working papers in economics and econometrics

... in the form αt+ βu, is unbiased if and only if α = 1 − β In other words,any unbiased estimator which is a linear combination of t and u can be written inthe form Trang 13• b 2 points By solving ... point Assumet and uare two unbiased estimators of the same unknownscalar nonrandom parameter θ tanduhave finite variances and satisfy var[u−t] 6= 0 Show that a linear combination of t and u, i.e., ... certainty by increasing the sample size Strictly speaking, asymptotic properties do not refer to individual estimatorsbut to sequences of estimators, one for each sample size n And strictly speaking,

Ngày tải lên: 04/07/2014, 15:20

... for counterfeiting Picasso paintings, andyou are an expert witness who has developed fool-proof statistical significance testsfor identifying the painter of a given painting • a 2 points There are ... who is in the process of acquiring a very expensive alleged Picasso painting, and who wants to be sure that this painting is not one of Jones’s falsifications Would you now set up your test in the ... there are exactly 4 successes in our 9 trials And we have no information aboutthe probability of having indeed four successes, it might be 1 in a million However incertain situations, the conditional

Ngày tải lên: 04/07/2014, 15:20

... 17Causality and Inference This chapter establishes the connection between critical realism and Holland andRubin’s modelling of causality in statistics as explained in [Hol86] and [WM83, pp.3–25] (and ... detail in order to get at the essence of things Holland defines: xis not a Granger cause ofyrelative to the information inz(which in the timeseries contextcontains the past values of y) if and only ... only thing known about the distribution is that mean and variance exist, callthem µ and σ2 In order to write this as a special case of the “linear model,” define Trang 10εi=yi−µ, and define the

Ngày tải lên: 04/07/2014, 15:20

... betweeny and x You are allowed to use the results of Problems229and240 To set notation, callthe minimum MSE in the first prediction (Problem 229) MSE[constant term;y], andthe minimum MSE in the ... MSE[constant term,x, andy1;y2] MSE[constant term and x;y2] . Problem256 Using the definitions in terms of MSE’s, show that the followingrelationship holds between the squares of multiple and partial correlation ... first and have second highest correlation,and so on Here is the mathematical construction needed:Letxandybe two column vectors consisting of p and q scalar random variables,respectively, and let

Ngày tải lên: 04/07/2014, 15:20

... to virus attacks and breakins In Linux, the user is the master of the computer and can exploit its fullpotential • You spend too much time pointing and clicking In GNU/Linux and otherunix systems, ... go into the Windows menu anddouble-click on the SAS icon It will give you two windows, the command window on the bottom and a window for output on the top Type your commands into thecommand window, ... character-based terminal or in X-windows On acharacter-based terminal you simply type emacs In a windows setting, it is probablyavailable in one of the menus, but you can also get into it by just typing emacs

Ngày tải lên: 04/07/2014, 15:20

... MSE[˜φ1+ ˜φ2;φ1+φ2] Hint: it is easiest to use an example in which all random variables are constants Another hint: the geometricanalog would be to find two vectors in a plane ˆφ and ˜φ In each component ... nonrandom, formula (23.1.2) simplifies slightly, since in this case V[θˆ−θ] =V[θˆ] In this case, the MSE matrix is the covariance matrix plus the squared biasmatrix If θ is nonrandom and in addition ... estimators An alternative and more enlightening characterization of Theorem 24.2.2 βˆ is a linear minimax estimator of the parameter vector β in the following sense: for every nonrandom coefficient vector

Ngày tải lên: 04/07/2014, 15:20

... matrix-algebraictricks than those familiar from linear estimators The problem at hand can bereduced to a minimum trace problem as defined in Rao [Rao73, pp 65–66], andpart of the following proof draws on a private ... onecan not only unify some known results in linear estimation and prediction, but onealso obtains a far-reaching analogy between linear estimation of β and quadraticestimation of σ2 The most important ... diagonal matrix with λ in the diagonal, and write A = M ΛM + D Then DX = O and D has zeros in the diagonal, therefore tr(M ΛM D) =tr(ΛM DM ) = tr(ΛD) = 0, since ΛD still has zeros in the diagonal Thereforetr(A2)

Ngày tải lên: 04/07/2014, 15:20

... words, thematrix of constraints R does not include “redundant” constraints which are linearcombinations of the other constraints Trang 229.1 Building the Constraint into the ModelProblem 337 Given ... corresponding β =βˆsatisfies the constraint Thisβˆis the solution ofthe constrained minimization problem we are looking for.Problem 339 4 points Show the following: If β = βˆ is the unconstrainedminimum ... green line which does not start at the origin In other words: if one projects y on a plane, and also on a line in that plane, and then connects the footpoints of these two projections, one obtains

Ngày tải lên: 04/07/2014, 15:20

... standard procedures Problem 373 1 point Define multicollinearity • a 2 points What are the symptoms of multicollinearity? • b 2 points How can one detect multicollinearity? Trang 20• c 2 points ... Filling in the missingyby the arithmetic mean of the observed ydoes not give an unbiased estimator General conclusion: in a single-equation context, filling in missingynot a goodidea Now missing ... Decide in the following situations whether you want predictiveresiduals or ordinary residuals, and whether you want them standardized or not.• a 1 point You are looking at the residuals in order

Ngày tải lên: 04/07/2014, 15:20

... within-group or between-group phenomena or both.:• negative relationship of protein % and oil % (both within • and ◦); • positive relationship of oil % and seed size (both within • and ◦ and ... of seed size and height; • positive relationship of height and lodging (within ◦ and between groups); • negative relationship of oil % and lodging (between groups and possibly within •); • negative ... regression searches for an interesting and informative tion of the data by maximizing a criterion function A logical candidate would forinstance be the variance ratio as defined in (8.6.7), but there

