Moment Information Research Articles

On Mis-Measured Binary Regressors: New Results and Some Comments on the Literature

This paper studies the use of a discrete instrumental variable to identify the causal effect of a endogenous, mis-measured, binary treatment in a homogeneous effects model with additively separable errors. We begin by showing that the only existing identification result for this case, which appears in Mahajan (2006), is incorrect. As such, identification in this model remains an open question. We provide a convenient notational framework to address this question and use it to derive a number of results. First, we prove that the treatment effect is unidentified based on conditional first-moment information, regardless of the number of values that the instrument may take. Second, we derive a novel partial identification result based on conditional second moments that can be used to test for the presence of mis-classification and to construct bounds for the treatment effect. In certain special cases, we can in fact obtain point identification of the treatment effect based on second moment information alone. When this is not possible, we show that adding conditional third moment information point identifies the treatment effect and completely characterizes the measurement error process.

Distributionally Robust Control of Constrained Stochastic Systems

We investigate the control of constrained stochastic linear systems when faced with limited information regarding the disturbance process, i.e., when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. In the first case, we require that the constraints hold with a given probability for all disturbance distributions sharing the known moments. These constraints are commonly referred to as distributionally robust chance constraints. In the second case, we impose conditional value-at-risk (CVaR) constraints to bound the expected constraint violation for all disturbance distributions consistent with the given moment information. Such constraints are referred to as distributionally robust CVaR constraints with second-order moment specifications. We propose a method for designing linear controllers for systems with such constraints that is both computationally tractable and practically meaningful for both finite and infinite horizon problems. We prove in the infinite horizon case that our design procedure produces the globally optimal linear output feedback controller for distributionally robust CVaR and chance constrained problems. The proposed methods are illustrated for a wind blade control design case study for which distributionally robust constraints constitute sensible design objectives.

How Robust is the Value-at-Risk of Credit Risk Portfolios?

In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, i.e., what is the maximum and minimum Value-at-Risk (VaR) of a portfolio of risky loans that can be justified given a certain amount of available information. Puccetti and Ruschendorf (2012b) and Embrechts et al. (2013) propose the rearrangement algorithm (RA) as a general method to approximate VaR bounds when the loss distributions of the different loans are known but not their interdependence. Their numerical results show that the gap between worst-case and best-case VaR is typically very high, a feature that can only be explained by lack of using dependence information. In this paper, we propose a modification of the RA that makes it possible to approximate sharp VaR bounds when besides the marginal distributions also higher order moments of the aggregate portfolio such as variance and skewness are available as sources of dependence information. A numerical study shows that the use of moment information makes it possible to significantly improve the (unconstrained) VaR bounds. However, VaR assessments of credit portfolios that are performed at high confidence levels (as it is the case in Solvency II and Basel III) remain subject to significant model uncertainty and are not robust. We provide some suggestions for strengthening future (capital) regulation.

A Survey of Support Vector Machines with Uncertainties

Support Vector Machines (SVM) is one of the well known supervised classes of learning algorithms. SVM have wide applications to many fields in recent years and also many algorithmic and modeling variations. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper presents a survey of SVM when the data points are uncertain. When a direct model cannot guarantee a generally good performance on the uncertainty set, robust optimization is introduced to deal with the worst case scenario and still guarantee an optimal performance. The data uncertainty could be an additive noise which is bounded by norm, where some efficient linear programming models are presented under certain conditions; or could be intervals with support and extremum values; or a more general case of polyhedral uncertainties with formulations presented. Another field of the uncertainty analysis is chance constrained SVM which is used to ensure the small probability of misclassification for the uncertain data. The multivariate Chebyshev inequality and Bernstein bounding schemes have been used to transform the chance constraints through robust optimization. The Chebyshev based model employs moment information of the uncertain training points. The Bernstein bounds can be less conservative than the Chebyshev bounds since it employs both support and moment information, but it also makes a strong assumption that all the elements in the data set are independent.

