798 research outputs found
Higher Moment Estimators for Linear Regression Models With Errors in the Variables
This paper proposes instrumental variable estimators for multiple linear regression models with errors in the explanatory variables, that require no extraneous information. As is very well known, the ordinary least squares estimator (OLS), which is based on the sample moments of order two, is unbiased when there are no errors in the variables, but it becomes biased and inconsistent when there are such errors [Fuller (1987)]. In contrast, the suggested estimators are based on higher sample moments and can be considered as a special type of instrumental variable estimator. They are consistent, under quite reasonable assumptions, when there are measurement errors. While most consistent estimators based on higher moments (HM) proposed previously in the literature [Geary (1942), Drion (1951), Durbin (1954), Pal (1980)] for regressions with errors in the variables seem to be quite erratic [Kendall and Stuart (1963), Malinvaud (1978)], the suggested estimators appear to perform remarkably well in many situations. Although most data do contain errors of measurement, this fact is often ignored by the analysts and statistical procedures designed for data measured without error are applied. It is shown that ignoring the presence of even small measurement errors and using traditonal OLS estimators may lead to performing standard Student t-tests with type I errors of considerably higher sizes than intended, while this is not so with the proposed HM estimators. Our experimental findings suggest also that even if the sample is not very large, when the errors in the variables are non-negligible, our estimators do perform better than the OLS estimators in terms of root mean squared errors, when the explanatory variables are strongly correlated and the multiple correlation of the regression is high. Such situations are typical of many statistical analyses based on aggregate data. When the multiple correlation coefficient is smaller and the explanatory variables are less correlated, our HM estimators will still outperform the OLS estimator if the sample is large, even if the measurement errors are not very important. Such cases are frequently encountered in analyses of survey data. Tests for the presence of errors in the variables are also described, and the power of the tests are assessed in the Monte Carlo experiments. Nous proposons, pour les modĂšles de rĂ©gression linĂ©aire oĂč les variables explicatives contiennent des erreurs de mesure, des estimateurs de variables instrumentales d'un type particulier, qui n'exigent aucune information extrinsĂšque. On sait que l'estimateur des moindres carrĂ©s ordinaires (MCO), qui est basĂ© sur les moments Ă©chantillonnaux d'ordre deux, est centrĂ© lorsqu'il n'y a pas d'erreurs sur les variables0501s qu'il devient biaisĂ© et non convergent en prĂ©sence de telles erreurs [Fuller (1987)]. Par ailleurs, les estimateurs que nous suggĂ©rons sont basĂ©s sur des moments d'ordres supĂ©rieurs et peuvent ĂȘtre vus comme des estimateurs de variables instrumentales. Sous des hypothĂšses trĂšs raisonnables, ces estimateurs demeurent convergents mĂȘme lorsqu'il y a des erreurs de mesure. Alors que la plupart des estimateurs convergents basĂ©s sur des moments d'ordres supĂ©rieurs (MOS) proposĂ©s antĂ©rieurement [Geary(1942), Drion(1951), Durbin (1954), Pal (1980)] pour les modĂšles de rĂ©gression avec erreurs sur les variables, semblent trĂšs erratiques [Kendall et Stuart (1963), Malinvaud (1978)], les estimateurs que nous proposons se comportent remarquablement bien, dans un grand nombre de cas. Quoique la plupart des donnĂ©es contiennent des erreurs de mesure, ce fait est souvent ignorĂ© par les analystes qui appliquent, la plupart du temps, des procĂ©dures statistiques conçues pour le traitement de donnĂ©es mesurĂ©es sans erreur. Nous dĂ©montrons que le fait de nĂ©gliger la prĂ©sence d'erreurs de mesure mĂȘme relativement faibles et d'utiliser les estimateurs MCO traditionnels, peut faire en sorte que les tests de Student standards comportent des erreurs de type I dont le niveau est considĂ©rablement plus Ă©levĂ© que le niveau dĂ©sirĂ©, alors que ce n'est pas le cas si on utilise les estimateurs MOS proposĂ©s. MĂȘme si les Ă©chantillons ne sont pas trĂšs grands, les rĂ©sultats de nos expĂ©riences suggĂšrent Ă©galement que dans les cas oĂč les erreurs sur les variables ne sont pas nĂ©gligeables, le comportement de nos estimateurs lorsqu'on l'Ă©value en termes de la racine carrĂ©e des Ă©carts quadratiques moyens, est