce the estimation risk of expected returns and the variance-covariance matrix of asset returns by imposing additional constraints on the portfolio weights. With results from linear regression models, we show that portfolio weights derived from new approaches enjoy two favorable properties: sparsity and stability. Moreover, we present insights into these new approaches as well as their connections to alternative strategies in literature. Four empirical studies show that the proposed strategies have better out-of-sample performance and lower turnover than many other strategies, especially when the estimation risk is large. [ABSTRACT FROM PUBLISHER]

We examine the relationship between Mi(xed) Da(ta) S(ampling) (MIDAS) regressions and the Kalman filter when forecasting with mixed frequency data. In general, state space models involve a system of equations, whereas MIDAS regressions involve a single equation. As a consequence, MIDAS regressions might be less efficient, but could also be less prone to parameter estimation error and/or specification errors. We examine how MIDAS regressions and Kalman filters match up under ideal circumstances, that is in population, and in cases where all the stochastic processes—low and high frequency—are correctly specified. We characterize cases where the MIDAS regression exactly replicates the steady state Kalman filter weights. We compare MIDAS and Kalman filter forecasts in population where the state space model is misspecified. We also compare MIDAS and Kalman filter forecasts in small samples. The paper concludes with an empirical application. Overall we find that the MIDAS and Kalman filter methods give similar forecasts. In most cases, the Kalman filter is a bit more accurate, but it is also computationally much more demanding. [ABSTRACT FROM PUBLISHER]

The authors express their views on an article on bootstrap-based methods for statistical estimation, that is published in this issue. Topics discussed include correlation coefficients in a linear regression model; estimation of confidence intervals for adaptive bootstrap methods; and normalized estimation error in regression analysis.