Estimation Step Research Articles

A notion of depth for sparse functional data

Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It has also been used as a building block for functional outlier detection methods and classification. Several notions of depth for functional data were introduced in the literature in the last few decades. These functional depths can only be directly applied to samples of curves measured on a fine and common grid. In practice, this is not always the case, and curves are often observed at sparse and subject dependent grids. In these scenarios, the usual approach consists in estimating the trajectories on a common dense grid, and using the estimates in the depth analysis. This approach ignores the uncertainty associated with the curves estimation step. Our goal is to extend the notion of depth so that it takes into account this uncertainty. Using both functional estimates and their associated confidence intervals, we propose a new method that allows the curve estimation uncertainty to be incorporated into the depth analysis. We describe the new approach using the modified band depth although any other functional depth could be used. The performance of the proposed methodology is illustrated using simulated curves in different settings where we control the degree of sparsity. Also a real data set consisting of female medflies egg-laying trajectories is considered. The results show the benefits of using uncertainty when computing depth for sparse functional data.

Multinomial Logistic Mixed Models for Clustered Categorical Data in a Complex Survey Sampling Setup

In a finite/survey population setup, where categorical/multinomial responses are collected from individuals belonging to a cluster, in a recent study Skinner (International Statistical Review, 87, S64-S78 2019) has modeled the means of the clustered categorical responses as a function of regression parameters, and suggested a ‘working’ correlations based GEE (generalized estimating equations) approach for the estimation of the regression parameters. However, this mean model involving only regression parameters is not justified for clustered multinomial responses because of the fact that these responses share a common cluster effect which compels the clustered correlation parameter to enter into the mean function on top of the regression parameters. Consequently, the so-called GEE approach, which requires the means to be free of correlations, is not applicable for regression analysis in the clustered multinomial setup. As a remedy, in this paper we consider a multinomial mixed model which accommodates the clustered correlation parameter in the mean functions. For inferences in the present finite population setup, as the GQL (generalized quasi-likelihood) approach is known to produce consistent and more efficient estimate than the MM (method of moments) approach in an infinite population setup, we estimate the regression parameters of primary interest by using the first order response based survey weighted GQL (WGQL) approach. For the estimation of the random effects variance (also known as clustered correlation) parameter, as it is of secondary interest, we use the second order response based survey weighted MM (WMM) approach, which is simpler than the corresponding WGQL estimation approach. The estimation steps are presented clearly for the benefit to the practitioners. Also because, in practice, survey practitioners such as statistical agencies frequently deal with a large health or socio-economic data set at national or state levels, for example, we make sure for their benefit that our proposed WGQL and WMM estimators are consistent. Thus, the asymptotic properties such as asymptotic unbiasedness and consistency for both regression and clustered correlation parameters are studied in details. The asymptotic normality property, for the benefit of constructing confidence interval for the main regression parameters, is also studied.

Iterative Carrier Frequency Offset Estimation Scheme for Faster-Than-Nyquist Signaling Systems

As a nonorthogonal mode, faster-than-Nyquist (FTN) signaling transmission can effectively improve the spectrum efficiency of a system. However, FTN signaling inevitably causes inter-symbol interference (ISI). The ISI hinders traditional synchronization methods from operating accurately, and this makes the carrier synchronization of FTN systems more complex. To overcome this issue, we propose an iterative carrier frequency offset (CFO) estimation scheme for an FTN signaling system. The proposed CFO estimation scheme consists of two steps: i) a coarse estimation step based on discrete Fourier transform and ii) a fine estimation step based on a golden-section search algorithm. The simulation results show that the mean square error of the proposed scheme is lower than that of the conventional CFO estimation schemes and approaches the Cramer-Rao Bound, which is an optimal estimation performance bound.

