class notes in c programming language

... actually counting the number of cars in the first halfhour? Answer First a few definitions: x is the total number of occurrences in the interval [0, 1] y is the number of occurrences in the interval ... if the intervals become very short the probability of havingtwo occurrences in the same interval becomes negligible.)In this discrete approximation, the probability to have k successes in time ... number of independent possibilities, each of which has only a small chance ofoccurring (law of rare events) The expected number of occurrences is proportional to time with a proportionality factor

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... errors in both variables We also showedthat this lack of identification is not complete, because one can specify an intervalwhich in the plim contains the true parameter value Chapter 53 has a much ... linear function of x and the second a linear function of y Draw the two lines representing these linearfunctions into Figure1 Use (10.3.18) for this intersects the ellipse where it is vertical ... given country and asking them abouttheir incomey and consumptionccan be modeled as the independent observations oftwo random variables which satisfy y=yp+yt,(11.0.19) c=cp+ct,(11.0.20) cp= βyp.(11.0.21)

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... the technical property E[t] = θ has created a lot of confusion. Besides having no advantages, the category of unbiasedness even has some in- convenient properties: In some cases, in which consistent ... reasons not to be working with an asymptotically efficient estimator. Problem 195. Can you think of situations in which an estimator is acceptable which is not asymptotically efficient? 13.2. SMALL ... will argue in these class notes that unbiasedness itself is not a desirable property. 362 13. ESTIMATION PRINCIPLES 13.3. Comparison Unbiasedness Consistency Let us compare consistency with unbiasedness.

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... Significance Tests and Confidence Regions There is a duality between confidence regions with confidence level 1 − α and certain significance tests. Let us look at a family of significance tests, which ... CHAPTER 15 Hypothesis Testing Imagine you are a business p e rson considering a major investment in order to launch a new product. The sales prospects of this product are not known with certainty. ... test exists in this situation. It is a so-called likelihood-ratio te st, which has the following critical [...]... HYPOTHESIS TESTING • b 1 point Government agencies enforcing discrimination laws

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... points in 3-dimensionalspace (a 3-dimensional scatter plot), or 3 points in 15-dimensional space In thefirst case, each point corresponds to an observation, in the second case, each pointcorresponds ... [LN81] which comes from a Bayesian point of view) Adifferent approach to causality and inference, [Roy97], is discussed in chapter/section 2.8 Regarding critical realism and econometrics, also ... Trang 1CHAPTER 17Causality and Inference This chapter establishes the connection between critical realism and Holland andRubin’s modelling of causality in statistics as explained in [Hol86]

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... 919.3 Canonical CorrelationsNow what happens with the correlation coefficients if both predictor and predic-tand are vectors? In this case one has more than one correlation coefficient One firstfinds ... Trang 1CHAPTER 19Digression about Correlation Coefficients 19.1 A Unified Definition of Correlation Coefficients Correlation coefficients measure linear association The usual definition of ... several numbers, the “canonical correlations.” The multiple or partial correlation coefficients are usually defined as simple relation coefficients involving the best linear predictor or its residual

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... buffers in emacs, and switch between them if needed. The command C-x C-c terminates emacs. Another thing I recommend you to learn is how to send and receive electronic mail from inside emacs. To ... having 39 missing values at the beginning People who want to use some Citibase data should include the following options... beginning of statistical models, chapter 11 A Mini Quiz will check ... the number of days since Jan 1, 1960, but it prints in several formats... by Cobb and Douglas in their original article [CD28] introducing the production function which would bear their

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... C[y,z], C[x,y+z] = C[x,y] + C[x,z], and C[y, c] = O if c is Trang 13(here consisting of one row only) that contains all the covariances(24.1.2) C[¯y,βˆ] ≡cov[¯y,βˆ1] cov[¯y,βˆ2] · · · cov[¯y,βˆk] ... X(X>X)−1t + c
] = = σ2 t>(X>X)−1X>+ c>
X(X>X)−1t + c
= σ2t>(X>X)−1t + σ2c>c,Here we needed again c>X = o> Clearly, this is minimized if c = o, in which case Answer (Compare ... 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 θˆis unbiased, then the MSE -matrixcoincides

Ngày tải lên: 04/07/2014, 15:20

... be particulary interested in estimates whoseMSE is independent of β? The research following up on Hsu tried to get rid of thisassumption again C R Rao, in [Rao52], replaced independence of the ... which makes it so popular in the classroom—it iseasy to check—gains here objective relevance For the best nonnegative quadraticunbiased estimator one needs to know ΩΩΩ only up to a scalar factor, ... of bounded MSE (This is particularly satisfying since such a replacement is also called for in the case of linear estimators.) Then puzzle (2)disappears: the Theil-Schweitzer estimator is no longer

