Robust Estimation Procedure Research Articles

Robust estimation for semiparametric spatial autoregressive models via weighted composite quantile regression

In this article, the robust estimation for a class of semiparametric spatial autoregressive models has been investigated. By combining the QR decomposition technique for matrix and the weighted composite quantile regression method, we propose a robust estimation procedure for the parametric and non parametric components. Under certain regularity conditions, asymptotic properties of the resulting estimators are proved. Several simulation analyses have been conducted for further illustrating the performance of the proposed method, and the simulation results demonstrate that the proposed method improve the robustness of the models.

Robust Demand Estimation With Customer Choice-Based Models for Sales Transaction Data

We develop a novel statistical method to estimate customer choice among a firm’s portfolio of offerings when the firm cannot directly observe customers who choose not to purchase any product. This censored demand problem is prevalent in many industries such as hotels, airlines, and retail. Although several methods have been proposed to address this problem, they require some level of data aggregation across arrivals and/or choice sets, which results in information loss and potentially biased estimates. Therefore, they have limited applicability in an environment where the prices of a firm’s portfolio of offerings vary over time and sometimes even across different customers. Our proposed method combines several desirable properties, which makes it a better fit for realistic datasets where the available choice sets or attributes of the products in the choice sets change over time. We consider two additional types of information for identification of our model parameters: (1) additional mild assumptions on the customers’ utility function, and (2) external information about a firm’s market share. We then develop a robust estimation procedure that accounts for inaccuracies in either information type and let the data determine the best approach. Through Monte Carlo simulations, we show that our approach provides promising predictions of customer choice behavior when compared with other generally used methods and clearly outperforms those methods in scenarios where the product prices change frequently over time. Utilizing a real hotel transaction dataset provided by Oracle Labs, we further illustrate the improved estimation accuracy of our method compared to benchmark methods. Relative to existing approaches for estimating customer choice-based models, our proposed methodology better suits environments employing dynamic pricing and personalized offering practices, such as hospitality or online retailing.

Regulating stochastic clocks§

Stochastic clocks represent a class of time change methods for incorporating trading activity into continuous-time financial models, with the ability to deal with typical asymmetrical and tail risks in financial returns. In this paper we propose a significant improvement of stochastic clocks for the same objective but without decreasing the number of trades or changing the trading intensity. Our methodology targets any Lévy subordinator, or more generally any process of nonnegative independent increments, and is based on various choices of regulating kernels motivated from repeated averaging. By way of a hyperparameter linked to the degree of regulation, arbitrarily large skewness and excess kurtosis of returns can be easily achieved. Generic-time Laplace transforms, characterizing triplets, and cumulants of the regulated clocks and subsequent mixed models are analyzed, serving purposes ranging from statistical estimation and option price calibration to simulation techniques. Under specified jump–diffusion processes and tempered stable processes, a robust moment-based estimation procedure with profile likelihood is developed and a comprehensive empirical study involving S&P500 and Bitcoin daily returns is conducted to demonstrate a series of desirable effects of the proposed methods.

Minimum density power divergence estimation for the generalized exponential distribution

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001a). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.

Statistical inference for the extended non linear models

In this article, an orthogonality-projection-based estimation method is first employed to study an extended non linear model, which can separately estimate the linear and non linear parts without losing some efficiency and increasing computation burden. To overcome the non robustness of classical least squares methods, we further propose a robust and efficient estimation procedure based on the exponential squares loss function, which is robust against outliers or heavy-tailed errors while asymptotically efficient as the non linear least squares estimation under the normal error case. Under some regularity conditions, the asymptotic properties of the proposed estimators are established. In addition, simulation studies are conducted to examine the finite sample performance of the proposed estimation methods.

Calibrated regression estimation using empirical likelihood under data fusion

Data analysis based on information from different sources, typically known as the data fusion problem, is common in economic and biomedical studies. An interesting question concerns the regression of an outcome variable on certain covariates when combining two distinct datasets. These datasets consist of a primary sample containing the outcome and a subset of the covariates, and a supplemental sample comprising information only on the full set of covariates. Previous methods have proposed doubly robust estimation procedures that employ a single propensity score model for the data fusion process and a single imputation model for the covariates available only in the supplemental dataset. However, it may be questionable to assume that either model is correctly specified due to an unknown data generating process. To address this issue, an empirical likelihood based approach that calibrates multiple propensity scores and imputation models is introduced. The resulting estimator is consistent when any one of the models is correctly specified and is robust against extreme values of the fitted propensity scores. The asymptotic normality property and the estimation efficiency are also discussed. Simulation studies show that the proposed estimator has substantial advantages over existing estimators, and an assembled U.S. household expenditure data example is used for illustration.

