Academic literature on the topic 'Empirical calibration'

Master of Science<br>Department of Civil Engineering<br>Mustaque Hossain<br>The Kansas Department of Transportation is transitioning from adherence to the 1993 American Association of State Highway and Transportation Officials (AASHTO) Pavement Design Guide to implementation of the new AASHTO Mechanistic-Empirical Pavement Design Guide (MEPDG) for flexible and rigid pavement design. This study was initiated to calibrate MEPDG distress models for Kansas. Twenty-seven newly constructed projects were selected for flexible pavement distress model calibration, 21 of which were used for calibration and six that were selected for validation. In addition, 22 newly constructed jointed plain concrete pavements (JPCPs) were selected to calibrate rigid models; 17 of those projects were selected for calibration and five were selected for validation. AASHTOWare Pavement ME Design (ver. 2.2) software was used for design analysis, and the traditional split sampling method was followed in calibration. MEPDG-predicted distresses of Kansas road segments were compared with those from Pavement Management Information System data. Statistical analysis was performed using the Microsoft Excel statistical toolbox. The rutting and roughness models for flexible pavement were successfully calibrated with reduced bias and accepted null hypothesis. Calibration of the top-down fatigue cracking model was not satisfactory due to variability in measured data, and the bottom-up fatigue cracking model was not calibrated because measured data was unavailable. AASHTOWare software did not predict transverse cracking for any projects with global values. Thus thermal cracking model was not calibrated. The JPCP transverse joint faulting model was calibrated using sensitivity analysis and iterative runs of AASHTOWare to determine optimal coefficients that minimize bias. The IRI model was calibrated using the generalized reduced gradient nonlinear optimization technique in Microsoft Excel Solver. The transverse slab cracking model could not be calibrated due to lack of measured cracking data.

This thesis introduces the eBAEL (extended Empirical Balanced Augmented Likelihood) method for general analytical moment conditions. It proves that eBAEL has a X2 - limit distribution and provides a consistent estimator. Numerical results demonstrate that the eBAEL ratio statistics exhibits less bias than AEL ratio statistics and has smaller type I errors. This thesis also presents a general framework for calibrating financial agent-based models using eBAEL, where the aim is to find the model parameter for which the true model moments match the given empirical values. It is demonstrated that our proposed approach is able to retrieve that parameter with probability approaching one as the number of simulations increase. Furthermore this thesis demonstrates that the EL approach may also be used for estimating financial agent-based models. In contrast to calibration, estimation via moment matching in particular emphasizes that empirical moments are estimates themselves and the aim is to find a parameter configuration for which the true model moments and true empirical moments coincide. As a numerical benchmark case, the parameters of a Geometric Brownian Motion are calibrated and estimated from its simulated sample paths in comparison to the SMM. In this case the EL approach is able to provide the best mean squared errors for both calibration and estimation and in particular is the most robust calibration method. In terms of calibration efficiency this robustness holds figuratively, as the SMM is only more efficient in cases where it provides worse mean squared errors. Additionally, this thesis also estimates an actual agent-based model of a financial market against empirical moments that are generated at some known model parameter setting. Similarly, the resulting EL mean squared errors are mostly better than those of the SMM.

Medical cost has received increasing interest recently in Biostatistics and public health. Statistical analysis and inference of life time medical cost have been challenging by the fact that the survival times are censored on some study subjects and their subsequent cost are unknown. Huang (2002) proposed the calibration regression model which is a semiparametric regression tool to study the medical cost associated with covariates. In this thesis, an inference procedure is investigated using empirical likelihood ratio method. The unadjusted and adjusted empirical likelihood confidence regions are constructed for the regression parameters. We compare the proposed empirical likelihood methods with normal approximation based method. Simulation results show that the proposed empirical likelihood ratio method outperforms the normal approximation based method in terms of coverage probability. In particular, the adjusted empirical likelihood is the best one which overcomes the under coverage problem.

This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a Lévy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to Lévy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump Lévy component for some tail index greater than 2.