supĂ©rieur Ă celui des MCO, quand les variables explicatives sont fortement corrĂ©lĂ©es et que le coefficient de corrĂ©lation multiple est Ă©levĂ©. Ce genre de situations est typique des analyses statistiques basĂ©es sur des donnĂ©es agrĂ©gĂ©es. Si le coefficient de corrĂ©lation multiple est moins Ă©levĂ© et que les variables explicatives sont moins corrĂ©lĂ©es, nos estimateurs MOS peuvent encore s'avĂ©rer supĂ©rieurs aux estimateurs MCO lorsque les Ă©chantillons sont suffisamment grands, et cela mĂȘme si les erreurs de mesure ne sont pas aussi importantes. De tels cas se rencontrent frĂ©quemment lorsqu'on a affaire Ă des donnĂ©es d'enquĂȘtes. Nous dĂ©crivons Ă©galement des tests d'erreurs sur les variables et nous Ă©valuons la puissance de ces tests au moyen d'expĂ©riences de Monte-Carlo.Errors in the variables; Measurement errors; Higher moment estimators; Instrumental variable estimators, Erreurs sur les variables ; Erreurs de mesure ; Variables instrumentales ; Moments d'ordres supĂ©rieurs
Lâestimation de modĂšles de rĂ©gression linĂ©aire autorĂ©gressifs avec erreurs rĂ©siduelles autocorrĂ©lĂ©es et erreurs sur les variables
Nous prĂ©sentons, pour des modĂšles de sĂ©ries chronologiques, une mĂ©thode dâestimation qui tient compte de la prĂ©sence dâerreurs de mesure sur les donnĂ©es, lorsque ces erreurs ne sont pas autocorrĂ©lĂ©es. Lâapproche suggĂ©rĂ©e utilise des valeurs dĂ©calĂ©es des variables indĂ©pendantes comme variables instrumentales. Nous employons lâestimateur convergent proposĂ© par Fuller (1987) et comparons analytiquement les erreurs quadratiques moyennes de cet estimateur avec celles dâun estimateur similaire qui ne tiendrait pas compte des erreurs de mesure. Finalement, nous rapportons, Ă partir dâun Ă©chantillon de 150 observations, les rĂ©sultats dâĂ©tudes de Monte Carlo sur ces deux estimateurs ainsi que sur un estimateur alternatif qui est une somme pondĂ©rĂ©e des deux premiers. Ces expĂ©riences montrent que lâestimateur alternatif semble relativement mieux se comporter. On constate Ă©galement que lâinconvĂ©nient de la prĂ©sence dâerreurs sur les variables nâest pas seulement de biaiser les estimateurs des coefficients ou dâaccroĂźtre les erreurs quadratiques moyennes, mais Ă©galement de sous-estimer considĂ©rablement le niveau des erreurs de type I des tests de signification.This paper presents, for models based on time series data, a method of estimation to take into account errors in the variables, when these errors are not autocorrelated. The suggested approach utilizes shifted values of the independent variables as instruments. We use Fuller's (1987) consistent estimator and compare analytically the mean squared errors of this estimator with those of a similar estimator which would ignore the presence of errors in the variables. Finally, from Monte-Carlo studies based on samples of 150 observations, we evaluate the relative performance of the above estimators as well as that of an alternative estimator which is a weighted sum of the first two. Our experiments show that the alternative estimator appears to behave relatively better. They also indicate that the inconveniences associated with the presence of errors in the variables is not only to bias the parameter estimators or to increase their mean squared errors but also to underestimate notably the size of the type I errors of significance tests
Analyse de la performance dâĂ©tudiants au baccalaurĂ©at en administration en fonction de leurs caractĂ©ristiques Ă lâentrĂ©e
Les Ă©conomistes sâintĂ©ressent depuis longtemps Ă divers aspects de lâĂ©ducation comme, par exemple : la mesure de lâoutput, lâanalyse des dĂ©terminants du succĂšs scolaire ou la pĂ©dagogie.Cette Ă©tude se situe dans cette ligne de prĂ©occupations. En effet, elle cherche Ă voir si certaines caractĂ©ristiques acadĂ©miques contenues dans le dossier de lâĂ©tudiant au moment de son admission contribuent Ă expliquer en partie ses rĂ©sultats Ă lâuniversitĂ©. Cette Ă©tude porte sur des Ă©tudiants inscrits Ă un baccalaurĂ©at en administration. Toutefois Ă©tant donnĂ© les liens qui existent entre lâĂ©conomie et lâadministration, il est probable que plusieurs des rĂ©sultats obtenus se vĂ©rifieraient aussi dans le cadre dâĂ©tudes sur des Ă©tudiants en Ă©conomie.Cette analyse fait ressortir plusieurs Ă©lĂ©ments importants. On note par exemple, une relation positive trĂšs significative entre la performance de lâĂ©tudiant dans le programme et ses rĂ©sultats scolaires au cĂ©gep ainsi que ses rĂ©sultats Ă des tests dâadmission. De plus lâĂ©tudiant qui a choisi la concentration « sciences » au cĂ©gep