| Library: | gam |
| See also: | intest intestpl gintest gintestpl backfit |
| Quantlet: | wavetest | |
| Description: | Additive component analysis in additive separable models using wavelet estimation. The first (additive) component is tested against a given polynomial form of degree p, e.g., if p=1 is to test linearity, p=0 is to test for significant influence of the first component at all etc. For details see Haerdle, Sperlich, Spokoiny (1997), DP 52, SFB 373 Berlin. |
| Usage: | erg = wavetest(x,y,p{,dis{,data{,adjust}}}}) | |
| Input: | ||
| x | n x d matrix , the observed explanatory variable where all dummy inputs (0-1 variables) are expected to be in the last ('dis') columns. | |
| y | n x 1 matrix , the observed response variable | |
| p | scalar , the polynomial degree of the Hypothesis, see Description. | |
| dis | scalar , the number of dummy variables in x. Have to be the last columns in x. Default is dis=0. | |
| data | optional string, if output file for the wavelet coefficient estimates is wished, this string will be the name of that output file. | |
| adjust | optional 2 x 1 vector, multiplicators for the critical values. E.g. adjust=(0.5, 1) give about 5% first kind error, adj=(1, 2.5) give about 1%. Default is (1, 1). For details see Haerdle, Sperlich, Spokoiny (1997). | |
| Output: | ||
| erg | object of string, the table of results | |
| data | data file , containing the wavelet estimates | |
library("gam")
randomize(1234)
n = 100 ; sample size
x = normal(n,3) ; regressor variables
eps = normal(n,1) * sqrt(0.8) ; error term
y = sin(2*x[,1]) + x[,2]^2 + 2*x[,3] +eps ; model
; first component of the model is sin-function
p = 1 ; H_0: first component is linear
erg = wavetest(x,y,p) ; no dis, as dis=0 is already default
erg ; show table of results
Contents of erg [ 1,] " " [ 2,] "-------------------------------------------------------" [ 3,] "no output of function estimates" [ 4,] "-------------------------------------------------------" [ 5,] "HYPOTHESIS: 1.add.component is polynomial of degree 1" [ 6,] "-------------------------------------------------------" [ 7,] "Hypothesis has been rejected at level 0" [ 8,] "-------------------------------------------------------" [ 9,] "highest possible level is 3" [10,] " " [11,] "-------------------------------------------------------" [12,] "-------------------------------------------------------" [13,] " local Test chi-2 like Test " [14,] "- - - - - - - - - - - - - - - - - - - - - - - - - - - -" [15,] "level crit.value test stat. crit.value test stat. " [16,] "-------------------------------------------------------" [17,] " 0 2.74767 4.34917 3.24940 12.66804" [18,] "-------------------------------------------------------" [19,] "-------------------------------------------------------" [20,] " "