concept theory and methods

... Inverse Problem Theory and Methods for Model Parameter Estimation OT89 Tarantola FM2.qxp 11/18/2004 3:50 PM Page OT89 Tarantola FM2.qxp 11/18/2004 3:50 PM Page Inverse Problem Theory and Methods for ... study is a random realization of a Gaussian random field, with given mean mprior and given covariance CM (examples of realizations of such random fields are displayed in chapter (Figure 2.4) and chapter ... As is traditional in probability theory, a subset A ⊆ X is called an event The union and the intersection of two events A and B are respectively denoted A ∪ B and A∩B The field of events is called,...

Ngày tải lên: 31/03/2014, 15:24

... β1 and β2 , and an unobserved error term, ut Thus, of the five quantities that appear in (1.01), two, yt and Xt , are observed, and three, β1 , β2 , and ut , are not Three of them, yt , Xt , and ... k2 , X21 of dimensions n2 × k1 , and X22 of dimensions n2 × k2 , with n1 + n2 = n and k1 + k2 = k Thus X11 and X12 have the same number of rows, and also X21 and X22 , as required for the submatrices ... normal random variable is 0, and that its variance is These two properties account for the use of the term “standard.” 1.7 A normally distributed random variable can have any mean µ and any positive...

Ngày tải lên: 08/04/2014, 12:28

... estimation for any family of nonstationary random processes” by J Sandberg and M Hansson-Sandsten, the covariance function estimate of a zero-mean nonstationary random process in discrete time is accomplished ... optimal for many other random processes as well Three papers are concerned with applications of wavelet and wideband signal processing In the paper “Nonstationary system analysis methods for underwater ... contains an elementary introduction to the Zak transform methods, a survey of recent results in Zak space sequence design and analysis, and a discussion of the main open problems in this area...

Ngày tải lên: 21/06/2014, 05:20

... β1 and β2 , and an unobserved error term, ut Thus, of the five quantities that appear in (1.01), two, yt and Xt , are observed, and three, β1 , β2 , and ut , are not Three of them, yt , Xt , and ... k2 , X21 of dimensions n2 × k1 , and X22 of dimensions n2 × k2 , with n1 + n2 = n and k1 + k2 = k Thus X11 and X12 have the same number of rows, and also X21 and X22 , as required for the submatrices ... normal random variable is 0, and that its variance is These two properties account for the use of the term “standard.” 1.7 A normally distributed random variable can have any mean µ and any positive...

Ngày tải lên: 04/07/2014, 15:20

... vectors w and z of length More generally, let x = αw and y = γz, for positive scalars α and γ Then x = α and y = γ Thus we have x, y = x y = αγ w z = αγ w, z Because x is parallel to w, and y is ... Figure 2.8, and imagine that the angle θ between x1 and x2 tends to zero If θ = 0, then x1 and x2 are parallel, and we can write x1 = αx2 , for some scalar α But this means that x1 −αx2 = 0, and so ... residuals and fitted values are unaffected by our choice of temperature scale Let us denote the constant term and the slope coefficient as β1 and β2 if we use the Celsius scale, and as α1 and α2 if...

Ngày tải lên: 04/07/2014, 15:20

... for which the regressors, and consequently the regressand, vary a lot, and we estimate Model using a second set of data for which both the regressors and the regressand vary much less Then, even ... Calculate γ and its standard error in two different ways One method should explicitly use the result (3.33), and the other should use a transformation of regression (3.69) which allows γ and its standard ... β1 and β4 as well ˆ as on their variances If this covariance is large and positive, Var(ˆ ) may be γ ˆ ˆ small, even if Var(β1 ) and Var(β4 ) are both large Copyright c 1999, Russell Davidson and...

Ngày tải lên: 04/07/2014, 15:20

... y1 , y2 and X ≡ X1 , X2 where y1 and y2 are, respectively, an n1 vector and an n2 vector, while X1 and X2 are n1 × k and n2 × k matrices Even if we need different parameter vectors, β1 and β2 ... to the PDF of the standard normal distribution The F Distribution If y1 and y2 are independent random variables distributed as χ2 (m1 ) and χ2 (m2 ), respectively, then the random variable F ≡ ... distribution function, or EDF, of a random sample The EDF was introduced in Exercises 1.1 and 3.4 Suppose that X is a random variable with CDF F (X) and that we obtain a random sample of size n with typical...