Weight-of-evidence process for assessing human health risk of mixture of metal oxide nanoparticles and corresponding ions in aquatic matrices

This study proposed a framework to estimate health risks due to exposure of mixture of nanoparticles (NPs) from surface water, for the first time, as per authors’ best knowledge. The framework consisted of hazard identification, exposure assessment, dose-response assessment, risk characterization and risk management steps. Concentrations of mixture of NPs and associated ions were compiled and range of values were used for exposure estimation. The resulting concentrations of nanoparticle and metal ions in simulated digestive fluid were calculated and used to estimate exposure dose to digestive system organs during a hypothetical exposure of water during recreational activity. Exposure doses of different possible combinations of ZnO NP, CuO NP, Zn2+ and Cu2+ ions were considered. The ECHA weight-of- evidence framework was used for formulating hypotheses and collecting evidence for determining reference dose (RfD) and interaction parameter for estimating hazard interaction value (an index for risk) as per the USEPA modified weight-of-evidence method for estimating risks of binary NPs and ions. RfD values of CuO (0.0262 mg/kg/d) and ZnO NP (0.0315 mg/kg/d) were derived using information from rat-based oral toxicity studies and assumed values of uncertainty factors. The results showed that mixture of NPs under environmentally-relevant conditions do not pose any health risk. The uncertainty analysis indicated that ZnO + CuO + Zn + Cu ion suspension posed the highest risk. The switchover analysis indicated that NP concentration >0.207 mg/L resulted in risk estimate greater than 1 and pose risk. Although risk estimate was found to be smaller than 1 under the studied natural water condition, efforts should be made to continue monitoring mixture of NPs as a precautionary approach. More efforts are required to obtain data on (i)toxicity of mixture of NPs, (ii)their interaction effects, (iii)fractions of NPs reaching target organ in order to accurately predict risk. Potential benefit of this framework is in its usage for development of structure for estimating exposure risks due to mixture of NPs and ions from surface water. This can also be used to adopt methodology for gathering information on evidence required in different steps of risk assessment process, like obtaining RfD/uncertainty factor -related parameters in dose-response assessment step, deriving interaction and mixture toxicity-related parameters in risk estimation step.

Determining marine mammal detection functions for a stationary land-based survey site

Abstract ContextThe shore-based survey is a common, non-invasive, and low-cost method in marine mammal science, but its scientific applications are currently limited. Such studies typically target populations whose distributions are not random with respect to nearshore sites and involve repeated scans of the same area from single, stationary platforms. These circumstances prohibit the use of classic distance sampling techniques for estimating animal densities or distributions, particularly the derivation of a detection function that describes the probability of detecting targets at various distances from the observer. AimsHere, we present a technique for estimating land-based detection functions, as well as quantifying uncertainty in their parameterisation, on the basis of the range-specific variability of observations from one scan to the next. MethodsThis Bayesian technique uses Monte Carlo simulation to determine the likelihood of thousands of candidate detection functions, then conducts weighted sampling to generate a posterior distribution estimate of the detection function parameterisation. We tested the approach with both archival and artificial datasets built from known detection functions that reflect whale and porpoise detectability. Key resultsWhen the base distribution of targets was random, the whale detection function was estimated without error (i.e. the difference of the median of the posterior and the true value was 0.00), and the porpoise detection function was estimated with an error equal to 4.23% of the true value. When the target base distribution was non-random, estimation error remained low (2.57% for targets concentrated offshore, 1.14% when associated with nearshore habitats). When applied to field observations of humpback whales and Dall’s porpoises from a land-based study in northern British Columbia, Canada, this technique yielded credible results for humpback whales, but appeared to underestimate the detectability of Dall’s porpoises. ConclusionThe findings presented here indicate that this approach to detection function estimation is appropriate for long-running surveys in which scan regularity is high and the focus is on large, slow-moving, low herd-size, and easily detectable species. ImplicationsThe derivation of a detection function is a critical step in density estimation. The methodology presented here empowers land-based studies to contribute to quantitative monitoring and assessment of marine mammal populations in coastal habitats.

Six-way decomposition of causal effects: Unifying mediation and mechanistic interaction.

