R Under development (unstable) (2024-07-29 r86934 ucrt) -- "Unsuffered Consequences"
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> library(longmemo)
> 
> options(digits = 5) # since we want to "R CMD Rdiff" the output
> data(NileMin)
> fF <- FEXPest(NileMin, order.poly=3, pvalmax= .5, verbose=TRUE)
glm() [0]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   6.6596     0.0544     122   <2e-16 ***
xlong        -0.8109     0.0625     -13   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.98001)

    Null deviance: 713.99  on 330  degrees of freedom
Residual deviance: 394.88  on 329  degrees of freedom
AIC: 5076

Number of Fisher Scoring iterations: 6

   P-val[eta]: <2e-16
glm() [1]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   6.7895     0.1784   38.06  < 2e-16 ***
xlong        -0.7436     0.1128   -6.59  1.7e-10 ***
ffr          -0.0836     0.1085   -0.77     0.44    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.99118)

    Null deviance: 713.99  on 330  degrees of freedom
Residual deviance: 394.27  on 328  degrees of freedom
AIC: 5077

Number of Fisher Scoring iterations: 6

   P-val[eta]: 1.73e-10, 0.442
glm() [2]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)      6.657      0.055  120.97  < 2e-16 ***
xlong           -0.910      0.193   -4.72  3.6e-06 ***
poly(ffr, j)1    0.861      2.730    0.32     0.75    
poly(ffr, j)2   -1.958      1.703   -1.15     0.25    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 1.0013)

    Null deviance: 713.99  on 330  degrees of freedom
Residual deviance: 392.85  on 327  degrees of freedom
AIC: 5078

Number of Fisher Scoring iterations: 6

   P-val[eta]: 3.56e-06, 0.753, 0.251
> fF
'FEXP' estimator, call:  FEXPest(x = NileMin, order.poly = 3, pvalmax = 0.5, verbose = TRUE) 
 polynomial order 1 - selected by stopping early (P = 0.753 > pvalmax); H = 0.87178
 coefficients 'theta' =
             Estimate Std. Error t value  Pr(>|t|)
(Intercept)  6.789501   0.178383 38.0614 < 2.2e-16
1 - 2*H     -0.743568   0.112790 -6.5925 1.729e-10
ffr         -0.083562   0.108507 -0.7701    0.4418
  ==>            H = 0.87  (0.06) 
 <==> d := H - 1/2 = 0.37  (0.06) 

 $ early.stop: logi TRUE
 $ maxPv     : num 0.753
 $ yper      : num [1:331] 56564 5379 52555 1098 2916 ...
 $ spec      : num [1:331] 28365 16928 12512 10095 8545 ...
> plot(fF)
> 
> data(videoVBR)
> for(max.poly in 0:2) {
+     cat("-------------------------------------------\n",
+         "max.poly= ", max.poly,":\n------------\n",sep='')
+     fv <- FEXPest(videoVBR, order.poly=max.poly, pvalmax= .5, verbose=TRUE)
+     print(fv["H"])
+ }
-------------------------------------------
max.poly= 0:
------------
glm() [0]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.9654     0.0534    74.2   <2e-16 ***
xlong        -2.6269     0.0607   -43.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 1.4247)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  701.23  on 497  degrees of freedom
AIC: 4943

Number of Fisher Scoring iterations: 11

   P-val[eta]: <2e-16
used full 'order.poly'
$H
[1] 1.8135

-------------------------------------------
max.poly= 1:
------------
glm() [0]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.9654     0.0534    74.2   <2e-16 ***
xlong        -2.6269     0.0607   -43.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 1.4247)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  701.23  on 497  degrees of freedom
AIC: 4943

Number of Fisher Scoring iterations: 11

   P-val[eta]: <2e-16
glm() [1]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   5.6377     0.1434    39.3   <2e-16 ***
xlong        -1.3650     0.0895   -15.2   <2e-16 ***
ffr          -1.1554     0.0871   -13.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.97997)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  566.85  on 496  degrees of freedom
AIC: 4819

Number of Fisher Scoring iterations: 8

   P-val[eta]: <2e-16, <2e-16
used full 'order.poly'
$H
[1] 1.1825

-------------------------------------------
max.poly= 2:
------------
glm() [0]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.9654     0.0534    74.2   <2e-16 ***
xlong        -2.6269     0.0607   -43.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 1.4247)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  701.23  on 497  degrees of freedom
AIC: 4943