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... CHAPTER 27 Best Linear Prediction Best Linear Prediction is the second basic building block for the linear model, in addition to the OLS model. Instead of estimating a nonrandom ... d. Now continue as in the proof of theorem 27.1.1. I must still carry out this proof much more carefully!  Problem 326. 4 points According to (27.1.2), the prediction error z ∗ − z is uncorrelated ... same, but the intercept changes • c 1 point Assume again E[z|x, y] = 1 + 2x... and the prediction error is uncorrelated with x • b Express β in terms of the variances and covariances of x

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... linearly indep endent (which is called: R has full row rank). In other words, the matrix of constraints R does not include “redundant” constraints which are linear combinations of the other constraints. ... imposing the constraint itself, one imposes a penalty function which has such a form that the agents will “voluntarily” heed the constraint. This is a familiar principle in neoclassical economics: ... equivalent to a linear constraint on E [y]. The decision not to include certain explanatory variables in the regression can be considered the decision to set certain elements of β zero, which is the

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... How can one detect multicollinearity? Trang 20• c 2 points How can one remedy multicollinearity?32.1 Missing ObservationsFirst case: data ony are missing If you use a least squares predictor ... ongraphics, therefore it has only recently become part of the standard procedures Problem 373 1 point Define multicollinearity • a 2 points What are the symptoms of multicollinearity? • b 2 points ... General conclusion: in a single-equation context, filling in missingynot a goodidea Now missing values in the X-matrix If there is only one regressor and a constant term, then the zero order filling

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... consists in slicing or binning the data, and taking the mean of the data in each bin. But if you have too many explanatory variables, this local averaging becomes infeasible, because of the “curse ... data scarcity. Projection pursuit regression searches for an interesting and informative projec- tion of the data by maximizing a criterion function. A logical candidate would for instance be ... the scatterplot matrix will b e oriented all in 1 direction.  33.2. Conditional Plots In order to account for the effect of excluded variables in a scatter plot, the function coplot makes scatter

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... variances of three linear combinations of two parameters imply for thecorrelation between them! I can think of two justifications of Bayesian approaches In certain situationsthe data are very insensitive, ... something 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 ... distribution combines all the information, prior informationand sample information, aboutβ.According to (??), this posterior mean can be written as Trang 15These formulas are correct, but the

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... continuous approximation to one Since the discontinuity is removed, one can expect that it has, under certain circumstances, better properties than the indicator function itself Write down the formula ... equivariant and the shrinkage seems arbitrary Discussing them here brings out two things: the formulas for random constraints etc are a pattern according to which one can build good operational ... estimator by using the following function I(F ) instead: I(F ) = 0 if F ≤ 1 and I(F ) = 1 − 1/F if F > 1 This is no longer an indicator function, but can be considered a continuous approximation

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... is also defined if the covariance matrix of y is singular In this case, certain nonzero linear combinations of the elements of y are known with certainty Certain vectors can... 2 1 1 1 = 0 0 ... variance may not be constant—in which case the intuition that y is some function of X plus some error term may no longer be appropriate; y may for instance be the outcome of a binary choice, the ... this linear combination, normalized in such a way that the expected value of this distance is 1. 900 40. THE MAHALANOBIS DISTANCE Definition 40.1.1. Given a random n-vector y which has expected

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... 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 ... 2-dimensional case in which the confidenceregion for β is an ellipse, as drawn in Figure 1, called Bβ;π(y) Starting with thisellipse, the above criterion defines individual confidence intervals for linear ... the whole vector Projections of thesame confidence region have the same confidence level, independent of thedirection in which this projection goes The confidence regions for β with coverage probability

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... the infinitely manyt tests ofall linear combinations of β Or one looks at only certain kinds of linear combinations, for instance, at allcontrasts, i.e., linear combinations whose coefficients ... Rectangular Confidence RegionsAssume you are interested in two linear combinations of β at the same time, i.e.,you want separate confidence intervals for them If you use the Cartesian product(or the intersection, ... intersection, depending on how you look at it) of the individual confidenceintervals, the confidence level of this rectangular confidence region will of necessity be different that of the individual

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... 2, linear splines, place knots at points where the data exhibit a change in slope For m = 3, quadratic splines, locate knots near local maxima, minima or tion points in the data Trang 12inflec-For ... attempt used in rics was to use a family of functions which is not as complete as the polynomials butwhich ecompasses many functional forms encountered in Economics These functions Trang 9Economet-are ... coefficient for ptwill be negative, because the intercept in peacetimes is below the intercept in war times) Answer Now the intercept of the whole equation is the intercept of the war regression line,

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... Normality based on entropy CHAPTER 48 Measuring Economic Inequality 48.1 Web Resources about Income Inequality • UNU/Wider-UNDP World Income Inequality Database (4500 Gini-coefficients www.wider.unu.edu/wiid/wiid.htm... ... mean equal income ratios • Lorenz curve: Line up everybody in ascending... inequality the area between the 1046 48 MEASURING ECONOMIC INEQUALITY Parade curve and this horizontal line, divided ... i’s income,... looking down on a field On one side, there is a long straight fence marked off with income categories: the physical distance between any two points directly corresponds to the income

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