Problem Set 2
... to overflow (e.g., in the case a, b ≈ 10180 ), underflow (e.g., in the case a, b ≈ 10−180 ), and severe cancellation (e.g., in the case |a| |b|). Write (on paper) a matlab program to evaluate F that should be more robust against overflow, underflow and cancellation than the direct implementation. It i ...
... to overflow (e.g., in the case a, b ≈ 10180 ), underflow (e.g., in the case a, b ≈ 10−180 ), and severe cancellation (e.g., in the case |a| |b|). Write (on paper) a matlab program to evaluate F that should be more robust against overflow, underflow and cancellation than the direct implementation. It i ...
Least Squares Adjustment
... where b is the number of histogram classes, ai is the observed frequency in class i and ei is the expected frequency in class i. Failure of the chi2 goodness of fit test is an indication that the observations are not normally distributed and/or that there is a problem in the model. Another test for ...
... where b is the number of histogram classes, ai is the observed frequency in class i and ei is the expected frequency in class i. Failure of the chi2 goodness of fit test is an indication that the observations are not normally distributed and/or that there is a problem in the model. Another test for ...
Simulation Methods Based on the SAS System
... are the non negative square roots of the eigenvalues of X' X j they are called the singular values. Using the singular value decomposition defined above we get the following representation of the OLS estimator b : b = VE-1U'y, ...
... are the non negative square roots of the eigenvalues of X' X j they are called the singular values. Using the singular value decomposition defined above we get the following representation of the OLS estimator b : b = VE-1U'y, ...
Parameter estimation in multivariate models Let X1,..., Xn be i.i.d.
... Let X1 , . . . , Xn be i.i.d. sample from the Pθ distribution, where θ ∈ Θ and Θ ⊂ Rk is the parameter space. The unknown parameter θ is estimated by means of a T = T(X1 , . . . , Xn ) = T(X) ∈ Rk statistic, which depends on the sample condensed into the p × n matrix X column-wise. Here XT is the da ...
... Let X1 , . . . , Xn be i.i.d. sample from the Pθ distribution, where θ ∈ Θ and Θ ⊂ Rk is the parameter space. The unknown parameter θ is estimated by means of a T = T(X1 , . . . , Xn ) = T(X) ∈ Rk statistic, which depends on the sample condensed into the p × n matrix X column-wise. Here XT is the da ...
OLS regression in the SAS system-
... 4. Look over these results, checking the t-statistic results to determine which regerssors need to be booted out. Cook up different sets of regressors and run the models, again looking over the results. Consider not only the "raw" statistics when choosing your regressors, but also the underlying the ...
... 4. Look over these results, checking the t-statistic results to determine which regerssors need to be booted out. Cook up different sets of regressors and run the models, again looking over the results. Consider not only the "raw" statistics when choosing your regressors, but also the underlying the ...
PresentationAbstracts2012
... Sparse factor modelling for high dimensional time series Analyzing multiple time series via factor model is one of the frequently used methods to achieve dimension reduction. Modern time series analysis concentrates on the situation when the number of time series p is as large as or even larger than ...
... Sparse factor modelling for high dimensional time series Analyzing multiple time series via factor model is one of the frequently used methods to achieve dimension reduction. Modern time series analysis concentrates on the situation when the number of time series p is as large as or even larger than ...
3. Model Fitting 3.1 The bivariate normal distribution
... What precisely does the P-value mean? “If the galaxy flux density really is constant, and we repeatedly obtained sets of 15 measurements under the same conditions, then only 2% of the F 2 values derived from these sets would be expected to be greater than our one actual measured value of 26.76” From ...
... What precisely does the P-value mean? “If the galaxy flux density really is constant, and we repeatedly obtained sets of 15 measurements under the same conditions, then only 2% of the F 2 values derived from these sets would be expected to be greater than our one actual measured value of 26.76” From ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 16. Given the following Revenue (R) and Cost (C) functions for a firm = 20 + 2, find the equilibrium level of output, price, total revenue, total cost and profit. ...
... 16. Given the following Revenue (R) and Cost (C) functions for a firm = 20 + 2, find the equilibrium level of output, price, total revenue, total cost and profit. ...
(pdf).
... (b) Let a = 0 in C. Assume that such a matrix is an echelon form of some matrix A. What value of c and d so that rank(A) = 2? (c) Let d = 1 and c = 1 and a = 0 in the matrix C. Assume that the matrix you obtain is the reduced echelon form of some matrix A. Write the last column of A as linear combin ...
... (b) Let a = 0 in C. Assume that such a matrix is an echelon form of some matrix A. What value of c and d so that rank(A) = 2? (c) Let d = 1 and c = 1 and a = 0 in the matrix C. Assume that the matrix you obtain is the reduced echelon form of some matrix A. Write the last column of A as linear combin ...
Macro
... • Put formulas on the top row and the variable we wish to vary in the column • Highlight the table area • Data/sensitivity analysis/ Data table • Select the cell input in row or in column ...
... • Put formulas on the top row and the variable we wish to vary in the column • Highlight the table area • Data/sensitivity analysis/ Data table • Select the cell input in row or in column ...
Let v denote a column vector of the nilpotent matrix Pi(A)(A − λ iI)ni
... Pi (A)(A − λi I)ni −1 where ni is the so called nilpotency. Theorem 3 in [1] shows that APi (A)(A − λi I)ni −1 = λi Pi (A)(A − λi I)ni −1 . which means a column vector v of the matrix is an eigenvector corresponding to the eigenvalue λi . The symbols are explained in [1]. However it is worth noting ...
... Pi (A)(A − λi I)ni −1 where ni is the so called nilpotency. Theorem 3 in [1] shows that APi (A)(A − λi I)ni −1 = λi Pi (A)(A − λi I)ni −1 . which means a column vector v of the matrix is an eigenvector corresponding to the eigenvalue λi . The symbols are explained in [1]. However it is worth noting ...
Simultaneous Equation Models
... one equation at a time (this is called limited information estimation) ...
... one equation at a time (this is called limited information estimation) ...
sheet
... The result of lm() is an object that contains various quantities related to the linear model. The following functions return some of these: > residuals(ld) > fitted(ld) > coef(ld) Printing the model object ld itself returns the coefficients. Inference for the Linear Model ...
... The result of lm() is an object that contains various quantities related to the linear model. The following functions return some of these: > residuals(ld) > fitted(ld) > coef(ld) Printing the model object ld itself returns the coefficients. Inference for the Linear Model ...
Ordinary least squares
In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model, with the goal of minimizing the differences between the observed responses in some arbitrary dataset and the responses predicted by the linear approximation of the data (visually this is seen as the sum of the vertical distances between each data point in the set and the corresponding point on the regression line - the smaller the differences, the better the model fits the data). The resulting estimator can be expressed by a simple formula, especially in the case of a single regressor on the right-hand side.The OLS estimator is consistent when the regressors are exogenous and there is no perfect multicollinearity, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Under these conditions, the method of OLS provides minimum-variance mean-unbiased estimation when the errors have finite variances. Under the additional assumption that the errors be normally distributed, OLS is the maximum likelihood estimator. OLS is used in economics (econometrics), political science and electrical engineering (control theory and signal processing), among many areas of application. The Multi-fractional order estimator is an expanded version of OLS.