ICU capacity expansion under uncertainty in the early stages of a pandemic

We propose a general modular approach to support decision‐makers' response in the early stages of a pandemic with resource expansion, motivated by the shortage of Covid‐19‐related intensive care units (ICU) capacity in 2020 in Italy. Our approach uses (1) a stochastic extension of an epidemic model for scenarios of projected infections, (2) a capacity load model to translate infections into scenarios of demand for the resources of interest, and (3) an optimization model to allocate this demand to the projected levels of resources based on different values of investment. We demonstrate this approach with the onset of the first and second Covid‐19 waves in three Italian regions, using the data available at that time. For epidemic modeling, we used a parsimonious stochastic susceptible‐infected‐removed model with a robust estimation procedure based on bootstrap resampling, suitable for a noisy and data‐limited environment. For capacity loading, we used a Cox queuing model to translate the projected infections into demand for ICU, using stochastic intensity to capture the variability of the patient arrival process. Finally, we used stochastic dynamic optimization to select the best policy (when and how much to expand) to minimize the expected number of patients denied ICU for any level of investment in capacity expansion and obtain an efficient frontier. The frontier allows a trade‐off between investment in additional resources and the number of patients denied intensive care. Moreover, in the panic‐driven early days of a pandemic, decision‐makers can also obtain the time until which they can postpone action, potentially reducing investment costs without increasing the expected number of denied patients.

An efficient methodology to select high-performance M-estimators for robust data reconciliation

Within the framework of Chemical Engineering, many exponential M-estimators have been proposed and tested. As usual, extensive simulation procedures are run to compare their performances. This work presents a deterministic methodology that reduces the computational endeavor of the comparative analysis. It becomes an effective technique for proposing and selecting high-performance M-estimators. The strategy uses the weight functions’ standardization to provide a common basis for the posterior application of Equivalent M-estimators and Tails Discrepancy definitions. In this way, identical M-estimators are figured out and those that behave likewise are identified. Whichever robust estimation procedure applied to estimate process variables and parameters can take advantage of the methodology results. For validation purposes, its conclusions are contrasted to the traditional performance measures obtained solving robust data reconciliation problems for two chemical processes.

Determination of the psychometric properties of the digital addiction scale for children

AimTo determine the psychometric properties of the Digital Addiction Scale for Children. Design and methodThis methodological study included 506 children aged 9–12 years. Data were collected using the child and family information form, the digital addiction scale for children and the digital game addiction scale for children. The data were evaluated using confirmatory factor analysis Cronbach's alpha, convergent validity, and gender-based measurement invariance analysis. Confirmatory factor analysis was applied using Mplus 8.7 with robust maximum likelihood estimation procedures. ResultsConfirmatory factor were performed for construct validity. The scale was found to have good model fit indicators. The factor loadings of all the components were found to be >0.40. Convergent validity of Digital addiction scale for children and digital game addiction scale showed a significant positive high correlation. The total Cronbach alpha value of the scale was determined as 0.94, and the Cronbach alpha values of the subscales as Interpersonal 0.89, and Intrapersonal 0.91. ConclusionThe use of the digital addiction scale for children was determined to be a valid and reliable scale for the screening of digital device use and digital addiction in a Turkish sample. Practice implicationsNurses and other health professionals have an important role in detecting situations that put children's health at risk and promoting positive behaviors. It is especially important that school health nurses use valid and reliable tools that can determine children's digital addictions. Since this scale is easy and practical, it is thought that it will contribute significantly to the literature.

Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution

The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression.

Robust Estimation for Semi-Functional Linear Model with Autoregressive Errors

It is well-known that the traditional functional regression model is mainly based on the least square or likelihood method. These methods usually rely on some strong assumptions, such as error independence and normality, that are not always satisfied. For example, the response variable may contain outliers, and the error term is serially correlated. Violation of assumptions can result in unfavorable influences on model estimation. Therefore, a robust estimation procedure of a semi-functional linear model with autoregressive error is developed to solve this problem. We compare the efficiency of our procedure to the least square method through a simulation study and two real data analyses. The conclusion illustrates that the proposed method outperforms the least square method, providing random errors follow the heavy-tail distribution.

Experimental estimation of the local heat transfer coefficient for thin liquid film evaporation in a capillary tube

• Local heat transfer coefficient was estimated for thin liquid film evaporation in a capillary tube. • Temperature infrared measurements were employed as input data of the inverse heat conduction problem. • A robust estimation procedure was adopted. • Procedure validation through the application to both synthetic and experimental data. • Original insight of thin liquid film evaporation was given. Two-phase heat transfer devices consisting of mini and microtubes represent a powerful solution to the continuous reduction of electronic components' dimensions and to the increase of the power to dissipate. Despite many studies on the two-phase heat transfer phenomenon in minitubes, most provided outcomes regarding the average heat transfer coefficient or Nusselt number. A technique to assess the local convective wall heat flux and heat transfer coefficient is proposed, validated, and then applied to the experimental case of thin-film evaporation in a heated capillary tube. The evaporation of the thin film of liquid plays a vital part in the two-phase heat transfer phenomenon inside mini/microtubes. Our study investigated this phenomenon by examining a semi-infinite slug flow. The estimation method used is represented by the inverse heat conduction problem solution in the tube wall, applying the Tikhonov regularisation method. The temperature distributions on the outer surface of the channel measured by an infrared camera were employed as input data for the inverse problem. The estimated heat transfer coefficient distributions confirm the available correlations in average values and provide insight into these complex phenomena in local and instantaneous quantities.