A Method to Deconvolve Errors in GPS RO-Derived Water Vapor Histograms

AbstractWater vapor is an important constituent in the earth’s atmosphere that must be understood to predict weather and climate. Water vapor is challenging to measure, and observations of water vapor must be as independent of weather and climate models as possible in order to assess and improve those models. When combined with independent atmospheric temperature estimates, GPS radio occultation (RO) refractivity profiles yield unique, all-weather, high-vertical-resolution, globally distributed profiles of tropospheric water vapor whose vertical extent is maximum at low latitudes. A method for retrieving water vapor, known as the direct method, combines GPS RO-derived refractivity with temperatures from global weather analyses. Unlike variational methods, the direct method does not use the water vapor estimates from analyses because of their potential systematic errors. While utilization of the direct method has been limited because it produces negative values, these unphysical negative values reveal unique information about errors. A deconvolution technique is presented here that uses the negative values to estimate and remove random errors in histograms of water vapor derived via the direct method. Results indicate direct method specific humidity errors at low latitudes range from 0.4 g kg−1 at 725 hPa to 0.14 g kg−1 near 350 hPa, which can be removed via deconvolution. The deconvolved histograms extend to about the 240-K level in the troposphere, corresponding to 10 km at low latitudes. Unlike the limited information of low-order statistical moments like means and variances, histograms capture the full range of variability, which opens a new window into water vapor behavior and increases understanding of processes at work in the hydrological cycle.

Design and calibration of a six-axis MEMS sensor array for use in scoliosis correction surgery

A six-axis sensor array has been developed to quantify the 3D force and moment loads applied in scoliosis correction surgery. Initially this device was developed to be applied during scoliosis correction surgery and augmented onto existing surgical instrumentation, however, use as a general load sensor is also feasible. The development has included the design, microfabrication, deployment and calibration of a sensor array. The sensor array consists of four membrane devices, each containing piezoresistive sensing elements, generating a total of 16 differential voltage outputs. The calibration procedure has made use of a custom built load application frame, which allows quantified forces and moments to be applied and compared to the outputs from the sensor array. Linear or non-linear calibration equations are generated to convert the voltage outputs from the sensor array back into 3D force and moment information for display or analysis.

모멘트 변화와 객체 크기 비율을 이용한 객체 행동 및 위험상황 인식

This paper proposes a method to track object of real-time video transferred through single web-camera and to recognize risk-situation and human actions. The proposed method recognizes human basic actions that human can do in daily life and finds risk-situation such as faint and falling down to classify usual action and risk-situation. The proposed method models the background, obtains the difference image between input image and the modeled background image, extracts human object from input image, tracts object’s motion and recognizes human actions. Tracking object uses the moment information of extracting object and the characteristic of object’s recognition is moment’s change and ratio of object’s size between frames. Actions classified are four actions of walking, waling diagonally, sitting down, standing up among the most actions human do in daily life and suddenly falling down is classified into risk-situation. To test the proposed method, we applied it for eight participants from a video of a web-cam, classify human action and recognize risk-situation. The test result showed more than 97 percent recognition rate for each action and 100 percent recognition rate for risk-situation by the proposed method.

Large deviation for a least squares estimator in a nonlinear regression model

By using a large deviation theory of the stochastic process and the moment information of errors, some large deviation results for the least squares estimator θn in a nonlinear regression model are obtained when errors satisfy some general conditions. For some p>1, examples are presented to show that our results can be used in the case for supn≥1E|ξn|p=∞ and a better bound can be obtained in the case for supn≥1E|ξn|p<∞. Our results generalize and improve the corresponding ones.

