Function Estimation Method Research Articles

A robust approach to estimating production functions: Replication of the ACF procedure

SummaryWe study Ackerberg, Caves, and Frazer's (Econometrica, 2015, 83, 2411–2451; hereafter ACF) production function estimation method using Monte Carlo simulations. First, we replicate their results by following their procedure to confirm the existence of a spurious minimum in the estimation, as noted by ACF. In the population, or when sample sizes are sufficiently large, this “global” identification problem may not be a concern because the spurious minimum occurs only at extreme values of capital and labor coefficients. However, in finite samples, their estimator can produce estimates that may not be clearly distinguishable from the spurious ones. In our second experiment, we modify the ACF procedure and show that robust estimates can be obtained using additional lagged instruments or sequential search. We also provide some arguments for why such modifications help in the ACF setting.

Unrestricted and controlled identification of loss functions: Possibility and impossibility results

The property that the conditional mean is the unrestricted optimal forecast characterizes the Bregman class of loss functions, while the property that the α-quantile is the unrestricted optimal forecast characterizes the generalized α-piecewise linear (α-GPL) class. However, in settings where the forecaster’s choice of forecasts is limited to the support of the predictive distribution, different Bregman losses lead to different forecasts. This is not true for the α-GPL class: the failure of identification is more fundamental. Motivated by these examples, we state simple conditions that can be used to ascertain whether loss functions that are consistent for the same statistical functional become identifiable when off-support forecasts are disallowed. We also study the identifying power of unrestricted forecasts within the class of smooth, convex loss functions. For any such loss ℓ, the set of losses that are consistent for the same statistical functional as ℓ is a tiny subset of this class in a precise mathematical sense. Finally, we illustrate the identification problem that is posed by the non-uniqueness of consistent losses for the moment-based loss function estimation methods proposed in the literature.

Application of the Functional Size Measurement Method on the Example of the National Register of Ukraine

An example of using the COSMIC functional size estimation method for calculating the size of the Unified State Information and Telecommunication System “Electronic Register of Apostilles” at COSMIC functional points is considered. The approaches to estimating the complexity and cost of creating this system based on its functional size are discussed.

An alternative distribution function estimation method using rational Bernstein polynomials

This paper gives a general method for nonparametric distribution function estimation using the rational Bernstein polynomials as an alternative to the current estimators. The proposed new method is compared with Bernstein polynomials and empirical distribution function methods by simulation studies. The new method guarantees monotone nondecreasing function by applying linear constraints on the coefficients of the rational Bernstein basis functions and smooth the empirical distribution function. Furthermore, as a special case, it reduces to Bernstein polynomial estimator method. Some theoretical properties of the new estimator are investigated. Simulation study shows that the proposed estimator is preferable to the Bernstein polynomials and empirical distribution function estimator methods.

Barrier-Certified Adaptive Reinforcement Learning With Applications to Brushbot Navigation

This paper presents a safe learning framework that employs an adaptive model learning algorithm together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique. We use the learned model in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding particular undesirable regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate an action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring the greedy policy improvement under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has previously been used under stationarity assumptions in the safe learnings literature, and is then tested on a real robot, the brushbot, whose dynamics is unknown, highly complex and nonstationary.

Personalized HRTF Modeling Based on Deep Neural Network Using Anthropometric Measurements and Images of the Ear

This paper proposes a personalized head-related transfer function (HRTF) estimation method based on deep neural networks by using anthropometric measurements and ear images. The proposed method consists of three sub-networks for representing personalized features and estimating the HRTF. As input features for neural networks, the anthropometric measurements regarding the head and torso are used for a feedforward deep neural network (DNN), and the ear images are used for a convolutional neural network (CNN). After that, the outputs of these two sub-networks are merged into another DNN for estimation of the personalized HRTF. To evaluate the performance of the proposed method, objective and subjective evaluations are conducted. For the objective evaluation, the root mean square error (RMSE) and the log spectral distance (LSD) between the reference HRTF and the estimated one are measured. Consequently, the proposed method provides the RMSE of −18.40 dB and LSD of 4.47 dB, which are lower by 0.02 dB and higher by 0.85 dB than the DNN-based method using anthropometric data without pinna measurements, respectively. Next, a sound localization test is performed for the subjective evaluation. As a result, it is shown that the proposed method can localize sound sources with higher accuracy of around 11% and 6% than the average HRTF method and DNN-based method, respectively. In addition, the reductions of the front/back confusion rate by 12.5% and 2.5% are achieved by the proposed method, compared to the average HRTF method and DNN-based method, respectively.

