Rank-Invariance Conditions for the Comparison of Volatility Forecasts

2021 ◽  
Author(s):  
Alessandro Palandri
Keyword(s):  
Monte Carlo ◽  
Measurement Error ◽  
Measurement Errors ◽  
Conditional Variance ◽  
Loss Functions ◽  
Moment Condition ◽  
Model Estimation ◽  
Triplet Model ◽  
Functional Forms ◽  
Bias Variance

Abstract The paper derives four conditions which guarantee rank–invariance, i.e. that the empirical rankings (based on measurement error–affected variance proxies) of competing volatility forecasts be consistent with the true rankings (based on the unobservable conditional variance). The first three establish bounds beyond which the separation between the forecasts is enough for their rankings not to be affected by the measurement error. The conditions’ ability to establish rank-invariance with respect to forecast characteristics, such as bias, variance and correlation, is studied via Monte Carlo simulations. An additional moment condition identifies the functional forms of the triplet {model, estimation criterion, loss} for which the effects of measurement errors on the rankings cancel altogether. Both theoretical and empirical results show the extension of admissible loss functions achieving ranking consistency in forecast evaluations.

Optimization Method for Trajectory Correction Accuracy of Target Measurement Based on Monte-Carlo

2013 ◽  
Vol 441 ◽  
pp. 493-497
Author(s):  
Hui Juan Yang ◽  
Zheng Huang ◽  
Peng Fei Huo ◽  
Jia Wei Wang
Keyword(s):  
Monte Carlo ◽  
Measurement Error ◽  
Measurement Errors ◽  
Coupling Effect ◽  
System Development ◽  
Optimization Method ◽  
Design Solution ◽  
Design Basis ◽  
Trajectory Correction ◽  
Objective Indicators

Aiming at the coupling effect of target radiation measurement error and trajectory correction threshold to the hitting accuracy on the Last revised bullets, the optimal design solution based on Monte - Carlo method is proposed, and the CEP curve under the conditions of different correction threshold and target measurement errors by simulation is obtained. Moreover, objective indicators of measurement error and the corresponding threshold of amendments are given. A design basis for system development is obtained.

scholarly journals Qualitative Comparative Analysis: How Inductive Use and Measurement Error Lead to Problematic Inference

2013 ◽  
Vol 21 (2) ◽  
pp. 252-265 ◽  
Author(s):  
Simon Hug
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Comparative Analysis ◽  
Measurement Error ◽  
Boolean Algebra ◽  
Political Science ◽  
Measurement Errors ◽  
Qualitative Comparative Analysis ◽  
Research Areas

An increasing number of analyses in various subfields of political science employ Boolean algebra as proposed by Ragin's qualitative comparative analysis (QCA). This type of analysis is perfectly justifiable if the goal is to test deterministic hypotheses under the assumption of error-free measures of the employed variables. My contention is, however, that only in a very few research areas are our theories sufficiently advanced to yield deterministic hypotheses. Also, given the nature of our objects of study, error-free measures are largely an illusion. Hence, it is unsurprising that many studies employ QCA inductively and gloss over possible measurement errors. In this article, I address these issues and demonstrate the consequences of these problems with simple empirical examples. In an analysis similar to Monte Carlo simulation, I show that using Boolean algebra in an exploratory fashion without considering possible measurement errors may lead to dramatically misleading inferences. I then suggest remedies that help researchers to circumvent some of these pitfalls.

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

scholarly journals ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

2021 ◽  
pp. 1-22
Author(s):  
Daisuke Kurisu ◽  
Taisuke Otsu
Keyword(s):  
Multivariate Analysis ◽  
Measurement Error ◽  
Uniform Convergence ◽  
Measurement Errors ◽  
Convergence Rates ◽  
Free Variable ◽  
Error Model ◽  
Repeated Measurements ◽  
Empirical Characteristic Function ◽  
Measurement Error Model

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

Guidelines for choosing volume equations in the presence of measurement error in height