The sufficient component cause (SCC) model and counterfactual model are two common methods for causal inference, each with their own advantages: the SCC model allows the mechanistic interaction to be detailed, whereas the counterfactual model features a systemic framework for quantifying causal effects. Hence, integrating the SCC and counterfactual models may facilitate the conceptualization of causation. Based on the marginal SCC (mSCC) model, we propose a novel counterfactual mSCC framework that includes the steps of definition, identification, and estimation. We further propose a six-way effect decomposition for assessing mediation and the mechanistic interaction. The results demonstrate that when all variables are binary, the six-way decomposition is an extension of four-way decomposition and that without agonism, the six-way decomposition is reduced to four-way decomposition. To illustrate the utility of the proposed decomposition, we apply it to a Taiwanese cohort to examine the mechanism of hepatitis C virus (HCV)-induced hepatocellular carcinoma (HCC) with liver inflammation measured by alanine aminotransferase (ALT) as a mediator. Among the HCV-induced HCC cases, 62.27% are not explained by either mediation or interaction in relation to ALT; 9.32% are purely mediated by ALT; 16.53% are caused by the synergistic effect of HCV and ALT; and 9.31% are due to the mediated synergistic effect of HCV and ALT. In summary, we introduce an SCC model framework based on counterfactual theory and detail the required identification assumptions and estimation procedures; we also propose a six-way effect decomposition to unify mediation and mechanistic interaction analyses.

Sequential estimation of borehole resistance and ground thermal properties through thermal response test

Borehole thermal resistance and ground thermal properties (thermal conductivity and heat capacity) are the key parameters to implement the ground source heat pump (GSHP), usually obtained by thermal response test. In this study, a novel sequential parameters estimation method for the above three parameters is proposed, and the sensitivity analysis by using a special correlation method is performed to decide the best estimation sequences. At first, the Spearman partial rank correlation coefficient was used to represent the correlation between the estimated thermal properties and fluid temperature for the line source model (ILS), then the estimation sequence for the three parameters could be determined by the correlation results. Lastly, with the estimation step, Monte Carlo method was adopted to determine the parameters replacing conventional iterative algorithms. In addition, the effect of value bounds and initial inputs as well as random samples was investigated. The results showed that compared to the other estimation steps, the estimation sequence following borehole resistance firstly, then thermal conductivity, heat capacity lastly could get the best precision with 4.5%, 0.4%, 1% respectively. Specially, the estimation precision for ground heat capacity could be promoted by the sequential estimation. Also, the effect of value bounds on estimation precision was nearly eliminated by the proposed method.

Evaluating the impact of sampling schemes on leaf area index measurements from digital hemispherical photography in Larix principis-rupprechtii forest plots

BackgroundDigital hemispherical photography (DHP) is widely used to estimate the leaf area index (LAI) of forest plots due to its advantages of high efficiency and low cost. A crucial step in the LAI estimation of forest plots via DHP is choosing a sampling scheme. However, various sampling schemes involving DHP have been used for the LAI estimation of forest plots. To date, the impact of sampling schemes on LAI estimation from DHP has not been comprehensively investigated.MethodsIn this study, 13 commonly used sampling schemes which belong to five sampling types (i.e. dispersed, square, cross, transect and circle) were adopted in the LAI estimation of five Larix principis-rupprechtii plots (25 m × 25 m). An additional sampling scheme (with a sample size of 89) was generated on the basis of all the sample points of the 13 sampling schemes. Three typical inversion models and four canopy element clumping index (Ωe) algorithms were involved in the LAI estimation. The impacts of the sampling schemes on four variables, including gap fraction, Ωe, effective plant area index (PAIe) and LAI estimation from DHP were analysed. The LAI estimates obtained with different sampling schemes were then compared with those obtained from litter collection measurements.ResultsLarge differences were observed for all four variable estimates (i.e. gap fraction, Ωe, PAIe and LAI) under different sampling schemes. The differences in impact of sampling schemes on LAI estimation were not obvious for the three inversion models, if the four Ωe algorithms, except for the traditional gap-size analysis algorithm were adopted in the estimation. The accuracy of LAI estimation was not always improved with an increase in sample size. Moreover, results indicated that with the appropriate inversion model, Ωe algorithm and sampling scheme, the maximum estimation error of DHP-estimated LAI at elementary sampling unit can be less than 20%, which is required by the global climate observing system, except in forest plots with extremely large LAI values (~ > 6.0). However, obtaining an LAI from DHP with an estimation error lower than 5% is impossible regardless of which combination of inversion model, Ωe algorithm and sampling scheme is used.ConclusionThe LAI estimation of L. principis-rupprechtii forests from DHP was largely affected by the sampling schemes adopted in the estimation. Thus, the sampling scheme should be seriously considered in the LAI estimation. One square and two transect sampling schemes (with sample sizes ranging from 3 to 9) were recommended to be used to estimate the LAI of L. principis-rupprechtii forests with the smallest mean relative error (MRE). By contrast, three cross and one dispersed sampling schemes were identified to provide LAI estimates with relatively large MREs.

