Có 40+ tài liệu thuộc chủ đề "thống kê học"
tailieu.vn Xem trực tuyến Tải xuống
There is an imperfect analogy between linear estimation of the coefficients and quadratic estimation of the variance in the linear model. This chapter sorts out the principal commonalities and differences, a task obscured by the widespread but un- warranted imposition of the unbiasedness assumption. We will work in the usual regression model. (25.0.12) y = Xβ + ε ε ε,....
tailieu.vn Xem trực tuyến Tải xuống
Christensen’s [Chr87] is one of the few textbooks which treat best linear predic- tion on the basis of known first and second moments in parallel with the regression model. Minimum Mean Squared Error, Unbiasedness Not Required Assume the expected values of the random vectors y and z are known, and their joint covariance matrix is known up to an unknown...
tailieu.vn Xem trực tuyến Tải xuống
Remark (no proof required): this regression is equivalent to (29.1.1), and it allows you to test the constraint.. It you add z as additional regressor into (29.1.2), you get y t = α+β(x t +z t )+δz t +ε t . Now substitute the right hand side from (29.1.1) for y to get α + βx t + γz t...
tailieu.vn Xem trực tuyến Tải xuống
The first decision is whether to look at the ordinary residuals (31.1.1) ε ˆ i = y i − x >. Since ε ˆ = M y, the variance of the ith ordinary residual is. (31.1.3) var[ˆ ε i. (31.1.5) h ii = x >. (Note that x i is the ith row of X written as a column vector.)...
tailieu.vn Xem trực tuyến Tải xuống
The “regression” referred to in the title of this chapter is not necessarily linear regression. The population regression can be defined as follows: The random scalar y and the random vector x have a joint distribution, and we want to know how the conditional distribution of y|x = x depends on the value x. Someone said on an email list...
tailieu.vn Xem trực tuyến Tải xuống
i.e., x t is the tth row of X. It is written as a column vector, since we follow the “column vector convention.” The (marginal). Since the y i are stochastically independent, their joint density function is the product, which can be written as. To compute the maximum likelihood estimator, it is advantageous to start with the log likelihood function:....
tailieu.vn Xem trực tuyến Tải xuống
OLS With Random Constraint. A Bayesian considers the posterior density the full representation of the informa- tion provided by sample and prior information. Frequentists have discoveered that one can interpret the parameters of this density as estimators of the key unknown parameters, and that these estimators have good sampling properties. (37.0.55) Rβ = u + η, η ∼ (o, τ...
tailieu.vn Xem trực tuyến Tải xuống
Until now we always assumed that X was nonrandom, i.e., the hypothetical repetitions of the experiment used the same X matrix. The assumption which we will discuss first is that X is random, but the classical assumptions hold conditionally on X, i.e., the conditional expectation E [ε ε ε|X. Moreover, certain properties of the Least Squares estimator remain valid uncon-...
tailieu.vn Xem trực tuyến Tải xuống
then the confidence ellipse of the transformed vector Rβ is also a projection or. “shadow” of the confidence region for the whole vector. Projections of the same confidence region have the same confidence level, independent of the direction in which this projection goes.. For each possible value β ˜ of the parameter vector, the associated sum of squared errors is...
tailieu.vn Xem trực tuyến Tải xuống
Multiple Comparisons in the Linear Model. Rectangular Confidence Regions. If you use the Cartesian product (or the intersection, depending on how you look at it) of the individual confidence intervals, the confidence level of this rectangular confidence region will of necessity be different that of the individual intervals used to form this region. There are two main approaches for compute...
tailieu.vn Xem trực tuyến Tải xuống
So far we have assumed that the mean of the dependent variable is a linear func- tion of the explanatory variables. This can be done with the use of dummy variables, or by the use of variables coded as “factors.” If there are more than two categories, you need several several regressors taking only the values 0 and 1, which...
tailieu.vn Xem trực tuyến Tải xuống
Its expected value is the bias at u E[ f ˆ (u. and the expected value of its square is the MSE at u E f(u) ˆ − f (u) 2. This is a measure of the precision of the density estimate at point u only.. The overall deviation of the estimated density from the true density can be measured...
tailieu.vn Xem trực tuyến Tải xuống
β N x t−N + ε t This can be written in the form. (49.0.2) y = Xβ + ε ε ε where X. Two problems: lag length often not known, and X matrix often highly multi- collinear.. How to determine lag length? Sometimes it is done by the adjusted ¯ R 2 . Assume we know for sure that...
tailieu.vn Xem trực tuyến Tải xuống
The same problem can also happen in the continuous case. An attractor A is a compact set which has a neighborhood U such that A is the limit set of all trajectories starting in U. That means, every trajectory starting in U comes arbitrarily close to each point of the attractor.. But in R 3 and higher, chaos can occur,...
tailieu.vn Xem trực tuyến Tải xuống
(53.1.9) cov[x, ε. 2 (53.1.10). (53.1.11). (53.1.12) y. (53.1.14). (53.1.16). (53.1.17). (53.1.18) µ y = α + βµ x. (53.1.20) follows. (53.1.21). σ 2 y (53.1.22). (53.1.23). it is (53.1.24). compatible with (53.1.24).. (53.2.3) plim. (53.2.4) var 1. (53.2.4) converges toward zero.. α + x ∗ β (53.3.10). v (53.3.11). (53.3.12). (53.3.13) y = y. Qα − Qα e =...
tailieu.vn Xem trực tuyến Tải xuống
The choice of the step direction is the main characteristic of the program. Most programs (notable exception: simulated annealing) always choose directions at every step along which the objective function slopes downward, so that one will get lower values of the objective function for small increments in that direction. is the Jacobian of f at θ i , i.e., the...
tailieu.vn Xem trực tuyến Tải xuống
or may not be one of the explanatory variables in the regression). What properties do your estimates of the β i have?. ρσ 2 for i 6= j (i.e., the ε i are equicorrelated).. Now multiply the left sides and the righthand sides (use middle term in (57.3.4)) h >. k=1 (z k − µ) 2 be the population variance...
tailieu.vn Xem trực tuyến Tải xuống
µ defines the method of moments esti- mator µ ˆ of µ if one replaces the expected value in (59.0.8) with the sample mean of the elements of an observation vector y consisting of independent observations of y.. The generalized method of moments estimator extends this rule in several re- spects: the y i no longer have to be i.i.d.,...
tailieu.vn Xem trực tuyến Tải xuống
The random coefficient model first developed in [HH68] cannot be written in the form y = Xβ +ε ε ε because each observation has a different β. In tiles, this model is (61.0.32). (61.0.33). (61.0.34) v ∗ t = Σ Σ Σx t (x t >. (61.0.35) β ∗ t. (61.0.36) β ∗ t = ˆ ¯ β + Σ...
tailieu.vn Xem trực tuyến Tải xuống
This Chapter discusses a model that is a special case of the model in Chapter 62.2, but it goes into more depth towards the end.. y = n 1 y i is the vector of sample means, W = P. (63.1.10) Problem 518 . space, the “scatterplot geometry.” If r = 2, this is the scatter plot of the two...