Development of 3D camera-based robust bolt-hole detection system for bolting cabin

Abstract At high-rise building construction sites, construction workers still climb dangerous vertical steel beams. Hence, the bolting cabin helps construction workers to assemble bolts safely. In order to automatically assemble bolts to steel frame, the bolting cabin must estimate bolt-hole location. To do this, precise bolt-hole detection algorithms are important. Generally, a 2D camera is used for visual servoing in industrial fields. However, a construction site is an outdoor environment that does not have constant illumination. Recently, a 3D camera that provides depth images has been used in industrial fields. However, this 3D camera provides a low resolution image with strong noise around the edges. To overcome these problems, an edge detection filter that is robust to strong noise is needed for precise bolt-hole detection. Therefore, we propose a Modified Discrete Gaussian-Hermite Moments (MDGHM) filter based on moment information to detect edges precisely. Using the MDGHM filter, the results show that the proposed method can be effectively applied to bolt-hole detection better than wavelet filter and mixed matching method.

5,6,7,9-Tetrahydro-[1,3]dioxolo[4,5-h]carbazol-8-one: A solvatochromic PET-acceptor fluorescent probe

In the present work, 5,6,7,9-tetrahydro-[1,3]dioxolo[4,5-h]carbazol-8-one (TDCO) has been established as a solvatochromic probe and an acceptor of photoinduced electron transfer through electronic absorption spectroscopy, steady-state and time-resolved fluorescence measurements and also by using the laser flash photolysis technique. Fluorescence spectra of the compound are more sensitive than its absorption spectra towards the nature of solvent and the composition of solvent mixture. In solvents with higher dielectric constant and better H-bond formation ability, fluorescence maximum of the compound shifts toward red. The reasons behind such solvent sensitivity of TDCO in electronic excited state are its higher dipole moment in excited state and formation of hydrogen bond with solvents. TDCO interacts with aromatic amine bases N,N-dimethylaniline (DMA) and N,N-diethylaniline (DEA) in excited state and as a consequence its fluorescence intensity and lifetime are quenched. The quenching order is the same as the order of ionization potential of the amines. Transient absorption studies indicate the involvement of photoinduced electron transfer from the amines to TDCO as a result of which the corresponding radical cations and anions have been formed. Simulation studies show that TDCO has the tendency to remain in stacked conformation with DMA and DEA, which facilitates photoinduced electron transfer.

The Newsvendor Under Demand Ambiguity: Combining Data with Moment and Tail Information

Operations managers do not typically have full information about the demand distribution. Recognizing this, data-driven approaches have been proposed in which the manager has no information beyond the evolving history of demand observations. In practice, managers often have some partial information about the demand distribution in addition to demand observations. We consider a repeated newsvendor setting, and propose a non-parametric, maximum-entropy based technique, termed SOBME (Second Order Belief Maximum Entropy), which allows the manager to effectively combine demand observations with distributional information in the form of bounds on the moments or tails. In the proposed approach, the decision maker forms a belief about possible demand distributions, and dynamically updates it over time using the available data and the partial distributional information. We derive a closed-form solution for the updating mechanism, and highlight that it generalizes the traditional Bayesian mechanism with an exponential modifier that accommodates partial distributional information. We prove the proposed approach is (weakly) consistent under some technical regularity conditions and we analytically characterize its rate of convergence. We provide an analytical upper bound for the newsvendor's cost of ambiguity, i.e., the extra per-period cost incurred due to ambiguity, under SOBME, and show that it approaches zero quite quickly. Numerical experiments demonstrate that SOBME performs very well. We find that it can be very beneficial to incorporate partial distributional information when deciding stocking quantities, and that information in the form of tighter moment bounds is typically more valuable than information in the form of tighter ambiguity sets. Moreover, unlike pure data-driven approaches, SOBME is fairly robust to the newsvendor quantile. Our results also show that SOBME quickly detects and responds to hidden changes in the unknown true distribution. We also extend our analysis to consider ambiguity aversion, and develop theoretical and numerical results for the ambiguity-averse, repeated newsvendor setting.