A mobility compensation method for drones in SG-eIoT

In order to achieve the specific goal of a smart grid, the concept of electricity Internet of Things (eIoT) has been proposed to assist the monitoring and inspection of power transmission line state and optimize the asset utilization. The long power transmission line and the complex field operation environment urge the introduction of drones into the eIoT for fast power transmission line inspection, data collection from sensors for further big data analysis, adaptive control of power line voltage, etc. Additionally, drones can also act as a central communication control or relay point to serve the data exchange among sensors, drones and power transmission line maintenance personnel in the scenario where the conventional mobile communication service is not available. However, the fast mobility of drones may affect the signal transmission and position estimation performance, which may further deteriorate the networking performance. In order to solve this problem, a mobility compensation method is proposed, which includes the steps of frequency offset estimation and relative velocity calculation. Through the Monte Carlo simulations, the proposed algorithm shows favorable gains compared with the conventional ones.

Is Clustering Advantageous in Statistical Ill-Posed Linear Inverse Problems?

In many statistical linear inverse problems, one needs to recover classes of similar objects from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application. Routinely, in such problems clustering is carried out at a pre-processing step and then the inverse problem is solved for each of the cluster averages separately. As a result, the errors of the procedures are usually examined for the estimation step only. The objective of this paper is to examine, both theoretically and via simulations, the effect of clustering on the accuracy of the solutions of general ill-posed linear inverse problems. In particular, we assume that one observes $X_{m} = A f_{m} + \delta \epsilon _{m}$ , $m=1, \cdots, M$ , where functions $f_{m}$ can be grouped into $K$ classes and one needs to recover a vector function $\mathbf {f}= (f_{1},\cdots, f_{M})^{T}$ . We construct an estimator for $\mathbf {f}$ as a solution of a penalized optimization problem which corresponds to the clustering before estimation setting. We derive an oracle inequality for its precision and confirm that the estimator is minimax optimal or nearly minimax optimal up to a logarithmic factor of the number of observations. One of the advantages of our approach is that we do not assume that the number of clusters is known in advance. Subsequently, we compare the accuracy of the above procedure with the precision of estimation without clustering, and clustering following the recovery of each of the unknown functions separately. We conclude that clustering at the pre-processing step is beneficial when the problem is moderately ill-posed. It should be applied with extreme care when the problem is severely ill-posed.

On maximum likelihood estimation of competing risks using the cause-specific semi-parametric Cox model with time-varying covariates – An application to credit risk

Credit-granting institutions need to estimate the probability of loan default, which represents the chance a customer fails to make repayments as promised. Critically this estimation is intertwined with the competing risk a customer fully repays their loan while also having key predictive drivers with values that change over time. A conventional model in this setting is a competing risks Cox Model with time-varying covariates. However partial likelihood estimation of this model has two shortcomings: (1) the baseline hazard is not estimated, so calculating probabilities requires a further estimation step; and (2) a covariance matrix for both regression coefficients and the baseline hazard is not produced. This paper caters for these shortcomings by devising a maximum likelihood technique to jointly estimate regression coefficients and the cause-specific baseline hazards using constrained optimisation to ensure the latter’s non-negativity. We show via simulation our technique produces regression coefficients estimates with lower bias in small samples with heavy censoring. When applied to a real-world credit risk dataset consisting of home loan data our Maximum Likelihood approach produces a smoother estimate of the cause-specific baseline hazards for default and redemption than those obtained using the Partial Likelihood and Breslow approach. This provides better clarity of the shape of these functions through both a less volatile central estimate as well as quantifying the error of this central estimate. We implement our method in R.

High dimensional, robust, unsupervised record linkage

Abstract We develop a technique for record linkage on high dimensional data, where the two datasets may not have any common variable, and there may be no training set available. Our methodology is based on sparse, high dimensional principal components. Since large and high dimensional datasets are often prone to outliers and aberrant observations, we propose a technique for estimating robust, high dimensional principal components. We present theoretical results validating the robust, high dimensional principal component estimation steps, and justifying their use for record linkage. Some numeric results and remarks are also presented.