A unified framework of multiply robust estimation approaches for handling incomplete data

Missing data occur frequently in practice. Inverse probability weighting and imputation are regarded as two important approaches for handling missing data. However, the validity of these approaches depends on underlying model assumptions. A new general framework for multiply robust estimation procedures by combining multiple nonresponse and imputation models is proposed in the paper. The proposed method can be used to estimate both smooth and non-smooth parameters defined as the solution of some estimating equations. It includes population means, quantiles, and distribution functions as special cases. The asymptotic results of the proposed methods are established. The results of a simulation study and a real data application suggest that the proposed methods perform well in terms of bias and efficiency.

Robust estimation for varying coefficient partially functional linear regression models based on exponential squared loss function

Abstract In this article, we present a new robust estimation procedure based on the exponential squared loss function for varying coefficient partially functional linear regression models, where the slope function and nonparametric coefficients are approximated by functional principal component basis functions and B splines, respectively. Under some mild conditions, the convergence rates of the resulted estimators are obtained. Simulation studies indicate that our proposed method can achieve robustness against outliers or heavy-tail error distributions and perform no worse than the popular least-squares estimation method for the normal error case. Finally, a real data example is used to illustrate the application of the proposed method.

Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction

Recently, Wang and Tchetgen Tchetgen (2018) showed that the global average treatment effect is identifiable even in the presence of unmeasured confounders so long as they do not modify the instrument’s additive effect on the treatment. We use a simple and direct method to show that this no-interaction assumption allows identification of the entire outcome distribution, which leads to multiply robust estimation procedures for nonlinear functionals like the quantile and Mann–Whitney treatment effects. Similarly, we can bound these causal estimands through the outcome distribution in sensitivity analysis against confounder–instrument interaction.

Robust estimation in beta regression via maximum L$$_q$$-likelihood

Beta regression models are widely used for modeling continuous data limited to the unit interval, such as proportions, fractions, and rates. The inference for the parameters of beta regression models is commonly based on maximum likelihood estimation. However, it is known to be sensitive to discrepant observations. In some cases, one atypical data point can lead to severe bias and erroneous conclusions about the features of interest. In this work, we develop a robust estimation procedure for beta regression models based on the maximization of a reparameterized L\(_q\)-likelihood. The new estimator offers a trade-off between robustness and efficiency through a tuning constant. To select the optimal value of the tuning constant, we propose a data-driven method which ensures full efficiency in the absence of outliers. We also improve on an alternative robust estimator by applying our data-driven method to select its optimum tuning constant. Monte Carlo simulations suggest marked robustness of the two robust estimators with little loss of efficiency when the proposed selection scheme for the tuning constant is employed. Applications to three datasets are presented and discussed. As a by-product of the proposed methodology, residual diagnostic plots based on robust fits highlight outliers that would be masked under maximum likelihood estimation.

Robust functional principal component analysis via a functional pairwise spatial sign operator.

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy-tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large-scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among olderwomen.

COOPERATIVE IMAGE ORIENTATION CONSIDERING DYNAMIC OBJECTS

Abstract. In the context of image orientation, it is commonly assumed that the environment is completely static. This is why dynamic elements are typically filtered out using robust estimation procedures. Especially in urban areas, however, many such dynamic elements are present in the environment, which leads to a noticeable amount of errors that have to be detected via robust adjustment. This problem is even more evident in the case of cooperative image orientation using dynamic objects as ground control points (GCPs), because such dynamic objects carry the relevant information. One way to deal with this challenge is to detect these dynamic objects prior to the adjustment and to process the related image points separately. To do so, a novel methodology to distinguish dynamic and static image points in stereoscopic image sequences is introduced in this paper, using a neural network for the detection of potentially dynamic objects and additional checks via forward intersection. To investigate the effects of the consideration of dynamic points in the adjustment, an image sequence of an inner-city traffic scenario is used; image orientation, as well as the 3D coordinates of tie points, are calculated via a robust bundle adjustment. It is shown that compared to a solution without considering dynamic points, errors in the tie points are significantly reduced, while the median of the precision of all 3D coordinates of the tie points is improved.

Robust mixture regression via an asymmetric exponential power distribution

Finite mixture of linear regression (FMLR) models are an efficient tool to fit the unobserved heterogeneous relationships. The parameter estimation of FMLR models is usually based on the normality assumption, but it is very sensitive to outliers. Meanwhile, the traditional robust methods often need to assume a specific error distribution, and are not adaptive to dataset. In this paper, a robust estimation procedure for FMLR models is proposed by assuming that the error terms follow an asymmetric exponential power distribution, including normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. The proposed method can select the suitable loss function from a broad class in a data driven fashion. Under some conditions, the asymptotic properties of proposed method are established. In addition, an efficient EM algorithm is introduced to implement the proposed methodology. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze a tone perception data.

Adult/child ratio and group size in early childhood education or care to promote the development of children aged 0-5 years: A systematic review.

Adult/child ratio and group size in early childhood education or care to promote the development of children aged 0-5 years: A systematic review.