* using log directory 'd:/Rcompile/CRANpkg/local/4.6/ddst.Rcheck' * using R version 4.6.1 (2026-06-24 ucrt) * using platform: x86_64-w64-mingw32 * R was compiled by gcc.exe (GCC) 14.3.0 GNU Fortran (GCC) 14.3.0 * running under: Windows Server 2022 x64 (build 20348) * using session charset: UTF-8 * current time: 2026-08-12 22:22:04 UTC * checking for file 'ddst/DESCRIPTION' ... OK * checking extension type ... Package * this is package 'ddst' version '1.4' * checking package namespace information ... OK * checking package dependencies ... OK * checking if this is a source package ... OK * checking if there is a namespace ... OK * checking for hidden files and directories ... OK * checking for portable file names ... OK * checking whether package 'ddst' can be installed ... OK * checking installed package size ... OK * checking package directory ... OK * checking DESCRIPTION meta-information ... OK * checking top-level files ... OK * checking for left-over files ... OK * checking index information ... OK * checking package subdirectories ... OK * checking code files for non-ASCII characters ... OK * checking R files for syntax errors ... OK * checking whether the package can be loaded ... [0s] OK * checking whether the package can be loaded with stated dependencies ... [0s] OK * checking whether the package can be unloaded cleanly ... [0s] OK * checking whether the namespace can be loaded with stated dependencies ... [0s] OK * checking whether the namespace can be unloaded cleanly ... [0s] OK * checking loading without being on the library search path ... [0s] OK * checking use of S3 registration ... OK * checking dependencies in R code ... OK * checking S3 generic/method consistency ... OK * checking replacement functions ... OK * checking foreign function calls ... OK * checking R code for possible problems ... [3s] OK * checking Rd files ... [1s] NOTE checkRd: (-1) ddst-package.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$W_k=[1/sqrt(n) sum_{i=1}^n l(Z_i)]I^{-1}[1/sqrt(n) sum_{i=1}^n l(Z_i)]'$}, | ^ checkRd: (-1) ddst-package.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$W_k=[1/sqrt(n) sum_{i=1}^n l(Z_i)]I^{-1}[1/sqrt(n) sum_{i=1}^n l(Z_i)]'$}, | ^ checkRd: (-1) ddst-package.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$W_k=[1/sqrt(n) sum_{i=1}^n l(Z_i)]I^{-1}[1/sqrt(n) sum_{i=1}^n l(Z_i)]'$}, | ^ checkRd: (-1) ddst-package.Rd:31: Lost braces; missing escapes or markup? 31 | where \emph{$l(Z_i)$}, i=1,...,n, is \emph{k}-dimensional (row) score vector, the symbol \emph{'} denotes transposition while \emph{$I=Cov_{theta_0}[l(Z_1)]'[l(Z_1)]$}. Following Neyman's idea of modelling underlying distributions one gets \emph{$l(Z_i)=(phi_1(F(Z_i)),...,phi_k(F(Z_i)))$} and \emph{I} being the identity matrix, where \emph{$phi_j$}'s, j >= 1, are zero mean orthonormal functions on [0,1], while \emph{F} is the completely specified null distribution function. | ^ checkRd: (-1) ddst-package.Rd:35: Lost braces; missing escapes or markup? 35 | \emph{$W_k^{*}(tilde gamma)=[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)][I^*(tilde gamma)]^{-1}[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)]'$}, | ^ checkRd: (-1) ddst-package.Rd:35: Lost braces; missing escapes or markup? 35 | \emph{$W_k^{*}(tilde gamma)=[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)][I^*(tilde gamma)]^{-1}[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)]'$}, | ^ checkRd: (-1) ddst-package.Rd:35: Lost braces; missing escapes or markup? 35 | \emph{$W_k^{*}(tilde gamma)=[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)][I^*(tilde gamma)]^{-1}[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)]'$}, | ^ checkRd: (-1) ddst-package.Rd:35: Lost braces; missing escapes or markup? 