Number of Fisher Scoring iterations: 11

   P-val[eta]: <2e-16
glm() [1]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   5.6377     0.1434    39.3   <2e-16 ***
xlong        -1.3650     0.0895   -15.2   <2e-16 ***
ffr          -1.1554     0.0871   -13.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.97997)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  566.85  on 496  degrees of freedom
AIC: 4819

Number of Fisher Scoring iterations: 8

   P-val[eta]: <2e-16, <2e-16
glm() [2]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)      3.799      0.044   86.37  < 2e-16 ***
xlong           -0.713      0.149   -4.79  2.2e-06 ***
poly(ffr, j)1  -33.864      2.610  -12.97  < 2e-16 ***
poly(ffr, j)2    8.177      1.644    4.97  9.1e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.96466)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  546.61  on 495  degrees of freedom
AIC: 4800

Number of Fisher Scoring iterations: 7

   P-val[eta]: 2.18e-06, < 2e-16, 9.10e-07
used full 'order.poly'
$H
[1] 0.85633

> max.poly <- 3
> cat("-------------------------------------------\n",
+     "max.poly= ", max.poly,":\n------------\n",sep='')
-------------------------------------------
max.poly= 3:
------------
> ## IGNORE_RDIFF_BEGIN
> (fv <- FEXPest(videoVBR, order.poly=max.poly, pvalmax= .5, verbose=TRUE))
glm() [0]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.9654     0.0534    74.2   <2e-16 ***
xlong        -2.6269     0.0607   -43.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 1.4247)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  701.23  on 497  degrees of freedom
AIC: 4943

Number of Fisher Scoring iterations: 11

   P-val[eta]: <2e-16
glm() [1]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   5.6377     0.1434    39.3   <2e-16 ***
xlong        -1.3650     0.0895   -15.2   <2e-16 ***
ffr          -1.1554     0.0871   -13.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.97997)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  566.85  on 496  degrees of freedom
AIC: 4819

Number of Fisher Scoring iterations: 8

   P-val[eta]: <2e-16, <2e-16
glm() [2]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)      3.799      0.044   86.37  < 2e-16 ***
xlong           -0.713      0.149   -4.79  2.2e-06 ***
poly(ffr, j)1  -33.864      2.610  -12.97  < 2e-16 ***
poly(ffr, j)2    8.177      1.644    4.97  9.1e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.96466)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  546.61  on 495  degrees of freedom
AIC: 4800

Number of Fisher Scoring iterations: 7

   P-val[eta]: 2.18e-06, < 2e-16, 9.10e-07
glm() [3]:

Call:
glm(formula = frml, family = Gamma(link = "log"))

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     3.79852    0.04403   86.27  < 2e-16 ***
xlong          -0.71379    0.20852   -3.42  0.00067 ***
poly(ffr, j)1 -33.84546    3.53106   -9.59  < 2e-16 ***
poly(ffr, j)2   8.16767    2.09431    3.90  0.00011 ***
poly(ffr, j)3   0.00946    1.37726    0.01  0.99452    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for Gamma family taken to be 0.96664)

    Null deviance: 3280.63  on 498  degrees of freedom
Residual deviance:  546.61  on 494  degrees of freedom
AIC: 4802

Number of Fisher Scoring iterations: 7

   P-val[eta]: 0.00067, < 2e-16, 0.00011, 0.99452
'FEXP' estimator, call:  FEXPest(x = videoVBR, order.poly = max.poly, pvalmax = 0.5, verbose = TRUE) 
 polynomial order 2 - selected by stopping early (P = 0.995 > pvalmax); H = 0.85633
 coefficients 'theta' =
                Estimate Std. Error  t value  Pr(>|t|)
(Intercept)     3.798516   0.043978  86.3733 < 2.2e-16
1 - 2*H        -0.712654   0.148702  -4.7925 2.181e-06
poly(ffr, j)1 -33.864487   2.610367 -12.9731 < 2.2e-16
poly(ffr, j)2   8.177403   1.644290   4.9732 9.096e-07
  ==>            H = 0.86  (0.07) 
 <==> d := H - 1/2 = 0.36  (0.07) 

 $ early.stop: logi TRUE
 $ maxPv     : num 0.995
 $ yper      : num [1:499] 5145 22812 40031 7476 33737 ...
 $ spec      : num [1:499] 51315 30682 22521 17979 15029 ...
> ## IGNORE_RDIFF_END
> plot(fv, type = "o", cex = 0.5)
> 
> cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''
Time elapsed:  0.45 0.09 0.51 NA NA 
> 
> proc.time()
   user  system elapsed 
   0.45    0.09    0.51