Title from PDF of title page.<br>Document formatted into pages; contains 75 pages.<br>Thesis (M.S.C.E.)--University of South Florida, 2003.<br>Includes bibliographical references.<br>Text (Electronic thesis) in PDF format.<br>ABSTRACT: Analytical baseflow separation techniques such as those used in the automated hydrograph separation program HYSEP rely on a single input parameter that defines the period of time after which surface runoff ceases and all streamflow is considered baseflow. In HYSEP, this input parameter is solely a function of drainage basin contributing area. This method cannot be applied universally since in most regions the time of surface runoff cessation is a function of a number of different hydrologic and hydrogeologic basin characteristics, not just contributing drainage area. This study demonstrates that streamflow conductivity can be used as a natural tracer that integrates the different hydrologic and hydrogeologic basin characteristics that influence baseflow response. Used as an indicator of baseflow as a component of total flow, streamflow conductivity allows for an empirical approach to hydrograph separation using a simple mass balance algorithm.<br>ABSTRACT: Although conductivity values for surface-water runoff and ground-water baseflow must be identified to apply this mass balance algorithm, field studies show that assumptions based on streamflow at low flow and high flow conditions are valid for estimating these end member conductivities. The only data required to apply the mass balance algorithm are streamflow conductivity and discharge measurements. Using minimal data requirements, empirical hydrograph separation techniques can be applied that yield reasonable estimates of baseflow. This procedure was performed on data from 10 USGS gaging stations for which reliable, real-time conductivity data are available. Comparison of empirical hydrograph separations using streamflow conductivity data with analytical hydrograph separations demonstrates that uncalibrated, graphical estimation of baseflow can lead to substantial errors in baseflow estimates.<br>ABSTRACT: Results from empirical separations can be used to calibrate the runoff cessation input parameter used in analytical separation for each gaging station. In general, collection of stream conductivity data at gaging stations is relatively recent, while discharge measurements may extend many decades into the past. Results demonstrate that conductivity data available for a relatively short period of record can be used to calibrate the runoff cessation input parameter used for analytical separation. The calibrated analytical method can then be applied over a much longer period record since discharge data are the only requirement.<br>System requirements: World Wide Web browser and PDF reader.<br>Mode of access: World Wide Web.

Le 1er chapitre présente une série de 50 ans sur les hauts revenus chiliens basée sur des données fiscales et comptes nationaux. L’étude contredit les enquêtes, selon lesquelles les inégalités diminuent les 25 dernières années. Au contraire, elles changent de direction à partir de 2000. Le Chili est parmi les pays les plus inégalitaires de l’OCDE et l’Amérique latine. Le 2ème chapitre mesure la sous-estimation des revenus factoriels dans les données distributives. Les ménages ne reçoivent que 50% des revenus du capital brut, par opposition aux firmes. L’hétérogénéité des taux de réponse et autres problèmes font que les enquêtes ne capturent que 20% de ceux-ci, contre 70% du revenu du travail. Cela sous-estime l’inégalité,dont les estimations deviennent insensibles à la "capital share" et sa distribution. Je formalise à partir d’identités comptables pour ensuite calculer des effets marginaux et contributions aux variations d’inégalité. Le 3ème chapitre présente une méthode pour ajuster les enquêtes. Celles-ci capturent souvent mal le sommet de la distribution. La méthode présente plusieurs avantages par rapport aux options précédentes : elle est compatible avec les méthodes de calibration standard ; elle a des fondements probabilistes explicites et préserve la continuité des fonctions de densité ; elle offre une option pour surmonter les limites des supports d’enquête bornées; et elle préserve la structure de micro données en préservant la représentativité des variables sociodémographiques. Notre procédure est illustrée par des applications dans cinq pays, couvrant à la fois des contextes développés et moins développés<br>The 1st chapter presents historical series of Chilean top income shares over a period of half a century, mostly using data from tax statistics and national accounts. The study contradicts evidence based on survey data, according to which inequality has fallen constantly over the past 25 years. Rather, it changes direction, increasing from around the year 2000. Chile ranks as one of the most unequal countries among both OECD and Latin American countries over the whole period of study. The 2nd chapter measures the underestimation of factor income in distributive data. I find that households receive only half of national gross capital income,as opposed to corporations. Due to heterogeneous non-response and misreporting, Surveys only capture 20% of it, vs. 70% of labor income. This understates inequality estimates, which become insensitive to the capital share and its distribution. I formalize this system based on accounting identities. I then compute marginal effects and contributions to changes in fractile shares. The 3rd chapter, presents a method to adjust surveys. These generally fail to capturethe top of the income distribution. It has several advantages over previous ones: it is consistent with standard survey calibration methods; it has explicit probabilistic foundations and preserves the continuity of density functions; it provides an option to overcome the limitations of bounded survey-supports; and it preserves the microdata structure of the survey