35 | \emph{$W_k^{*}(tilde gamma)=[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)][I^*(tilde gamma)]^{-1}[1/sqrt(n) sum_{i=1}^n l^*(Z_i;tilde gamma)]'$}, | ^ checkRd: (-1) ddst-package.Rd:36: Lost braces; missing escapes or markup? 36 | where \emph{$tilde gamma$} is an appropriate estimator of \emph{$gamma$} while \emph{$I^*(gamma)=Cov_{theta_0}[l^*(Z_1;gamma)]'[l^*(Z_1;gamma)]$}. More details can be found in Janic and Ledwina (2008), Kallenberg and Ledwina (1997 a,b) as well as Inglot and Ledwina (2006 a,b). | ^ checkRd: (-1) ddst-package.Rd:40: Lost braces 40 | \emph{$T = min{1 <= k <= d: W_k-pi(k,n,c) >= W_j-pi(j,n,c), j=1,...,d}$} | ^ checkRd: (-1) ddst-package.Rd:45: Lost braces 45 | $T^* = min{1 <= k <= d: W_k^*(tilde gamma)-pi^*(k,n,c) >= W_j^*(tilde gamma)-pi^*(j,n,c), j=1,...,d}$}. | ^ checkRd: (-1) ddst-package.Rd:49: Lost braces 49 | \emph{$pi(j,n,c)={jlog n, if max{1 <= k <= d}|Y_k| <= sqrt(c log(n)), 2j, if max{1 <= k <= d}|Y_k|>sqrt(c log(n)). }$} | ^ checkRd: (-1) ddst-package.Rd:49: Lost braces 49 | \emph{$pi(j,n,c)={jlog n, if max{1 <= k <= d}|Y_k| <= sqrt(c log(n)), 2j, if max{1 <= k <= d}|Y_k|>sqrt(c log(n)). }$} | ^ checkRd: (-1) ddst-package.Rd:49: Lost braces 49 | \emph{$pi(j,n,c)={jlog n, if max{1 <= k <= d}|Y_k| <= sqrt(c log(n)), 2j, if max{1 <= k <= d}|Y_k|>sqrt(c log(n)). }$} | ^ checkRd: (-1) ddst-package.Rd:54: Lost braces 54 | $pi^*(j,n,c)={jlog n, if max{1 <= k <= d}|Y_k^*| <= sqrt(c log(n)),2j if max(1 <= k <= d)|Y_k^*| > sqrt(c log(n))}$}. | ^ checkRd: (-1) ddst-package.Rd:54: Lost braces 54 | $pi^*(j,n,c)={jlog n, if max{1 <= k <= d}|Y_k^*| <= sqrt(c log(n)),2j if max(1 <= k <= d)|Y_k^*| > sqrt(c log(n))}$}. | ^ checkRd: (-1) ddst-package.Rd:58: Lost braces; missing escapes or markup? 58 | \emph{$(Y_1,...,Y_k)=[1/sqrt(n) sum_{i=1}^n l(Z_i)]I^{-1/2}$} | ^ checkRd: (-1) ddst-package.Rd:58: Lost braces; missing escapes or markup? 58 | \emph{$(Y_1,...,Y_k)=[1/sqrt(n) sum_{i=1}^n l(Z_i)]I^{-1/2}$} | ^ checkRd: (-1) ddst-package.Rd:62: Lost braces; missing escapes or markup? 62 | \emph{$(Y_1^*,...,Y_k^*)=[1/sqrt(n) sum_{i=1}^n l^*(Z_i; tilde gamma)][I^*(tilde gamma)]^{-1/2}$}. | ^ checkRd: (-1) ddst-package.Rd:62: Lost braces; missing escapes or markup? 62 | \emph{$(Y_1^*,...,Y_k^*)=[1/sqrt(n) sum_{i=1}^n l^*(Z_i; tilde gamma)][I^*(tilde gamma)]^{-1/2}$}. | ^ checkRd: (-1) ddst-package.Rd:65: Lost braces; missing escapes or markup? 65 | and \emph{$W_{T^*} = W_{T^*}(tilde gamma)$}, respectively. For details see Inglot and Ledwina (2006 a,b,c). | ^ checkRd: (-1) ddst-package.Rd:65: Lost braces; missing escapes or markup? 65 | and \emph{$W_{T^*} = W_{T^*}(tilde gamma)$}, respectively. For details see Inglot and Ledwina (2006 a,b,c). | ^ checkRd: (-1) ddst-package.Rd:67: Lost braces; missing escapes or markup? 67 | The choice of \emph{c} in \emph{T} and \emph{$T^*$} is decisive to finite sample behaviour of the selection rules and pertaining statistics \emph{$W_T$} and \emph{$W_{T^*}(tilde gamma)$}. In particular, under large \emph{c}'s the rules behave similarly as Schwarz's (1978) BIC while for \emph{c=0} they mimic Akaike's (1973) AIC. For moderate sample sizes, values \emph{c in (2,2.5)} guarantee, under `smooth' departures, only slightly smaller power as in case BIC were used and simultaneously give much higher power than BIC under multimodal alternatives. In genral, large \emph{c's} are recommended if changes in location, scale, skewness and kurtosis are in principle aimed to be detected. For evidence and discussion see Inglot and Ledwina (2006 c). | ^ checkRd: (-1) ddst-package.Rd:69: Lost braces; missing escapes or markup? 