Minimax Estimation of the <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math> </inline-formula> Distance

We consider the problem of estimating the $L_1$ distance between two discrete probability measures $P$ and $Q$ from empirical data in a nonasymptotic and large alphabet setting. When $Q$ is known and one obtains $n$ samples from $P$, we show that for every $Q$, the minimax rate-optimal estimator with $n$ samples achieves performance comparable to that of the maximum likelihood estimator (MLE) with $n\ln n$ samples. When both $P$ and $Q$ are unknown, we construct minimax rate-optimal estimators whose worst case performance is essentially that of the known $Q$ case with $Q$ being uniform, implying that $Q$ being uniform is essentially the most difficult case. The \emph{effective sample size enlargement} phenomenon, identified in Jiao \emph{et al.} (2015), holds both in the known $Q$ case for every $Q$ and the $Q$ unknown case. However, the construction of optimal estimators for $\|P-Q\|_1$ requires new techniques and insights beyond the approximation-based method of functional estimation in Jiao \emph{et al.} (2015).

Weighting Estimation Methods for Opponents' Utility Functions Using Boosting in Multi-Time Negotiations

Recently, multi-issue closed negotiations have attracted attention in multi-agent systems. In particular, multitime and multi-lateral negotiation strategies are important topics in multi-issue closed negotiations. In multi-issue closed negotiations, an automated negotiating agent needs to have strategies for estimating an opponent's utility function by learning the opponent's behaviors since the opponent's utility information is not open to others. However, it is difficult to estimate an opponent's utility function for the following reasons: (1) Training datasets for estimating opponents' utility functions cannot be obtained. (2) It is difficult to apply the learned model to different negotiation domains and opponents. In this paper, we propose a novel method of estimating the opponents' utility functions using boosting based on the least-squares method and nonlinear programming. Our proposed method weights each utility function estimated by several existing utility function estimation methods and outputs improved utility function by summing each weighted function. The existing methods using boosting are based on the counting method, which counts the number of values offered, considering the time elapsed when they were offered. Our experimental results demonstrate that the accuracy of estimating opponents' utility functions is significantly improved under various conditions compared with existing utility function estimation methods without boosting.

Application of an improved wavelet threshold algorithm in pulse measuring instrument

Aiming at the problem that the wavelet threshold algorithm is poor denoising effect in traditional pulse measuring instrument, an adaptive filtering algorithm of improved wavelet threshold function and threshold estimation is proposed in this system. This algorithm is used to eliminate the constant deviation of soft threshold function and the discontinuous shortcomings of hard threshold function by constructing a new threshold function and threshold estimation method and adjusting the adaptive adjustment coefficient, thus filtering out the interference noise in photoplethysmograph signals. The light intensity signals acquired by the photoelectric sensor are sequentially processed by signal amplifying circuit and filter circuit, the photoplethysmography signals are transmitted into LPC2103 for further processing, the results are displayed on the LCD screen. Experiments show that the improved wavelet threshold algorithm not only preserves the useful signal, but also avoids the oscillation. The algorithm is employed to denoise the pulse wave, which effectively improves the accuracy of the pulse measuring instrument.

Comparison of accepted and unaccepted living kidney donors: one-center experience

Background: Kidney transplantation from living donors (LD) has stagnated in many countries. This study aimed to check whether correction of LD selection practice could increase the number of kidney transplantations.Methods: From January 2003 to December 2012, 241 potential adult LD were evaluated in our hospital. Outcome (mortality and end-stage renal disease-ESRD) of accepted LD (182) was compared with unaccepted (59) donors.Results: Mortality of LD was comparable with that for the standardized Serbian population (SMR = 1.104; 95% CI (0.730–1.606). Among evaluated potential LD, almost every fourth had been unaccepted, but reasons were modifiable in 42.4% of them. In pre-donation period unaccepted donors were significantly older, measured glomerular filtration rate was lower, with higher 15-year and lifelong projected ESRD risks than accepted donors. Despite this, ten years outcome of both groups LD was similar: none of LD developed ESRD, 9.8% of accepted and 11.8% of unaccepted LD died (p = .803).Conclusions: During an average of 101 months of follow-up mortality of accepted LD did not differ significantly as compared to the age standardized Serbian population and none of them developed ESRD. In examination of potential LD, the use of accurate and precise methods for kidney function estimation and the evaluation of risk for ESRD and mortality as well as treatment of modifiable contraindications for kidney donation are necessary.

