Providing Intuition to the Fieller Method with Two Geometric Representations using STATA and Eviews

The Fieller Method for the construction of confidence intervals for ratios of the expected value of two normally distributed random variables has been shown by a number of authors to be a superior method to the delta approximation. However, it is not widely used due in part, to the tendency to present the intervals only in a formula context. In addition, potential users have been deterred by the potential difficulty in interpreting non-finite confidence intervals when the confidence level is less than 100%. In this paper we present two graphical methods which can be easily constructed using two widely used statistical software packages (Eviews and Stata) for the representation of the Fieller intervals. An application is presented to assess the results of a model of the non-accelerating inflation rate of unemployment (NAIRU).Fieller method, ratios of parameters, confidence interval, confidence ellipsoid,1st derivative function, NAIRU, EViews, STATA

Confidence Intervals for Estimates of Elasticities

Elasticities are often estimated from the results of demand analysis however, drawing inferences from them may involve assumptions that could influence the outcome. In this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the Fieller method for the construction of confidence intervals can be used to draw inferences. We estimate the elasticities of expenditure from Engel curves using a variety of estimation models. Parametric Engel curves are modelled using OLS, MM robust regression, and Tobit. Semiparametric Engel curves are estimated using a penalized spline regression. We demonstrate the construction of confidence intervals of the expenditure elasticities for a series of expenditure levels as well as the estimated cumulative density function for the elasticity evaluated for a particular household.Engel curves, Fieller method, Tobit, robust regression, semiparametric

Some contributions to finite-sample analysis in three econometric models

In the standard classical regression model the most commonly used procedures for estimation are based on the Ordinary Least Squares Method, which is justified on the basis of well known finite-sample properties. However, this model consists of a number of assumptions, such as, for example, homoskedastic, serially independent and normally distributed disturbances and nonstochastic regressors. By changing these assumptions in one way or another, different estimating situations are created, in many of which the OLS estimator may have no statistical justification at all. Further, alternative estimation methods have often been justified only on the basis of their asymptotic properties, although in practice economists frequently have to base their statistical analysis on a relatively small number of observations. This suggests that the particular estimator to use in any situation should be chosen on the basis of finite-sample considerations. The analysis of finite-sample properties of commonly used estimators in three well known Econometric models is the focus of this thesis. In particular the three models considered are: the limited-information simultaneous equations model, the nonnormal linear regression model and the nonnormal limited-information simultaneous equation model. The techniques used include the derivation of the estimators' exact distribution and when this is analytically intractable Monte Carlo methods are employed. The limited-information simultaneous equation model is analyzed in two stages. First, a useful method of numerically evaluating many of the commonly used estimators, including the two-stage least squares estimator, is presented. Secondly this method is then used, and combined with Monte Carlo analysis, to compare the distributions of the limited-information maximum likelihood and two-stage least squares estimators in misspecified simultaneous equations models. The result of this comparison indicates the superior performance of the limited-information maximum likelihood estimator over the two-stage least squares estimator in both correctly specified and misspecified simultaneous equations models. Recently, models with possibly nonnormal distributed disturbances have attracted more attention. For such models, independence and uncorrelatedness of the disturbance terms are not equivalent. Using the nonnormal regression model the statistical consequences of distinguishing between independence and uncorrelatedness are considered when the disturbances are Student-t distributed. The results obtained demonstrate that the distinction between the two assumptions is an important one and the consequences of making the wrong assumption can be serious. Consequently, specification tests are also presented which test for uncorrelatedness versus independence in the elliptically symmetric family. The nonnormal limited-information simultaneous equation model provides a relatively new area of analysis as there are few published results available on the effects of nonnormal disturbances in the limited-information simultaneous equation model. The objective here is to combine the themes pursued separately in the other two models previously considered. However, to narrow the range of possible models that can be examined, attention is focussed only on the exactly-identified simultaneous equation model. This model has a number of interesting features when the reduced-form disturbances are normally distributed. These features are illustrated and then comparisons are made with the same model when the distribution of the disturbances is widened to include the Student-t family. In this case, as for the nonnormal linear regression model, a distinction needs to be made between independently distributed and jointly distributed disturbances. The consequences of these different assumptions are shown to be important; specification tests relating to this distinction are therefore also presented

Classical noise and flux: the limits of multi-state atom lasers

By direct comparison between experiment and theory, we show how the classical noise on a multi-state atom laser beam increases with increasing flux. The trade off between classical noise and flux is an important consideration in precision interferometric measurement. We use periodic 10 microsecond radio-frequency pulses to couple atoms out of an F=2 87Rb Bose-Einstein condensate. The resulting atom laser beam has suprising structure which is explained using three dimensional simulations of the five state Gross-Pitaevskii equations.Comment: 4 pages, 3 figure