NURSE STAFFING UNDER DEMAND UNCERTAINTY TO REDUCE COSTS AND ENHANCE PATIENT SAFETY

Hospitals must maintain safe nurse-to-patient ratios in patient care units to offer adequate and safe patient care. Since the patient demand is highly variable, during high patient demand periods temporary or overtime nurses are hired to ensure safe nurse-to-patient ratios. These overtime nurses incur higher expense, and are often less effective. We study the problem of permanent nurse staffing level estimation under demand uncertainty as a newsvendor model. Our models are based on limited moment information of the demand distribution. Additionally, we introduce the use of asymmetric cost functions representing overstaffing and understaffing nursing costs. Findings using data from the general surgery and intensive care units at hospitals in Chicago, IL and Augusta, GA are presented. Computational results based on publically available cost data show that 3.1% and 7.3% annual cost savings result by introducing salvage value and newsvendor optimization in intensive care and general care units respectively. This new staffing scheme also improves patient safety as shifts are staffed with more permanent nurses.

A novel descriptor of protein sequences and its application

In this paper, a dynamic 3-D graphical representation of protein sequences is introduced based on three physical–chemical properties of amino acids. The coordinates of the graph have direct biological significance, which could reflect the innate structure of the proteins. The information of principal moments of inertia and range of axis coordinate are extracted as a novel mixed descriptor and proposed for the comparison of protein primary sequences. Meanwhile, the Euclidean distance of the normalized descriptor vectors which avoid the influence of the difference in length of protein sequences under consideration is employed as a quantitative measurement of the similarity of proteins. Finally, we take the nine ND5 (NADH dehydrogenase subunit 5) proteins for example and illustrate the effectiveness of our approach.

A Nonparametric Operational Risk Modeling Approach Based on Cornish-Fisher Expansion

It is generally accepted that the choice of severity distribution in loss distribution approach has a significant effect on the operational risk capital estimation. However, the usually used parametric approaches with predefined distribution assumption might be not able to fit the severity distribution accurately. The objective of this paper is to propose a nonparametric operational risk modeling approach based on Cornish-Fisher expansion. In this approach, the samples of severity are generated by Cornish-Fisher expansion and then used in the Monte Carlo simulation to sketch the annual operational loss distribution. In the experiment, the proposed approach is employed to calculate the operational risk capital charge for the overall Chinese banking. The experiment dataset is the most comprehensive operational risk dataset in China as far as we know. The results show that the proposed approach is able to use the information of high order moments and might be more effective and stable than the usually used parametric approach.

Second-order least-squares estimation for regression models with autocorrelated errors

In their recent paper, Wang and Leblanc (Ann Inst Stat Math 60:883---900, 2008) have shown that the second-order least squares estimator (SLSE) is more efficient than the ordinary least squares estimator (OLSE) when the errors are independent and identically distributed with non zero third moments. In this paper, we generalize the theory of SLSE to regression models with autocorrelated errors. Under certain regularity conditions, we establish the consistency and asymptotic normality of the proposed estimator and provide a simulation study to compare its performance with the corresponding OLSE and generalized least square estimator (GLSE). It is shown that the SLSE performs well giving relatively small standard error and bias (or the mean square error) in estimating parameters of such regression models with autocorrelated errors. Based on our study, we conjecture that for less correlated data, the standard errors of SLSE lie between those of the OLSE and GLSE which can be interpreted as adding the second moment information can improve the performance of an estimator.

Diagnosing Dynamic Asset Pricing Models with Generalized Entropy Bounds

I examine moment characteristics and predictability assumptions of dynamic asset pricing models. I propose a new measure --- the generalized entropy --- to summarize moment information of the multi-horizon pricing kernel for a dynamic model. Both static and dynamic strategy returns impose robust restrictions on the generalize entropy, providing a way to test candidate models. Applying this test to leading representative agent models and by creating dynamic strategies that depend on model-implied predictive signals, I find that models featuring growth uncertainty is able to explain market data better.