A Method for Point Spread Function Estimation for Accurate Quantitative Imaging

Aim: A method to determine the point spread function (PSF) of an imaging system based on a set of 3-D Gaussian functions is presented for a robust estimation of the recovery corrections for accurate activity quantification in positron emission tomography (PET) and single-photon emission computed tomography systems. Materials and Methods: The spatial resolution of the ALBIRA II PET subsystem was determined using a 370-kBq 22Na point source. The measured data were reconstructed with a maximum-likelihood expectation-maximization algorithm. The PSF was calculated based on the National Electrical Manufacturing Association (NEMA) NU-4 2008 protocol and on alternative methods based on three 3-D fitting functions for the xyz-directions: 1) a 3-D Gaussian function (3-D 1-Gauss) and convolutions of this function with a pixel size (3-D ${\text {Gauss}}_{p}$ ) or source dimension of O 0.25 mm (3-D ${\text {Gauss}}_{s}$ ); 2) the sum of two Gaussian functions (3-D 2-Gauss); and 3) three Gaussian functions (3-D 3-Gauss). Goodness of fit and the method based on an Akaike information criterion were used for choosing the best function. A MATLAB-based mathematical source simulation study was performed to quantify the relevance of PSFs calculated from the different methods. Results: Based on the PSFs calculated from the NEMA protocol, the full-width at half-maximum (FWHM) in xyz-directions were 1.68, 1.51, and 1.50 mm. The corresponding results using 3-D Gauss and 3-D ${\text {Gauss}}_{s}$ functions both were (1.87 ± 0.01), (1.70 ± 0.01), and (1.50 ± 0.01) mm and for 3-D ${\text {Gauss}}_{p}$ were (1.84 ± 0.01), (1.67 ± 0.01), and (1.47 ± 0.01) mm. The FWHMs calculated with 3-D 2-Gauss and 3-D 3-Gauss were (1.78 ± 0.01), (1.74 ± 0.01), and (1.83 ± 0.01) mm and (1.76 ± 0.03), (1.72 ± 0.03), and (1.78 ± 0.03) mm, respectively. All coefficients of variations of the fit parameters were ≤29% and the adjusted $R^{2}$ were ≥0.99. Based on Akaike weights $w_{i}$ , the 3-D 3-Gauss method was best supported by the data ( $w_{i} = 100$ %). The simulation study showed a relative error in quantification of spherical lesions in the range of 15%–45% for lesions of diameters 1–5 mm compared to the PSFs based on the NEMA method. Conclusion: An alternative method to calculate the PSFs of imaging systems to accurately correct for recovery effects is presented. The proposed method includes choosing and fitting of 3-D functions, validation of fitting quality, and choosing the function best supported by the data along with an estimation of the uncertainty.

Measuring Geographic Inequalities: Dealing with Multiple Health Resources by Data Envelopment Analysis.

The existence of geographic differences in health resources, health expenditures, the utilization of health services, and health outcomes have been documented by a lot of studies from various countries of the world. In a publicly financed health system, equal access is one of the main objectives of the national health policy. That is why inequalities in the geographic allocation of health resources are an important health policy issue. Measures of inequality express the complexity of variation in the observed variable by a single number, and there is a variety of inequality measures available. The objective of this study is to develop a measure of the geographic inequality in the case of multiple health resources. The measure uses data envelopment analysis (DEA), which is a non-parametric method of production function estimation, to transform multiple resources into a single virtual health resource. The study shows that the DEA originally developed for measuring efficiency can be used successfully to measure inequality. For the illustrative purpose, the inequality measure is calculated for the Czech Republic. The values of separate Robin Hood Indexes (RHIs) are 6.64% for physicians and 3.96% for nurses. In the next step, we use combined RHI for both health resources. Its value 5.06% takes into account that the combinations of two health resources serve regional populations.

