The general linear statistical model can be described in matrix notation as
(II.II.1-1)
where y is a stochastic T*1 vector, X is a deterministic (exogenous) T*K matrix, b is a K*1 vector of invariant parameters to be estimated by OLS, e is a T*1 disturbance vector, T is the number of observations in the sample, and K is the number of exogenous variables used in the right hand side of the econometric equation.
It is furthermore assumed that
(II.II.1-2)
which is the equivalent matrix expression of the weak set of assumptions under section II.I.3.
The least squares estimator minimizes e’e (the sum of squared residuals).
Solving the normal equations X’Xb = X’y with respect to b yields
(II.II.1-3)
where X’X must be a non singular symmetric K*K matrix!
Obviously, the OLS estimator is unbiased
(II.II.1-4)
since E(X’e) = 0 by assumption (X is exogenous). This result can be proved quite easily. Note that if X is not exogenously given (thus stochastic) the small sample property of unbiasedness only holds if E(X’e) = 0.
Under the assumption of OLS it can be proved that the covariance matrix of the parameters is
(II.II.1-5)
The Gauss-Markov theorem states that if
(II.II.1-6)
then any other estimator
(II.II.1-7)
has a parameter covariance matrix which is at least as large as the covariance matrix of the OLS parameters
(II.II.1-8)
This important theorem therefore proves that the OLS estimator is a best linear unbiased estimator (BLUE).
If D* is a K by T matrix which is independent from y and if
(II.II.1-9)
the parameter vector is by definition a linear estimator, and if
(II.II.1-10)
then it follows that
(II.II.1-11)
Evidently, it follows from (II.II.1-11) that the parameter vector can only be unbiased if DX = 0 and if E(D*e) = 0.
Now what happens to the covariance matrix of this estimator? Obviously, we find
(II.II.1-12)
which proves the theorem (on comparing (II.II.1-12) with (II.II.1-5); Q.E.D.).
It can be proved that
(II.II.1-13)
which states that the OLS estimator of the variance is unbiased.
The operational formula for calculating the variance is
(II.II.1-14)
The prediction of y values outside the sample range is
(II.II.1-15)
which is an unbiased prediction function
(II.II.1-16)
Example of extrapolation forecast
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Course: Alternative Fuels for Road Vehicles
The atmosphere of the earth is composed of 21% oxygen and 78% nitrogen, as well as vapor and trace gases. For millions of years, this atmospheric composition has been subjected to large or small variations. This is also true for trace gases such as carbon dioxide (CO2) water vapor, ozone (O3), nitrous oxide (N2O), methane (CH4), and various others. The composition of the atmosphere is the result of self-stabilizing interactive effects, which lead to a somewhat indifferent equilibrium. Within this environment, natural catastrophes such as volcanic eruptions can be compensated for without causing a collapse of the ecosystem. However, during the last 1000 years, a change with regard to trace gases has been monitored, which is evolving at increasing speed. This change is being attributed to anthropogenic activities. The phenomenon might be explained by the world population explosion and the resulting increase in energy consumption, as well as by increasing industrialization and agriculture.
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The advent of the Internet, which is seen as one of the most significant revolutions of the 20th century, has given rise to a new type of business, which is called electronic commerce. E-Commerce is the use of internetworked computers to create and transform business relationships. It is most commonly associated with buying and selling information, products, and services via the Internet, but it is also used to transfer and share information within organizations through intranets to improve decision-making and eliminate duplication of effort. The new paradigm of commerce is built not just on transactions but on building, sustaining and improving relationships, both existing and potential.
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The success of any business or consumer product depends in part on the target market’s ability to distinguish one product from another. Branding is the main tool marketers use to distinguish their products from the competition’s.
A brand is a name, term, symbol, design, or combination thereof that identifies a seller’s products and differentiates them from competitors’ product. A brand name is that part of a brand that can be spoken, including letters (GM, YMCA), words (Chevrolet), and numbers (WD-40, 7-eleven). The elements of a brand that cannot be spoken are called the brand mark- for example, the well-known Mercedes-Benz and Delta Airlines symbols. Branding has main purposes: product identification, repeat sales, and new-product sales. The most important purpose is product identification. Branding allows marketers to distinguish their products from all others. Many brand names are familiar to consumers and indicate quality. Exhibit 10.3 lists, in order, the 10 brand names that U.S. consumers believe signify the highest quality products. The coolest brands, according to U.S. teenagers, are Nike, Levi’s, Guess, Gap, Coke, Pepsi, and Sega.
