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econometrics

carme liu Inglés 34 fichas

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  1. 1OUTCOMESmutually exclusive potential results of a random process
  2. 2PROBABILITYproportion of the time that the outcome occurs in the long run
  3. 3SAMPLE SPACEset of all poss outcomes
  4. 4PROBABILITY DISTRIBUTIONlist of all possible values of the variable and the probability that each value will occur
  5. 5CUMULATIVE PROBABILITY DISTRIBUTIONrandom variable is less than or equal to a particular value
  6. 6BERNOULLI DISTRIBUTION-case of a discrete random variable
    -outcomes: 0 or 1
    - mean/expected value: p
    - variance: p(1-p)
  7. 7EXPECTED VALUE E(Y)weighted average of the possible outcomes of that random variable
  8. 8VARIANCE VAR(Y)-expected value of the square of the deviation of y from the mean
    E[(Y-my^2)]
    -multiplying it by the probability
  9. 9MOMENTSKurtosis
    skewness
    variance
    mean
  10. 10SKEWNESS-measures how much the distribution deviations from the symmetry
    E[(Y-my^3)]/var^3
    -symmetric =0
  11. 11KURTOSIS-measures how much mass is in its tails therefore it measures how much the variance of y will arise from extreme values
    E[(Y-my^4)]/var^4
    -the greater the kurtosis of a distribution, the more likely the outliers
    -kurtosis can not be negative because the numerator can not be negative
    distribution exceeding3 = leptokurtic
  12. 12JOINT DISTRIBUTIONPr[(X=x,Y=y)]
  13. 13CONDITONAL DISTRIBUTIONSPr[Y=ylX=x)
  14. 14BAYES THEOREMPr(Y=ylX=x) = Pr[X=xlY=y)Pr(Y=y)/Pr(X=x)
  15. 15CONDITIONAL EXPECTATIONE(YlX=x): Conditional expectation of y given x is the conditional mean of y given x
  16. 16CONDITIONAL VARIANCE-
  17. 17INDEPENDENCEIf knowing the value of one of the variable provides no info about the other
    Joint distribution = product of their marginal distribution
    Pr(X=x,Y=y) =Pr(X=x)*Pr(Y=y)
    Conditional distribution of Y given X = marginal distribution of Y
    Pr(Y=ylX=x) = Pr(Y=y)
    Var(X+Y) = VAR(X) + VAR(Y)
    cov(x,y)=0
    no correlation or covariance
  18. 18COVARIANCEE[(X-Mx)*(Y-My)]
    x and y = +ve: +ve
    x and y opp direction: -ve
    x and y independent = 0
  19. 19CORRELATIONmeasure of dependence between x and y
    corr(x,y)=cov(x,y)/sd(x)sd(y)
  20. 20E(YlX)=MyConditional mean = unconditional mean
    Covariance and covariance = 0 because independent
    independent: e(xy) = e(x)e(y)
  21. 21Var(a) Var(ax+b) Var(ax+by) Cov(x,y)Var(a)=0
    Var(ax+b)=a^2var(a)
    Var(ax+by) =a^2var(x)+b^2var(y)-2abcov(x,y)
    Cov(x,y) = e(xy)-e(x)e(y)
  22. 22NORMAL DISTRIBUTIONN(mean, variance) = (0,1)
  23. 23BIVARIATE NORMAL DISTRIBUTIONjoint distribution of two normally distributed variables
  24. 24MULTIVARIATE NORMAL DISTRIBUTION- joint distribution of more than two normally distributed variables
    PROPERTIES
  25. 25CHISQUARED DISTRIBUTION/
  26. 26STUDENT T DISTRIBZ - N(0,1) and W - X^2m
    Z/(SQUARE ROOT W/M)
    Distribution of the ratio of a standard normal random variable / by square root of an independently distributed chi squared random variable
    m>30: student t distrib is will approxed by standard nd. more centered around 0, closer to standard normal
    t infinity = n(0,1)
  27. 27F DISTRIBUTION/
  28. 28RANDOM SAMPLEeach element of the population has an equal chance of being
    chosen
    the selection of one element has no effect on the probability of
    another element being selected
    Because of random sampling, any two different observations in
    the sample are independent.
    same mean and variance
    non random sampling can lead to y bar being biased
  29. 29LAW OF LARGE NUMBERSn increases, the distribution of Y bar becomes more tightly
    centred around µY
  30. 30DESIRABLE CHARACTERISTICS OF AN ESTIMATORUNBIASED: E(Ybar) = My
    finite and sample property
    CONSISTENT: y bar (p)--->) My
    The probability that the estimator is close to the true value of the parameter increases to 1 as the sample size gets
    larger.
    asymptotic property
    EFFICIENT: lower variance = more efficient
    var(Y bar) shrinks as n increases
    finite property
    BLUE
  31. 31STANDARD ERRORsquare root sigma^2/n
    smaller SE the less variance
  32. 32HYPOTHESIS TESTING: 1 SIDED HYPOTHESIS TESTING: VAR UNKNOWN/
  33. 33P VALUEThe p-value, or significance probability, is the probability of obtaining
    a result equal to or ‘more extreme’ than what was actually observed,
    when the null hypothesis is true.
    2 Compute the p-value (instead of the critical values)
    reject H0 if p ≤ α. The smaller the p-value is, the more statistical evidence there is against Ho
  34. 34CLTSmall sample and therefore if n = 20, we use n-1

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Fichas sobre econometrics, creado por carme liu el 25/11/2017.
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carme liu
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