2000 ◽  
Vol 30 (2) ◽  
pp. 306-310 ◽  
Author(s):  
M S Williams ◽  
H T Schreuder
Keyword(s):  
Measurement Error ◽  
Tree Species ◽  
Measurement Errors ◽  
Tree Diameter ◽  
Total Height ◽  
Volume Equations

Assuming volume equations with multiplicative errors, we derive simple conditions for determining when measurement error in total height is large enough that only using tree diameter, rather than both diameter and height, is more reliable for predicting tree volumes. Based on data for different tree species of excurrent form, we conclude that measurement errors up to ±40% of the true height can be tolerated before inclusion of estimated height in volume prediction is no longer warranted.

scholarly journals An improved computational method to assess pituitary responsiveness to secretagogue stimuli

2002 ◽  
pp. 323-332 ◽  
Author(s):  
A Sartorio ◽  
G De Nicolao ◽  
D Liberati
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Pituitary Hormones ◽  
Computational Method ◽  
Kinetics Parameters ◽  
Thyrotrophin Releasing Hormone ◽  
Deconvolution Analysis ◽  
Releasing Hormone ◽  
Sampling Protocols ◽  
Peak Value

OBJECTIVE: The quantitative assessment of gland responsiveness to exogenous stimuli is typically carried out using the peak value of the hormone concentrations in plasma, the area under its curve (AUC), or through deconvolution analysis. However, none of these methods is satisfactory, due to either sensitivity to measurement errors or various sources of bias. The objective was to introduce and validate an easy-to-compute responsiveness index, robust in the face of measurement errors and interindividual variability of kinetics parameters. DESIGN: The new method has been tested on responsiveness tests for the six pituitary hormones (using GH-releasing hormone, thyrotrophin-releasing hormone, gonadotrophin-releasing hormone and corticotrophin-releasing hormone as secretagogues), for a total of 174 tests. Hormone concentrations were assayed in six to eight samples between -30 min and 120 min from the stimulus. METHODS: An easy-to-compute direct formula has been worked out to assess the 'stimulated AUC', that is the part of the AUC of the response curve depending on the stimulus, as opposed to pre- and post-stimulus spontaneous secretion. The weights of the formula have been reported for the six pituitary hormones and some popular sampling protocols. RESULTS AND CONCLUSIONS: The new index is less sensitive to measurement error than the peak value. Moreover, it provides results that cannot be obtained from a simple scaling of either the peak value or the standard AUC. Future studies are needed to show whether the reduced sensitivity to measurement error and the proportionality to the amount of released hormone render the stimulated AUC indeed a valid alternative to the peak value for the diagnosis of the different pathophysiological states, such as, for instance, GH deficits.

Use of simulation–extrapolation estimation in catch–effort analyses

1999 ◽  
Vol 56 (7) ◽  
pp. 1234-1240
Author(s):  
W R Gould ◽  
L A Stefanski ◽  
K H Pollock
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Mean Squared Error ◽  
Estimation Procedure ◽  
Bias Reduction ◽  
Estimation Methods ◽  
Effort Estimation ◽  
Stat Assoc ◽  
General Terms ◽  
Naive Estimator

All catch-effort estimation methods implicitly assume catch and effort are known quantities, whereas in many cases, they have been estimated and are subject to error. We evaluate the application of a simulation-based estimation procedure for measurement error models (J.R. Cook and L.A. Stefanski. 1994. J. Am. Stat. Assoc. 89: 1314-1328) in catch-effort studies. The technique involves a simulation component and an extrapolation step, hence the name SIMEX estimation. We describe SIMEX estimation in general terms and illustrate its use with applications to real and simulated catch and effort data. Correcting for measurement error with SIMEX estimation resulted in population size and catchability coefficient estimates that were substantially less than naive estimates, which ignored measurement errors in some cases. In a simulation of the procedure, we compared estimators from SIMEX with "naive" estimators that ignore measurement errors in catch and effort to determine the ability of SIMEX to produce bias-corrected estimates. The SIMEX estimators were less biased than the naive estimators but in some cases were also more variable. Despite the bias reduction, the SIMEX estimator had a larger mean squared error than the naive estimator for one of two artificial populations studied. However, our results suggest the SIMEX estimator may outperform the naive estimator in terms of bias and precision for larger populations.