Robust-BD Estimation and Inference for General Partially Linear Models

The classical quadratic loss for the partially linear model (PLM) and the likelihood function for the generalized PLM are not resistant to outliers. This inspires us to propose a class of “robust-Bregman divergence (BD)” estimators of both the parametric and nonparametric components in the general partially linear model (GPLM), which allows the distribution of the response variable to be partially specified, without being fully known. Using the local-polynomial function estimation method, we propose a computationally-efficient procedure for obtaining “robust-BD” estimators and establish the consistency and asymptotic normality of the “robust-BD” estimator of the parametric component β o . For inference procedures of β o in the GPLM, we show that the Wald-type test statistic W n constructed from the “robust-BD” estimators is asymptotically distribution free under the null, whereas the likelihood ratio-type test statistic Λ n is not. This provides an insight into the distinction from the asymptotic equivalence (Fan and Huang 2005) between W n and Λ n in the PLM constructed from profile least-squares estimators using the non-robust quadratic loss. Numerical examples illustrate the computational effectiveness of the proposed “robust-BD” estimators and robust Wald-type test in the appearance of outlying observations.

A Robust Approach to Estimating Production Functions: Replication of the ACF Procedure

We study Ackerberg, Caves, and Frazer (2015)'s production function estimation method using Monte Carlos simulations. First, we replicate their results by using the same procedure and confirm the existence, as noted by ACF, of a spurious minimum in the estimation. In the population, or when the sample size is large enough, this global identification problem may not be a concern because the spurious minimum holds only at the extreme values of the capital and the labor coefficients. However, in the finite samples, their estimator can produce estimates that may not be clearly regarded as the spurious ones. In our second experiment, we modify the ACF procedure and show that using additional lagged instruments or a sequential search help to obtain robust estimates. We also provide some arguments why such modifications help in the ACF setting.

Research on reliability of steel roof structures subjected to snow loads at representative sites in China

An appropriate probabilistic description of snow loads is important in reliability analysis. Probability distributions for annual maximum ground snow loads are studied in detail in this paper based on the samples of snow loads on the ground, which are simulated by a snowmelt model. Then, selection of probability distribution function and parameter estimation method for ground snow loads is found to have a great influence on reliability assessment results. The reliability of members of steel roof structures subjected to snow load at four representative sites in China is investigated. The reliability indices of studied roofs are found not to be enough to reach the target value 3.2. The possible reason is that characteristic value of snow loads on the ground specified in Chinese load code is not conservative and the partial factor 1.4 for snow loads on roofs is not enough. To ensure designed roofs subjected to extreme snow loads a target reliability index 3.2, large partial factors for snow load that varies with COV of ground snow loads are expected to be used.

Inverse Probability Weighted Cox Regression for Doubly Truncated Data

Doubly truncated data arise when event times are observed only if they fall within subject-specific, possibly random, intervals. While non-parametric methods for survivor function estimation using doubly truncated data have been intensively studied, only a few methods for fitting regression models have been suggested, and only for a limited number of covariates. In this article, we present a method to fit the Cox regression model to doubly truncated data with multiple discrete and continuous covariates, and describe how to implement it using existing software. The approach is used to study the association between candidate single nucleotide polymorphisms and age of onset of Parkinson's disease.

PP.04.01] LEFT ATRIUM FUNCTION IN SYSTEMIC ARTERIAL HYPERTENSION

Objective: Assessment of left atrium (LA) mechanic by 2-Dimensional Speckle tracking Imaging (STI) recently has been discussed as useful method for LA function estimation. The purpose of this study was to assess the relationship between LA function (particularly reservoir function) and LA structural remodeling in patients with systemic arterial hypertension. LA evaluation was made using conventional echocardiography, tissue Doppler, and 2-Dimensional STI. Design and method: 48 hypertensive patients without left ventricular hypertrophy and 36 healthy controls (age and gender matched), underwent routine transthoracic echocardiography and speckle tracking echocardiography of the left atrium. LA volume was calculated by the biplane Simpson's method. Peak early diastolic transmitral flow velocity, peak early diastolic mitral annular motion velocity (E/E1) and peak systolic LA strain were messured. Results: LV Mass was 132.7 ± 16.5 grams in control and 180.2 ± 60.4 grams in the hypertensive patients. Left atrium volume indexed to body surface area was 19.4 ± 5.4 versus 29.4 ± 4.3 ml/m2 in controls and hypertensive subjects respectively (p < 0.001). There were also significant differences between the measurements of transmitral flow velocities (E, A), and E/E1 and E/A ratios in both groups. Left atrium anteroposterior diameter was higher in the hypertensive group 4.20 ± 0.58 versus 3.4 ± 0.28 cm in the contols (p < 0.001). Left atrial longitudinal strain was 24.05 ± 3.18 in hypertensive patients and 32.7 ± 2.8 among controls (p < 0.001). Conclusions: Speckle tracking imaging might be assumed as method for early detection of LA function impairment in arterial hypertension.