Ngày tải lên: 04/07/2014, 15:20

... evaluated at θ0 , and V ∞ (θ) is the ˆ k × k asymptotic covariance matrix of n1/2 (θ − θ0 ) ˆ 5.15 Suppose that γ = exp(β) and β = 1.324, with a standard error of 0.2432 ˆ and its standard error Calculate ... the concept of a quantile of the distribution that the test statistic follows under the null hypothesis If F (x) denotes the CDF of a random variable X, and if the PDF f (x) ≡ F (x) exists and ... centiles The quantile function of the standard normal distribution is shown in Figure 5.1 All three quartiles, the first and ninth deciles, and the 025 and 975 quantiles are shown in the figure...

Ngày tải lên: 04/07/2014, 15:20

... Numerous more formal methods of dealing with multiple minima have been proposed See, among others, Veall (1990), Goffe, Ferrier, and Rogers (1994), Dorsey and Mayer (1995), and Andrews (1997) In ... parameters δ0 , δ1 , and ρ of this model and the parameters α, β, γ0 , and γ1 of (6.94) How Copyright c 1999, Russell Davidson and James G MacKinnon 6.10 Exercises 253 many and what restrictions ... above has mean 0, and the IID assumption in (6.02) is enough to allow us to apply a law of large numbers to that sum It follows that the right-hand side, and therefore also the left-hand side, of...

Ngày tải lên: 04/07/2014, 15:20

... The regressand and regressors are −1 simply the dependent and independent variables multiplied by ωt , and the variance of the error term is clearly Copyright c 1999, Russell Davidson and James ... Davidson and James G MacKinnon 7.6 Autoregressive and Moving Average Processes 269 unconditional expectation E(ut ) and the unconditional variance Var(ut ) exist and are independent of t, and if ... the columns of U −1X and U −1Z on UX and UZ jointly ¯ ¯ Save the resulting matrices of fitted values and call them X and Z, respectively Copyright c 1999, Russell Davidson and James G MacKinnon...

Ngày tải lên: 04/07/2014, 15:20

... respectively, in the demand and supply functions, βd and βs are corresponding vectors of parameters, γd and γs are scalar parameters, and ud and us are the error terms in the demand and t t supply functions ... Nelson (1998), Angrist, Imbens, and Krueger (1999), Blomquist and Dahlberg (1999), Donald and Newey (2001), Hahn and Hausman (2002), Kleibergen (2002), and Stock, Wright, and Yogo (2002) There remain ... Economic theory predicts that, in most cases, γd < and γs > 0, which is equivalent to saying that the demand curve slopes downward and the supply curve slopes upward Equations (8.06) and (8.07)...

Ngày tải lên: 04/07/2014, 15:20

... to have coined the name, and Pakes and Pollard (1989) Other important early papers include Lee and Ingram (1991), Keane (1994), McFadden and Ruud (1994), and Gallant and Tauchen (1996) An interesting ... application of the method is Duffie and Singleton (1993) Useful references include Hajivassiliou and Ruud (1994), Gouri´roux e and Monfort (1996), and van Dijk, Monfort, and Brown (1995), which is a ... See, among others, Hansen, Heaton, and Yaron (1996) and West and Wilcox (1996) Tests of Linear Restrictions Just as in the case of generalized IV, both linear and nonlinear restrictions on regression...

Ngày tải lên: 04/07/2014, 15:20

... estimators; see Donald and Paarsch (1993, 1996) However, because these estimators violate standard regularity conditions, such as those given in Theorems 8.2 and 8.3 of Davidson and MacKinnon (1993), ... we use y1 and y2 in place of the variables x2 and x1 , respectively, that appear in (1.15) It is permissible to apply (10.22) to situations in which y1 and y2 are really vectors of random variables ... Davidson and MacKinnon (1984b) and Godfrey, McAleer, and McKenzie (1988), among others Of course, either variant of the test may easily be bootstrapped, as discussed in Section 10.6, and the OPG...