Unstable regimes for a Bose-Einstein condensate in an optical lattice

We report on the experimental characterization of energetic and dynamical instability, two mechanisms responsible for the breakdown of Bloch waves in a Bose-Einstein condensate interacting with a 1D optical lattice. A clear separation of these two regimes is obtained performing measurements at different temperatures of the atomic sample. The timescales of the two processes have been determined by measuring the losses induced in the condensate. A simple phenomenological model is introduced for energetic instability while a full comparison is made between the experiment and the 3D Gross-Pitaevskii theory that accounts for dynamical instability

Synergistic action of thermophilic pectinases for pectin bioconversion into D-galacturonic acid

Large amounts of pectin-rich biomass are generated worldwide yearly, which can be hydrolysed by pectinases to obtain bio-based chemical building blocks such as D-galacturonic acid (GalA). The aim of this work was to investigate thermophilic pectinases and explore their synergistic application in the bioconversion of pectic substrates into GalA. Two exo-polygalacturonases (exo-PGs) from Thermotoga maritima (TMA01) and Bacillus licheniformis (BLI04) and two pectin methylesterases (PMEs) from Bacillus licheniformis (BLI09) and Streptomyces ambofaciens (SAM10) were cloned and expressed in Escherichia coli BL21 (DE3), purified and fully characterised. These pectinases exhibited optimum activity at temperatures above 50 °C and good stability at high temperature (40-90 °C) for up to 24 h. Exo-PGs preferred non-methylated substrates, suggesting that previous pectin demethylation by PMEs was necessary to achieve an efficient pectin monomerisation into GalA. Synergistic activity between PMEs and exo-PGs was tested using pectin from apple, citrus and sugar beet. GalA was obtained from apple and citrus pectin in a concentration of up to 2.5 mM after 4 h reaction at 50 °C, through the combined action of BLI09 PME with either TMA01 or BLI04 exo-PGs. Overall, this work contributes to expand the knowledge of pectinases from thermophiles and provides further insights into their application in the initial valorisation of sustainable pectin-rich biomass feedstocks

Non-destructive, dynamic detectors for Bose-Einstein condensates

We propose and analyze a series of non-destructive, dynamic detectors for Bose-Einstein condensates based on photo-detectors operating at the shot noise limit. These detectors are compatible with real time feedback to the condensate. The signal to noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counter-intuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily non-destructive . We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily non-destructive for a given signal to noise ratio

Stratospheric aircraft exhaust plume and wake chemistry studies

This report documents progress to date in an ongoing study to analyze and model emissions leaving a proposed High Speed Civil Transport (HSCT) from when the exhaust gases leave the engine until they are deposited at atmospheric scales in the stratosphere. Estimates are given for the emissions, summarizing relevant earlier work (CIAP) and reviewing current propulsion research efforts. The chemical evolution and the mixing and vortical motion of the exhaust are analyzed to track the exhaust and its speciation as the emissions are mixed to atmospheric scales. The species tracked include those that could be heterogeneously reactive on the surfaces of the condensed solid water (ice) particles and on exhaust soot particle surfaces. Dispersion and reaction of chemical constituents in the far wake are studied with a Lagrangian air parcel model, in conjunction with a radiation code to calculate the net heating/cooling. Laboratory measurements of heterogeneous chemistry of aqueous sulfuric acid and nitric acid hydrates are also described. Results include the solubility of HCl in sulfuric acid which is a key parameter for modeling stratospheric processing. We also report initial results for condensation of nitric acid trihydrate from gas phase H2O and HNO3

Microfluidic multi-input reactor for biocatalytic synthesis using transketolase

Biocatalytic synthesis in continuous-flow microreactors is of increasing interest for the production of specialty chemicals. However, the yield of production achievable in these reactors can be limited by the adverse effects of high substrate concentration on the biocatalyst, including inhibition and denaturation. Fed-batch reactors have been developed in order to overcome this problem, but no continuous-flow solution exists. We present the design of a novel multi-input microfluidic reactor, capable of substrate feeding at multiple points, as a first step towards overcoming these problems in a continuous-flow setting. Using the transketolase-(TK) catalysed reaction of lithium hydroxypyruvate (HPA) and glycolaldehyde (GA) to l-erythrulose (ERY), we demonstrate the transposition of a fed-batch substrate feeding strategy to our microfluidic reactor. We obtained a 4.5-fold increase in output concentration and a 5-fold increase in throughput compared with a single input reactor

Analysis of Localization Phenomena in Weakly Interacting Disordered Lattice Gases

Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases may be used for the production and observation of disordered quantum degenerate gases. A detailed analysis of localization effects for two possible realizations of a disordered potential is presented. In a theoretical analysis clear localization effects are observed when a superlattice is used to provide a quasiperiodic disorder. The effects of localization are analyzed by investigating the superfluid fraction and the localization length within the system. The theoretical analysis in this paper paves a clear path for the future observation of Anderson-like localization in disordered quantum gases.Comment: 9 pages, 13 figure