scholarly journals The Effect of Random Error in Exposure Measurement upon the Shape of the Exposure Response

Dose-Response ◽  
2005 ◽  
Vol 3 (4) ◽  
pp. dose-response.0 ◽  
Author(s):  
Kenny S. Crump
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Epidemiological Data ◽  
Epidemiological Studies ◽  
Random Errors ◽  
Exposure Measurement ◽  
Considerable Uncertainty ◽  
Exposure Response ◽  
Log Normal ◽  
Normally Distributed

Although statistical analyses of epidemiological data usually treat the exposure variable as being known without error, estimated exposures in epidemiological studies often involve considerable uncertainty. This paper investigates the theoretical effect of random errors in exposure measurement upon the observed shape of the exposure response. The model utilized assumes that true exposures are log-normally distributed, and multiplicative measurement errors are also log-normally distributed and independent of the true exposures. Under these conditions it is shown that whenever the true exposure response is proportional to exposure to a power r, the observed exposure response is proportional to exposure to a power K, where K < r. This implies that the observed exposure response exaggerates risk, and by arbitrarily large amounts, at sufficiently small exposures. It also follows that a truly linear exposure response will appear to be supra-linear—i.e., a linear function of exposure raised to the K-th power, where K is less than 1.0. These conclusions hold generally under the stated log-normal assumptions whenever there is any amount of measurement error, including, in particular, when the measurement error is unbiased either in the natural or log scales. Equations are provided that express the observed exposure response in terms of the parameters of the underlying log-normal distribution. A limited investigation suggests that these conclusions do not depend upon the log-normal assumptions, but hold more widely. Because of this problem, in addition to other problems in exposure measurement, shapes of exposure responses derived empirically from epidemiological data should be treated very cautiously. In particular, one should be cautious in concluding that the true exposure response is supra-linear on the basis of an observed supra-linear form.

Monte Carlo method for the reduction of measurement errors in the material parameter estimation with cavities

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ronny Peter ◽  
Luca Bifano ◽  
Gerhard Fischerauer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Measurement Errors ◽  
Input Data ◽  
Material Parameter ◽  
Cavity Resonator ◽  
Calculation Algorithm ◽  
The Monte Carlo Method ◽  
Electromagnetic Resonances

Abstract The quantitative determination of material parameter distributions in resonant cavities is a relatively new method for the real-time monitoring of chemical processes. For this purpose, electromagnetic resonances of the cavity resonator are used as input data for the reverse calculation (inversion). However, the reverse calculation algorithm is sensitive to disturbances of the input data, which produces measurement errors and tends to diverge, which leads to no measurement result at all. In this work a correction algorithm based on the Monte Carlo method is presented which ensures a convergent behavior of the reverse calculation algorithm.

Impact of Human Factors on Measurement Errors

2013 ◽  
pp. 274-291 ◽  
Author(s):  
Vinodkumar Jacob ◽  
M. Bhasi ◽  
R. Gopikakumari
Keyword(s):  
Experimental Study ◽  
Statistical Analysis ◽  
Measurement Error ◽  
Measurement Errors ◽  
Human Error ◽  
Quantitative Comparison ◽  
Measuring System ◽  
Measuring Instrument ◽  
Related Factors ◽  
Human Errors

Measurement is the act or the result, of a quantitative comparison between a given quantity and a quantity of the same kind chosen as a unit. It is for observing and testing scientific and technological investigations and generally agreed that all measurements contain errors. In a measuring system where both a measuring instrument and a human being taking the measurement using a preset process, the measurement error could be due to the instrument, the process or human error. This study is devoted to understanding the human errors in measurement. Work and human involvement related factors that could affect measurement errors have been identified. An experimental study has been conducted using different subjects where the factors were changed one at a time and the measurements made by them recorded. Errors in measurement were then calculated and the data so obtained was subject to statistical analysis to draw conclusions regarding the influence of different factors on human errors in measurement. The findings are presented in the paper.

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