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INTRODUCTION
Those who have ruled over seas also ruled over the world for centuries. Seas connecting continents to oceans have transformed into small lakes as a result of developping technology when entered in the 20’th century, and people have come close to each other so much that the old world has had global structure.
Technology has enabled shipping sector become the most rantable and the most economic transportation way in the transportation industry by bringing importance of shipping to a level higher than it had in the past. Due to this superiority of seas, countries using seas in a rantable way are able to control the world trade.
An important part of export is made by means of the sea. There are very close connection of the amount of export cargo and variation of export goods with economic level and development of the country. Thus the amount of export and the increase in it shows how much a country is economically grown.
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As we have seen before factor abundance leads to comparative advantage. Perhaps this theory overlooks an important point. When factors are abundant, it might lead to inefficient use of that factor as there is little incentive to use this factor in an efficient way. If factors are scarce, firms have a strong incentive to make efficient use of the available resources, and be innovative. There are numerous examples of cases where scarcity has led to innovation. Japan’s scarcity of land has delivered us the just-in-time production. In the North Sea, oil platforms are expensive to build and maintain; their scarcity has led to the development of horizontal drilling to reach distant under-sea oil reservoirs. Short building seasons in Sweden have led to prefabricated houses. Michael Porter is an very famous Harward professor who is especially well known with the theory of nations competitive advantage.According to the Porter the standard and classical theories on comparative advantage are wrong. Michael Porter (1990) proposed a model that provides conditions that have to be met for a firm to be
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CALL OFF:Cancel an event.
eg.)The football match was called off because of the bad weather.
CALL BACK:Telephone again later.
eg.)Thank you for ringing. I’ll call you back as soon as I have the information that you want.
CALL UP:Ring up, telephone.
eg.)Alper called up me to learn the date of the exams.
CALL UP:CONSCRIPT.
eg.)Men over eighteen years of age were called up the fight the enemy
in the war.
CALL BY:To make a short visit to a place or person.
eg.)I’ll call by to pick up the book on my way to work.
CALL FOR:Require, demand.
eg.)The situation calls for tact.
eg.)You have got the job!This calls for a celebration.
CARE FOR:To look after sb.
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1. – 12. sorularda, cümlede boş bırakılan yerlere uygun düşen sözcük ya da ifadeyi bulunuz?
1. I find it hard to believe that such a highly reputable firm could engage in a ………………………. of this magnitude.
a. recession
b. rejection
c. deception
d. taxation
e. component
(Cevap C) Doğru cevap hile, düzen anlamına gelen (c) şıkkıdır. Cümlenin Türkçe karşılığına baktığımızda “Bu kadar iyi tanınan bir şirketin bu derece büyük bir … yaptığına inanmak çok zor.” cümlesini en uygun tamamlayacak sözcüğün (a) şıkkındaki gerileme, (b) şıkkındaki reddetme, (d) şıkkındaki vergilendirme ve (e) şıkkındaki unsur, eleman anlamına gelen sözcüklerinin değil hile, düzenbazlık anlamına gelen deception kelimesinin olduğunu görmekteyiz.
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Read the passages and find the best mark the answers
The official language of the Czech Republic is Czech, a highly complex western Slavic tongue. Any attempt from foreigners to speak Czech will be heartily appreciated, so do not be discouraged if people fail to understand you, as most will be accustomed to hearing foreigners stumble through their language. If you don’t know any Czech, brush up on your German, since, among the older generation at least, it is still the most widely spoken second language. Russian, once the compulsory second language has been practically wiped off the school curriculum, and the number of English speakers has been steadily increasing, especially among the younger generation.
1-It is clear from the passage that…………. .
***A)more Czechs speak German than any other foreign language
B)as their own language is so difficult, Czechs prefer German
C)everyone in the Czech Republic speaks several languages
D)Czechs usually laugh at foreigners who try to speak Czech
E)Czechs learn English during childhood and German later
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