Blind quantum source separation: Quantum-processing qubit uncoupling systems based on disentanglement

Blind Quantum Source Separation (BQSS) deals with multi-qubit states, called “mixed states”, obtained by applying an unknown “mixing function” (which typically corresponds to undesired coupling, e.g. between qubits implemented as close electron spins 1/2) to unknown multi-qubit “source states”, which are product states (and pure in the simplest case, considered in this paper). Some other properties are also possibly requested from these source states and/or mixing function. Using mixed states, BQSS systems aim at restoring (the information contained in) source states, during the second phase of their operation (“inversion phase”). To this end, they estimate the unmixing function (inverse of mixing function), during the first phase of their operation (“adaptation phase”). Most previously reported BQSS systems first convert mixed states into classical-form data, that they then process with classical means. Besides, they estimate the unmixing function by using statistical methods related to classical Independent Component Analysis. On the contrary, the new BQSS systems proposed here use only quantum-form data and quantum processing in the inversion phase, and they use classical-form data during the adaptation phase only. Moreover, their unmixing function estimation methods are essentially based on using unentangled source states during that phase. They mainly consist of disentangling the output quantum state of the separating system (for a few source states). Afterwards, they can also restore entangled source states. They yield major improvements over previous systems, concerning restored source parameters, associated indeterminacies and approximations, number of source states required for adaptation, numbers of source state preparations in adaptation and inversion phases. Numerical tests confirm that they accurately restore quantum source states.

A New Car-Following Model Based on the Epsilon-Support Vector Regression Method using the Parameters Tuning and Data Scaling Techniques

Traffic simulation is a powerful tool for analyzing and solving several transportation issues and traffic problems. However, all traffic micro-simulation models require a suitable car-following model to show the real situation in the best way possible. Several car-following models have been proposed. An obvious disadvantage of the former models is the great number of parameters which are difficult to calibrate. Moreover, any change in these parameters creates considerable disturbances. In this paper, a car-following model was proposed using the Epsilon-Support Vector Regression (e-SVR) method whose output is the acceleration of the following car. Radial Basis Function was used as the kernel of the e-SVR method, and the model parameters were tuned using the Grid Search method. The best values for the parameters were obtained. Furthermore, linear scaling in the interval [−1, 1] was used for both the training and testing input data, and the method was proven to more accurate than the case where no scaling was used. Accordingly, a car-following model with the mean squared error equal to 0.005 and the squared correlation coefficient equal to 0.98 was proposed using the function estimation method through the e-SVR method. Finally, the e-SVR output was compared with the results of the well-known car-following models, including Helly linear model, the GHR model, and the Gipps model. It was shown that, when using the scaling and parameters tuning techniques, the proposed method was more accurate compared to all three models mentioned above. Moreover, a function fitting Artificial Neural Network was run for this purpose and the outputs showed that the result of the e-SVR method is better than that of the function fitting method by the proposed ANN. Implementing a microscopic validation of the proposed model showed that it can be used in the drivers’ assistance devices and other purposes of intelligent transportation systems.

A novel Retinex image enhancement approach via brightness channel prior and change of detail prior

In this paper, we propose a novel Retinex image enhancement approach by adopting two important prior named brightness channel prior (BCP) and change of detail (CoD) prior. We first derive a rough illumination map estimation method via BCP and Retinex model. Then, we present a combination refining method which involves the guided filter and a new total variation (TV) smoothing operator to eliminate the block effect in the rough illumination map while maintain the local smoothness property. In addition, we propose a novel sharping algorithm rely on CoD prior to improve the visual effect of the degraded image. Experimental results verify that our approach outperforms current approaches in terms of effectiveness, efficiency and universality.