69 | It \emph{c>0} then the limiting null distribution of \emph{$W_T$} and \emph{$W_{T^*}(tilde gamma)$} is central chi-squared with one degree of freedom. In our implementation, for given \emph{n}, both critical values and \emph{p}-values are computed by MC method. | ^ checkRd: (-1) ddst-package.Rd:71: Lost braces; missing escapes or markup? 71 | Empirical distributions of \emph{T} and \emph{$T^*$} as well as \emph{$W_T$} and \emph{$W_{T^*}(tilde gamma)$} are not essentially influenced by the choice of reasonably large \emph{d}'s, provided that sample size is at least moderate. | ^ checkRd: (-1) ddst.exp.test.Rd:27: Lost braces; missing escapes or markup? 27 | Modelling alternatives similarly as in Kallenberg and Ledwina (1997 a,b), e.g., and estimating \emph{$gamma$} by \emph{$tilde gamma= 1/n sum_{i=1}^n Z_i$} yields the efficient score | ^ checkRd: (-1) ddst.exp.test.Rd:30: Lost braces; missing escapes or markup? 30 | The matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and computed in a numerical way in case of cosine basis. In the implementation the default value of \emph{c} in \emph{$T^*$} is set to be 100. | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:29: Lost braces; missing escapes or markup? 29 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=-1/n sum_{i=1}^n Z_i + varepsilon G$}, where \emph{$varepsilon approx 0.577216 $} is the Euler constant and \emph{$ G = tilde gamma_2 = [n(n-1) ln2]^{-1}sum_{1<= j < i <= n}(Z_{n:i}^o - Z_{n:j}^o) $} while \emph{$Z_{n:1}^o <= ... <= Z_{n:n}^o$} | ^ checkRd: (-1) ddst.extr.test.Rd:33: Lost braces; missing escapes or markup? 33 | The related matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and numerical methods for cosine functions. In the implementation the default value of \emph{c} in \emph{$T^*$} was fixed to be 100. Hence, \emph{$T^*$} is Schwarz-type model selection rule. The resulting data driven test statistic for extreme value distribution is \emph{$W_{T^*}=W_{T^*}(tilde gamma)$}. | ^ checkRd: (-1) ddst.extr.test.Rd:33: Lost braces; missing escapes or markup? 33 | The related matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and numerical methods for cosine functions. In the implementation the default value of \emph{c} in \emph{$T^*$} was fixed to be 100. Hence, \emph{$T^*$} is Schwarz-type model selection rule. The resulting data driven test statistic for extreme value distribution is \emph{$W_{T^*}=W_{T^*}(tilde gamma)$}. | ^ checkRd: (-1) ddst.extr.test.Rd:33: Lost braces; missing escapes or markup? 33 | The related matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and numerical methods for cosine functions. In the implementation the default value of \emph{c} in \emph{$T^*$} was fixed to be 100. Hence, \emph{$T^*$} is Schwarz-type model selection rule. The resulting data driven test statistic for extreme value distribution is \emph{$W_{T^*}=W_{T^*}(tilde gamma)$}. | ^ checkRd: (-1) ddst.norm.test.Rd:30: Lost braces; missing escapes or markup? 30 | \emph{$gamma=(gamma_1,gamma_2)$} is estimated by \emph{$tilde gamma=(tilde gamma_1,tilde gamma_2)$}, where \emph{$tilde gamma_1=1/n sum_{i=1}^n Z_i$} and | ^ checkRd: (-1) ddst.norm.test.Rd:31: Lost braces; missing escapes or markup? 31 | \emph{$tilde gamma_2 = 1/(n-1) sum_{i=1}^{n-1}(Z_{n:i+1}-Z_{n:i})(H_{i+1}-H_i)$}, | ^ checkRd: (-1) ddst.norm.test.Rd:31: Lost braces; missing escapes or markup? 31 | \emph{$tilde gamma_2 = 1/(n-1) sum_{i=1}^{n-1}(Z_{n:i+1}-Z_{n:i})(H_{i+1}-H_i)$}, | ^ checkRd: (-1) ddst.norm.test.Rd:31: Lost braces; missing escapes or markup? 31 | \emph{$tilde gamma_2 = 1/(n-1) sum_{i=1}^{n-1}(Z_{n:i+1}-Z_{n:i})(H_{i+1}-H_i)$}, | ^ checkRd: (-1) ddst.norm.test.Rd:31: Lost braces; missing escapes or markup? 31 | \emph{$tilde gamma_2 = 1/(n-1) sum_{i=1}^{n-1}(Z_{n:i+1}-Z_{n:i})(H_{i+1}-H_i)$}, | ^ checkRd: (-1) ddst.norm.test.Rd:31: Lost braces; missing escapes or markup? 