Efficient interaction selection for clustered data via stagewise generalized estimating equations.

Model selection in the presence of interaction terms is challenging as the final model must maintain a hierarchy between main effects and interaction terms. This work presents two stagewise estimation approaches to appropriately select models with interaction terms that can utilize generalized estimating equations to model clustered data. The first proposed technique is a hierarchical lasso stagewise estimating equations approach, which is shown to directly correspond to the hierarchical lasso penalized regression. The second is a stagewise active set approach, which enforces the variable hierarchy by conforming the selection to a properly growing active set in each stagewise estimation step. The effectiveness in interaction selection and the superior computational efficiency of the proposed techniques are assessed in simulation studies. The new methods are applied to a study of hospitalization rates attributed to suicide attempts among 15 to 19 year old at the school district level in Connecticut.

Parameter estimation by type-2 fuzzy logic in case that data set has outlier

One of the problems encountered in estimating the unknown parameters of the regression models is the presence of outliers in the data set. This situation may cause problems in providing some assumptions such as the normal distribution for the parameter estimation process and the homogeneity of the variances. The case of the presence of outlier observations in the data set, estimation methods based on fuzzy logic that can be minimized the level of impact of this data are emerged as available methods. If fuzzy logic is used in regression analysis, there are two main steps for parameter estimation. The first of these is to define the clusters that compose the data set, and the other is calculate the degree of membership to determining the contributions of the data to each model for the clusters. In this study, type-2 fuzzy clustering algorithm defined as an expansion of fuzzy c-means algorithm in the determination of membership degrees of data sets was benefited. The presence of outliers in the data set is addressed. An algorithm has been proposed to estimate the unknown belonging to parameters of the regression model using the membership degrees obtained relating to the cluster elements. The parameters were estimated using regression methods to examine the effectiveness of the algorithm that called robust methods, and the results obtained were compared.

Inverse radiation problem with infrared images to monitor plasma-facing components temperature in metallic fusion devices

Abstract Infrared (IR) diagnostics are used to measure plasma-facing components (PFC) surface temperature in fusion devices. However, the interpretation of such images is complex in all-reflective environments because of unknown emissivity and multiple reflections issues. In order to assess these challenges an iterative inversion method based on a fast photonic model, the radiosity method, has been developed. The radiosity method is based on strong hypotheses including all diffuse surfaces. The inversion method allows retrieving the true surface temperature of PFC in two steps: a step of the target emissivity estimation in a baking scene and the use of the emissivity map to retrieve the temperature of metallic components with errors up to 3% during a plasma scenario.

Kalman-Based Calibration Algorithm for AgaMatrix Continuous Glucose Monitoring System

A continuous glucose monitoring system is composed of a glucose sensor and an estimation (calibration) algorithm. The glucose sensor is composed of an electrode that is inserted under the skin and generates a noisy electrical current in response to interstitial glucose levels. The relationship between the electrical current and the interstitial glucose levels varies between individuals and within the same individual (with sensor wear time). The estimation algorithm infers the glucose levels in the blood from the noisy electrical current signal and uses intermittent capillary glucose measurements to account for intra-and inter-individual variability. In this article, we propose a novel real-time Kalman filter-based estimation algorithm that is composed of three steps: 1) noise filtering step; 2) compartment matching step using sequential Kalman filter; and 3) parameters estimation step using the conventional Kalman filter. The initial estimate of the parameters and covariance matrix are extracted offline using a nonlinear cubature Kalman filter. Our algorithm is compared with four alternative algorithms using 20 sensor data sets. Each data set was generated over a seven-day sensor wear period, during which patients were tested on three in-clinic days (days 1, 4, and 7). The comparison is based on the mean absolute relative difference (MARD) between frequent reference glucose measurements and the sensor glucose levels. MARD for days 1, 4, and 7 were 10.3%, 10.7%, and 11.9% for our algorithm and 12.46%, 15.75%, and 14.17% for the alternative algorithm, respectively. Our algorithm is currently being integrated into a commercial continuous glucose monitoring system (AgaMatrix, Inc., Salem, NH, USA).