Ngày tải lên: 04/07/2014, 15:20

... mean and variance alone Problem 395 4 points Show that, if y is normally distributed, s2 and βˆ areindependent Answer We showed in question 300 that βˆand ε ˆ are uncorrelated, therefore in the ... κ2A)−1X>y, which hasbeen called a “shrinkage estimator” (Ridge regression), since the “denominator” isbigger: instead of “dividing by” X>X (strictly speaking, multiplying by (X>X)−1),one “divides” ... which he does not quite understand is in the above eliciation ofprior information It often happens that prior information gained in this way is self-contradictory, and the researcher is probably

Ngày tải lên: 04/07/2014, 15:20

... discussed in James and Stein [JS61], extending the work of Stein [Ste56] Stein himself did not introduce the estimator as an “empirical Bayes” estimator, and it is not certain that this is indeed ... is a linear combination of the first j ordered regressors  Trang 8•b 0 points Assume one has Bayesian prior knowledge that β ∼N(o, τ2I), andβ independent ofε In the general case, if prior information ... 0 and Φ positive definite Trang 2Both interpretations are possible here: either u is a constant, which means nec-essarily that β is random, or β is as usual a constant and u is random, coming

Ngày tải lên: 04/07/2014, 15:20

... Mahalanobis distance is also defined if the covariance matrix ofyis singular In this case, certain nonzero linear combinations of the elements ofyare known withcertainty Certain vectors can therefore ... could minimize the relative increase in the lanobis distance (instead of selecting its minimax value) because all parameters ofthe underlying distribution were known The simplest situation in which ... predict a n + 1st observation in such a way as to minimize the worst possiblerelative increase in this Mahalanobis distance? Minimizing the maximum possible relative increase in the Mahalanobis distancedue

Ngày tải lên: 04/07/2014, 15:20

... If one is only interested in certain coordinates of β and not in the others, or in some other linear transformation β, then the corresponding confidenceregions are the corresponding transformations ... numerator and denominator are independent To see this, look first at βˆand εˆ By Problem300 they are uncorrelated, and since they are also jointlyNormal, it follows that they are independent If βˆ and ... but, say, for i linearlyindependent linear combinations Rβ (here R is a i × k matrix with full row rank),then the above principle applies in the following way: the vector ˜u lies in the con-fidence

Ngày tải lên: 04/07/2014, 15:20

... situations in which one would want to obtain aF-confidence region inorder to get information about many different linear combinations of the parametersat the same time? For instance, one examines a ... looks at only certain kinds of linear combinations, for instance, at allcontrasts, i.e., linear combinations whose coefficients sum to zero This is a verythorough way to ascertain that all parameters ... regression line a standard 95% t interval What is the probability that the band created in this waycovers the true regression line over its entire length? Note: the Splus commandsqf(1-alpha,df1,df2) and

Ngày tải lên: 04/07/2014, 15:20

... (Choi and Shin, 1997; Spieckermann et al., 2004), or treat virtual resequencing (Inman and Schmeling, 2003; Gusikhin et al., 2008), where the physical production sequence remains unaltered and ... before resequencing is assigned to cycle t after resequencing, otherwise binary variable: 1, if sequencing rule defined for option o is violated in window starting in cycle t Big Integer T M O P ... high and only a few random access buffers are installed The following resequencing setting is taken from a major German truck manufacturer To regain a desirable model sequence after paint shop and...

Ngày tải lên: 23/03/2014, 05:22

... t≥ti ∈τn 34 Introduction to Itˆ-Calculus o which means that φ(ti ) has to be fixed at the beginning of each investment interval In other words: the Itˆ integral is non-anticipating, and o hence ... Preliminaries Note: In the following we will drop the argument ω in the integral and write shortly X dP Ω Let E denote the set of all discrete random variables (b) Consider the set of all random ... following are equivalent: P − lim Xn = X and (Xn ) is uniformly integrable, Xn −→ X in L1 Application: (Changing the order of differentiation and integration) Let X : I × Ω −→ I be a family of random...

Ngày tải lên: 22/02/2014, 06:20

... graduates in Economics, but it will imply graduates in Economics (and business administration) Master Thesis represents the main link between organisation and its employees, and also it defines the ... people are better in synthesizing, analyzing and comparing and should work with figures in their vocations, the people skilled in mentoring, negotiating, consulting or coaching should work with ... learning and training It is in tight connection with gaining new set of knowledge, skills and abilities that an employee need for quality performance with the new and more demanding tasks and...

Ngày tải lên: 17/03/2014, 06:20

... situation in paper production and printing industry ˿ The situation in printing and finishing industry ˿ Circumstances in the workshop ˿ Paper handling 11 ˿ ˿ ˿ ˿ Blistering Breaking in the fold Fluting ... situation in printing and finishing industry Normally speaking, there are few climate related problems in printing and finishing As a result, climate only becomes an issue when printing problems, ... Climate and Paper The interaction between climate and the processing of coated papers in printing and finishing Table of contents V Circumstances within the printer’s power to control I Introduction...

Ngày tải lên: 24/03/2014, 05:20

... a Graduate Program in Economics and Finance leading to the official degrees of Master in Economics and Finance and PhD in Economics The Master in Economics and Finance is a two-year program, which ... according to academic merit PhD in Economics Contents The PhD program in Economics is organized in two stages: > Master in Economics and Finance (120 ECTS), which lasts for two years > PhD in Economics: ... in Economics The Master combines rigorous training in advanced techniques of economic analysis with a special attention to applied and policy issues / UIMP The PhD in Economics aims at training...

Ngày tải lên: 31/03/2014, 03:20