31 | \emph{$tilde gamma_2 = 1/(n-1) sum_{i=1}^{n-1}(Z_{n:i+1}-Z_{n:i})(H_{i+1}-H_i)$}, | ^ checkRd: (-1) ddst.norm.test.Rd:32: Lost braces; missing escapes or markup? 32 | while \emph{$Z_{n:1}<= ... <= Z_{n:n}$} are ordered values of \emph{$Z_1, ..., Z_n$} and \emph{$H_i= phi^{-1}((i-3/8)(n+1/4))$}, cf. Chen and Shapiro (1995). | ^ checkRd: (-1) ddst.norm.test.Rd:32: Lost braces; missing escapes or markup? 32 | while \emph{$Z_{n:1}<= ... <= Z_{n:n}$} are ordered values of \emph{$Z_1, ..., Z_n$} and \emph{$H_i= phi^{-1}((i-3/8)(n+1/4))$}, cf. Chen and Shapiro (1995). | ^ checkRd: (-1) ddst.norm.test.Rd:32: Lost braces; missing escapes or markup? 32 | while \emph{$Z_{n:1}<= ... <= Z_{n:n}$} are ordered values of \emph{$Z_1, ..., Z_n$} and \emph{$H_i= phi^{-1}((i-3/8)(n+1/4))$}, cf. Chen and Shapiro (1995). | ^ checkRd: (-1) ddst.norm.test.Rd:35: Lost braces; missing escapes or markup? 35 | The pertaining matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and is computed in a numerical way in case of cosine basis. In the implementation of \emph{$T^*$} the default value of \emph{c} is set to be 100. Therefore, in practice, \emph{$T^*$} is Schwarz-type criterion. See Inglot and Ledwina (2006) as well as Janic and Ledwina (2008) for comments. The resulting data driven test statistic for normality is \emph{$W_{T^*}=W_{T^*}(tilde gamma)$}. | ^ checkRd: (-1) ddst.norm.test.Rd:35: Lost braces; missing escapes or markup? 35 | The pertaining matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and is computed in a numerical way in case of cosine basis. In the implementation of \emph{$T^*$} the default value of \emph{c} is set to be 100. Therefore, in practice, \emph{$T^*$} is Schwarz-type criterion. See Inglot and Ledwina (2006) as well as Janic and Ledwina (2008) for comments. The resulting data driven test statistic for normality is \emph{$W_{T^*}=W_{T^*}(tilde gamma)$}. | ^ checkRd: (-1) ddst.norm.test.Rd:35: Lost braces; missing escapes or markup? 35 | The pertaining matrix \emph{$[I^*(tilde gamma)]^{-1}$} does not depend on \emph{$tilde gamma$} and is calculated for succeding dimensions \emph{k} using some recurrent relations for Legendre's polynomials and is computed in a numerical way in case of cosine basis. In the implementation of \emph{$T^*$} the default value of \emph{c} is set to be 100. Therefore, in practice, \emph{$T^*$} is Schwarz-type criterion. See Inglot and Ledwina (2006) as well as Janic and Ledwina (2008) for comments. The resulting data driven test statistic for normality is \emph{$W_{T^*}=W_{T^*}(tilde gamma)$}. | ^ checkRd: (-1) ddst.uniform.test.Rd:25: Lost braces; missing escapes or markup? 25 | $W_k=[1/sqrt(n) sum_{j=1}^k sum_{i=1}^n phi_j(Z_i)]^2$}, | ^ checkRd: (-1) ddst.uniform.test.Rd:25: Lost braces; missing escapes or markup? 25 | $W_k=[1/sqrt(n) sum_{j=1}^k sum_{i=1}^n phi_j(Z_i)]^2$}, | ^ * checking Rd metadata ... OK * checking Rd cross-references ... OK * checking for missing documentation entries ... OK * checking for code/documentation mismatches ... OK * checking Rd \usage sections ... OK * checking Rd contents ... OK * checking for unstated dependencies in examples ... OK * checking examples ... [4s] OK * checking PDF version of manual ... [24s] OK * checking HTML version of manual ... [2s] OK * DONE Status: 1 NOTE Check process probably crashed or hung up for 20 minutes ... killed Most likely this happened in the example checks (?), if not, ignore the following last lines of example output: > # H0 is false > z = rbeta(80,4,2) > (t = ddst.uniform.test(z, compute.p=TRUE)) Data Driven Smooth Test for Uniformity data: z, base: ddst.base.legendre c: 2.4 WT = 58.513, n. coord = 4, p-value < 2.2e-16 > t$p.value [1] 0 > > > > > ### *