Ngày tải lên: 04/07/2014, 15:20

... 100 assuming that β1 = and β2 = 1, 100 assuming that β1 = −1 and β2 = 1, 100 assuming that β1 = and β1 = 2, 100 assuming that β1 = and β1 = −2, and 100 assuming that β1 = and β2 = For each of the ... is just unity, ˜ ˜ ˜ and Vt , Ft , and ft are all constants that not depend on t Since neither subtracting a constant from the regressand nor multiplying the regressand and regressors by a constant ... simulation-based methods, including the method of simulated moments, which was discussed in Section 9.6 See Hajivassiliou and Ruud (1994) and Gouri´roux and Monfort (1996) for discussions e of some of the methods...

Ngày tải lên: 04/07/2014, 15:20

... logarithms, Xtd and Xts are row vectors of exogenous or predetermined variables, βd and βs are the corresponding vectors of parameters, and γd and γs are the slopes of the demand and supply functions, ... literature on demand systems is vast; see, among many others, Christensen, Jorgenson, and Lau (1975), Barten (1977), Deaton and Muellbauer (1980), Pollak and Wales (1981, 1987), Browning and Meghir ... equations (12.08) for an arbitrary p × q matrix A and an arbitrary r × s matrix B Prove the second result for A and B as above, and for C and D arbitrary q ×t and s×u matrices, respectively Prove the...

Ngày tải lên: 04/07/2014, 15:20

... by Hendry and Anderson (1977) and Davidson, Hendry, Srba, and Yeo (1978) See Banerjee, Dolado, Galbraith, and Hendry (1993) for a detailed treatment Copyright c 1999, Russell Davidson and James ... only Not all software packages provide reliable estimates and standard errors; see McCullough and Renfro (1999) and Brooks, Burke, and Persand (2001) Therefore, we strongly recommend estimating ... Bollerslev and Wooldridge (1992) These and other possible variants are discussed and compared by Fiorentini, Calzolari, and Panattoni (1996).5 Simulating ARCH and GARCH Models ARCH and GARCH models...

Ngày tải lên: 04/07/2014, 15:20

... Davidson and James G MacKinnon 14.2 Random Walks and Unit Roots 597 This model is often called a random walk with drift, and the constant term is called a drift parameter To understand this terminology, ... commodities in different countries, disposable income and consumption, government spending and tax revenues, wages and prices, and the money supply and the price level Although deterministic relationships ... yt−1,2 + ut2 , ut1 ut2 ∼ IID(0, Ω) (14.36) Let zt and ut be vectors, the former with elements yt1 and yt2 and the latter with elements ut1 and ut2 , and let Φ be the × matrix with ij th element φij...

Ngày tải lên: 04/07/2014, 15:20

... of the bandwidth parameter h, and there is a very large and highly technical literature on how best to choose it See Silverman (1986), H¨rdle (1990), Wand and Jones a (1995), or Pagan and Ullah ... parameter, and τ (x) may be any scalar function that is monotonically increasing in its argument x and satisfies the conditions τ (0) = 0, τ (0) = 1, and τ (0) = 0, where τ (0) and τ (0) are the first and ... distributed The statistics τ3 , τ4 , and τ3,4 were proposed, in slightly different forms, by Jarque and Bera (1980) and Kiefer and Salmon (1983); see also Bera and Jarque (1982) Many regression packages...

Ngày tải lên: 04/07/2014, 15:20

... systematic in theory and algorithms, and easy to read For most methods, we motivate the idea, study the derivation, establish the global and local convergence, and indicate the efficiency and reliability ... systematically introduces optimization theory and methods, discusses in detail optimality conditions, and develops computational methods for unconstrained, constrained, and nonsmooth optimization Due ... methods and quasi-Newton methods were presented, the nonlinear programming developed greatly Now various modern optimization methods can solve difficult and large scale optimization problems, and...

Ngày tải lên: 20/08/2015, 15:18

... SOLID SHELL ELEMENT BASED ON RELATIVE DISPLACEMENTS CONCEPT: THEORY AND APPLICATIONS MA YONGQIAN B.Eng (Nanjing University of Aeronautics and Astronautics, P.R.China), M.Eng.(Zhejiang University,...

Ngày tải lên: 12/09/2015, 21:29