rĂ©ussit en gĂ©nĂ©ral mieux que celui qui vient de la concentration « sciences humaines » mĂȘme si, Ă lâintĂ©rieur de celle-ci, lâĂ©tudiant a choisi un profil « sciences administratives ».Economists have long been interested in different aspects of education such as, the measure of its output, the analysis of the determinants of scholarly achievement or the pedagogical approach. This study stands within the same lines of preoccupations. Indeed, it tries to find out whether some of the academic characteristics contained in the student record when admitted to the University contribute in part to explain his results.The study considers students enrolled in a bachelor degree program in administration. However, given that economics and administration are related topics, one can anticipate that several of the results of this study would also be verified in studies concerned with economics students.Our analysis reveals a number of important points. For example, a very significant positive relationship is shown to exist between the student's performance in the B.A.A. program and his grades at the cĂ©gep as well as his results at the admission tests.Furthermore, the cĂ©gep student who comes from the "science" concentration succeeds better, in general, than the student from the "social science" concentration even if, within this concentration, the student has selected a "business administration" profile
LâĂ©conomiste et les confitures
RĂ©flexions Ă partir dâune fable de Georges Duhamel intitulĂ©e « Les confitures », sur les difficultĂ©s auxquelles se heurtent les Ă©conomistes qui se livrent Ă une analyse avantages-coĂ»ts et sur les exigences de leur rĂŽle dans la sociĂ©tĂ©.Thoughts inspired by a fable written by Georges Duhamel entitled "Les Confitures", on the difficulties encountered by economists responsible for performing cost benefit analyses as well as on their role in society
CLĂMENT LEMELIN, LâĂ©conomiste et lâĂ©ducation, Presses de lâUniversitĂ© du QuĂ©bec, 1998, 612 p.
LâĂ©conomiste et les confitures
Thoughts inspired by a fable written by Georges Duhamel entitled "Les Confitures", on the difficulties encountered by economists responsible for performing cost benefit analyses as well as on their role in society. RĂ©flexions Ă partir dâune fable de Georges Duhamel intitulĂ©e « Les confitures », sur les difficultĂ©s auxquelles se heurtent les Ă©conomistes qui se livrent Ă une analyse avantages-coĂ»ts et sur les exigences de leur rĂŽle dans la sociĂ©tĂ©.
Multiatom and transit-time effects on photon-correlation measurements in resonance fluorescence
An expression is derived for the expected number of photon pairs separated by a time interval Ï that are detected in photoelectric correlation measurements of an atomic beam, when due account is taken of the fluctuations of the number of radiating atoms and of the effect of their finite transit time through the field of view. The theoretical expression is checked against some recent measurements and good agreement is obtained
Rating the intelligibility of dysarthic speech amongst people with Parkinsonâs Disease: a comparison of trained and untrained listeners
Intelligibility of speech is a key outcome in speech and language therapy (SLT) and research. SLT students frequently participate as raters of intelligibility but we lack information about whether they rate intelligibility in the same way as the general public. This paper aims to determine if there is a difference in the intelligibility ratings made by SLT students (trained in speech related topics) compared to individuals from the general public (untrained). The SLT students were in year 2 of a BSc programme or the first 6 months of a MSc programme. We recorded 10 speakers with Parkinsonâs disease (PD) related speech reading aloud the words and sentences from the Assessment of Intelligibility of Dysarthric Speech. These speech recordings were rated for intelligibility by âtrainedâ raters and âuntrainedâ raters. The effort required to understand the speech was also reported. There were no significant differences in the measures of intelligibility from the trained and untrained raters for words or sentences after adjusting for speaker by including them as a covariate in the model. There was a slight increase in effort reported by the untrained raters for the sentences. This difference in reported effort was not evident with the words. SLT students can be recruited alongside individuals from the general public as naĂŻve raters for evaluating intelligibility in people with speech disorders
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