This thesis documents the results of the calibration of the Highway Safety Manual (HSM) safety performance function (SPF) for rural two-lane two-way roadway segments in Utah and the development of new SPFs using negative binomial and hierarchical Bayesian modeling techniques. SPFs estimate the safety of a roadway entity, such as a segment or intersection, in terms of number of crashes. The new SPFs were developed for comparison to the calibrated HSM SPF. This research was performed for the Utah Department of Transportation (UDOT).The study area was the state of Utah. Crash data from 2005-2007 on 157 selected study segments provided a 3-year observed crash frequency to obtain a calibration factor for the HSM SPF and develop new SPFs. The calibration factor for the HSM SPF for rural two-lane two-way roads in Utah is 1.16. This indicates that the HSM underpredicts the number of crashes on rural two-lane two-way roads in Utah by sixteen percent. The new SPFs were developed from the same data that were collected for the HSM calibration, with the addition of new data variables that were hypothesized to have a significant effect on crash frequencies. Negative binomial regression was used to develop four new SPFs, and one additional SPF was developed using hierarchical (or full) Bayesian techniques. The empirical Bayes (EB) method can be applied with each negative binomial SPF because the models include an overdispersion parameter used with the EB method. The hierarchical Bayesian technique is a newer, more mathematically-intense method that accounts for high levels of uncertainty often present in crash modeling. Because the hierarchical Bayesian SPF produces a density function of a predicted crash frequency, a comparison of this density function with an observed crash frequency can help identify segments with significant safety concerns. Each SPF has its own strengths and weaknesses, which include its data requirements and predicting capability. This thesis recommends that UDOT use Equation 5-11 (a new negative binomial SPF) for predicting crashes, because it predicts crashes with reasonable accuracy while requiring much less data than other models. The hierarchical Bayesian process should be used for evaluating observed crash frequencies to identify segments that may benefit from roadway safety improvements.

Cette thèse présente trois parties liées à la théorie des sondages. La première partie présente deux résultats originaux de sondages qui ont eu des applications pratiques dans des enquêtes par sondage de l'Insee. Le premier article présente un théorème autorisant un plan de sondage stratifié constituant un compromis entre la dispersion des poids et l'allocation de précision optimale pour une variable d'intérêt spécifique. Les données d’enquête sont souvent utilisées pour estimer nombre de totaux ou modèles issus de variables exclues du design. La précision attendue pour ces variables est donc faible, mais une faible dispersion des poids permet de limiter les risques qu'une estimation dépendant d'une de ces variables ait une très mauvaise précision. Le second article concerne le facteur de repondération dans les estimateurs par calage. On propose un algorithme efficace capable de calculer les facteurs de poids les plus rapprochés autour de 1 tels qu'une solution au problème de calage existe. Cela permet de limiter les risques d'apparition d'unités influentes, particulièrement pour l'estimation sur des domaines. On étudie par simulations sur données réelles les propriétés statistiques des estimateurs obtenus. La seconde partie concerne l'étude des propriétés asymptotique des estimateurs sur données issues de sondage. Celles-ci sont difficiles à étudier en général. On présente une méthode originale qui établit la convergence faible vers un processus gaussien pour le processus empirique d'Horvitz-Thompson indexé par des classes de fonction, pour de nombreux algorithmes de sondage différents utilisés en pratique. Dans la dernière partie, on s'intéresse à des méthodes de sondage pour des données issues de graphes, qui ont des applications pratiques lorsque les graphes sont de taille telles que leur exploitation informatique est coûteuse. On détaille des algorithmes de sondage permettant d'estimer des statistiques d'intérêt pour le réseaux. Deux applications, à des données de Twitter puis à des données simulées, concluent cette partie<br>This thesis presents three different parts with ties to survey sampling theory. In the first part, we present two original results that led to practical applications in surveys conducted at Insee (French official statistics Institute). The first chapter deals with allocations in stratified sampling. We present a theorem that proves the existence of an optimal compromise between the dispersion of the sampling weights and the allocation yielding optimal precision for a specific variable of interest. Survey data are commonly used to compute estimates for variables that were not included in the survey design. Expected precision is poor, but a low dispersion of the weights limits risks of very high variance for one or several estimates. The second chapter deals with reweighting factors in calibration estimates. We study an algorithm that computes the minimal bounds so that the calibration estimators exist, and propose an efficient way of resolution. We also study the statistical properties of estimates using these minimal bounds. The second part studies asymptotic properties of sampling estimates. Obtaining asymptotic guarantees is often hard in practice. We present an original method that establishes weak convergence for the Horvitz-Thompson empirical process indexed by a class of functions for a lot of sampling algorithms used in practice. In the third and last part, we focus on sampling methods for populations that can be described as networks. They have many applications when the graphs are so big that storing and computing algorithms on them are very costly. Two applications are presented, one using Twitter data, and the other using simulated data to establish guidelines to design efficient sampling designs for graphs