Maximum likelihood estimation of gamma parameters for coarsely binned and truncated raindrop size data

AbstractThe gamma family of probability densities has recently been used to model raindrop size. However, the traditional approach of using the method of moments to estimate the gamma distribution parameters is known to be biased and can have substantial errors. A recently developed approach combining moment information and a weighted least‐squares analysis generally produces substantially better results. Other procedures superior to the method of moments approach include maximum likelihood. In particular, maximum likelihood estimates have been shown to outperform method of moments estimators, both for the case in which the full range of drop sizes are observed and for the case in which small drop sizes fail to be observed because of the inability of disdrometers to record observations below a threshold.The foregoing comments on maximum likelihood concern the situation in which drop sizes are measured on a continuous scale. In this work we consider drop sizes from gamma distributions which are classified into broad size bins, as would be the case with data obtained from many disdrometers; this requires some modification of the maximum likelihood procedure. We also allow for the possibility of drop sizes below a threshold, or above another threshold, not being observed. Maximum likelihood performance in this case is investigated through simulation of volume sampling from gamma distributions with known parameters. We compare the performance of the maximum likelihood estimates with those of method of moments (only a truncated‐data version is viable) and the recently developed weighted least‐squares procedure, and also apply the three estimation procedures to some experimental data. Since the experimental data are surface data, we indicate how drop fall velocity may be incorporated to obtain parameters for the volume distributions from the surface data.

Distributionally robust mixed integer linear programs: Persistency models with applications

In this paper, we review recent advances in the distributional analysis of mixed integer linear programs with random objective coefficients. Suppose that the probability distribution of the objective coefficients is incompletely specified and characterized through partial moment information. Conic programming methods have been recently used to find distributionally robust bounds for the expected optimal value of mixed integer linear programs over the set of all distributions with the given moment information. These methods also provide additional information on the probability that a binary variable attains a value of 1 in the optimal solution for 0–1 integer linear programs. This probability is defined as the persistency of a binary variable. In this paper, we provide an overview of the complexity results for these models, conic programming formulations that are readily implementable with standard solvers and important applications of persistency models. The main message that we hope to convey through this review is that tools of conic programming provide important insights in the probabilistic analysis of discrete optimization problems. These tools lead to distributionally robust bounds with applications in activity networks, vertex packing, discrete choice models, random walks and sequencing problems, and newsvendor problems.

Currency Carry Trades, Position-Unwinding Risk, and Sovereign Credit Premia

This is the first study that employs option pricing model to measure the position-unwinding risk of currency carry trade portfolios, which well covers the moment information. We show that high interest-rate currencies are exposed to higher position-unwinding risk than low interest-rate currencies. We also investigate the sovereign CDS spreads as the proxy for countries' credit conditions and find that high interest-rate currencies load up positively on sovereign default risk while low interest-rate currencies provide a hedge against it. Sovereign credit premia as the dominant economic fundamental risk, together with position-unwinding likelihood indicator as the market risk (nonneutrality) sentiment, captures over 90% cross-sectional variations of carry trade excess returns. We identify sovereign credit risk as the impulsive country-specific risk that drives market volatility, and also its global contagion channels. Then We propose an alternative carry trade strategy immunized from crash risk, and a composite story of sovereign credit premia, global liquidity imbalances and liquidity reversal/spiral for explaining the forward premium puzzle.

Design of an Intelligent Point-to-Point Swing Arm Controller

The point-to-point swing arm test is very important for large arms which have swing arm movement. Traditional point-to-point swing arm controller is relay control mode. The mode has many shortcomings, such as big volume, high power consumption, low stability, and so on. An intelligent point-to-point swing arm controller, using MCU as the control core, was designed for this reason. It was mainly composed of switch signal detecting module, solenoid valve drive module, USB storage interface module and MCU control module. According to the requirements of test, the controller was able to detect the valid signal of limit switch and control commutation operation of solenoid valve, meanwhile it could record the movement time between one point and another point, the time the arm swayed and the moment information, and these above information would be stored in USB memory. It has some advantages of small size, low power consumption, high stability and flexible functions.