Deep Convolutional Neural Network-Based Robust Phase Gradient Estimation for Two-Dimensional Phase Unwrapping Using SAR Interferograms

Two-dimensional phase unwrapping (2-D PU) is one of the key processes in reconstructing the topography or displacement of the Earth surface from its interferometric synthetic aperture radar (InSAR) data. Estimating the absolute phase gradient information is an unavoidable step utilized by almost all the 2-D PU methods. Traditionally, the gradient estimation step relies on the phase continuity assumption, which requests that the observed area has spatial continuity. However, the abrupt topographic changes and system noise usually results in the failure of the phase continuity assumption in reality. Under this condition, it is difficult for the traditional 2-D PU to provide the correct absolute phase over the area with abrupt interferometric fringe change or with strong system noise. To solve the issue, we propose a novel deep convolutional neural network (DCNN), abbreviated as PGNet, to estimate the phase gradient information instead of the phase continuity assumption in this article. The major advantage of PGNet lies in its deep architecture to learn the characteristics of phase gradients from enormous training images with different noise levels and topographic features. Subsequently, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm objective function is used to minimize the difference between unwrapped phase gradients and the gradients estimated by PGNet for obtaining the final PU result. Taking the phase gradient pattern of the TerraSAR-X-TanDEM-X interferogram as the learning object, experimental results demonstrate the absolute phase gradient estimated by PGNet is more credible than that from the phase continuity assumption such that the corresponding PU result outperforms those obtained by the traditional 2-D PU methods.

단안 카메라와 심층강화학습을 이용한 소형 무인기 실내 충돌 회피 시스템

Collision avoidance of drones in a complex environment, especially in an indoor environment, is a challenging task. This paper develops an obstacle avoidance system for small multi-rotor drones based on a deep reinforcement learning algorithm using only a monocular camera. The proposed method comprises two steps: depth estimation and navigation decision-making. For the depth estimation step, a pre-trained depth estimation algorithm based on a CNN (Convolutional Neural Network) is used. In the navigation decision-making step, a dueling double deep Q-network is employed. The entire training procedure is performed in a Gazebo simulation environment using a robot operating system. To validate the robustness of the proposed approach, various simulations and experiments are conducted using a Parrot Bebop2 drone in an indoor corridor. We demonstrate that the proposed algorithm successfully navigates through a narrow corridor comprising a texture-free wall, people, and boxes. A supplementary video clip of the experiments can be found at https://youtu.be/oSQHCsvuE-8.

A study on parameter estimation and suppression for smeared spectrum jamming based on short-time Fourier transform

We address the suppressing problem of smeared spectrum (SMSP) jamming from the mixed signal received by the radar. To this end, we resort to the time-frequency analysis algorithm and give the concrete expression formula of the short-time Fourier transform (STFT) of SMSP jamming. The proposed method is to estimate the parameters of the jamming signal based on the STFT result, and then the jamming signal is reconstructed and suppressed form the mixed signal. In order to perform effective interference even after the pulse compression process, the jamming-to-target ratio (JSR) is always positive. Based on this assumption, the estimation steps for different parameters of SMSP jamming are given, including the number of sub-waveforms, the amplitude, and the time delay. The influence of choosing different window is also considered in this paper. The estimated performance of this method is verified by Monte Carlo simulation, and the results show the effectiveness of the proposed method.

A parameter choice rule for Tikhonov regularization based on predictive risk

In this work, we propose a new criterion for choosing the regularization parameter in Tikhonov regularization when the noise is white Gaussian. The criterion minimizes a lower bound of the predictive risk, when both data norm and noise variance are known, and the parameter choice involves minimizing a function whose solution depends only on the signal-to-noise ratio. Moreover, when neither noise variance nor data norm is given, we propose an iterative algorithm which alternates between a minimization step of finding the regularization parameter and an estimation step of estimating signal-to-noise ratio. Simulation studies on both small- and large-scale datasets suggest that the approach can provide very accurate and stable regularized inverse solutions and, for small sized samples, it outperforms discrepancy principle, balancing principle, unbiased predictive risk estimator, L-curve method, generalized cross validation, and quasi-optimality criterion, and achieves excellent stability hitherto unavailable.