minor

Author: lionelvoirol

R/gmwmx2_new.R

@@ -123,7 +123,7 @@ gmwmx2_new_no_missing <- function(X = NULL, y = NULL, model = NULL, omega = NULL
   return(out)
 }
 
-#' Print method for gmwmx2_fit
+#' Print method for a \code{gmwmx2_fit} object
 #'
 #' Displays a table of regression coefficients with standard errors and
 #' summarizes the fitted stochastic model with estimated parameters.

vignettes/estimate_linear_models_with_dependent_errors.Rmd

@@ -68,9 +68,10 @@ linear combination of its elements.
 
 The variance-covariance matrix of the estimated regression parameters
 $\hat{\boldsymbol{\beta}}$ is then obtained as:
+
 \begin{equation}
-(\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T {\boldsymbol{\Sigma}}(\hat{\boldsymbol{\gamma}})  \mathbf{X} (\mathbf{X}^T \mathbf{X})^{-1} 
-\end{equation}.
+(\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T {\boldsymbol{\Sigma}}(\hat{\boldsymbol{\gamma}})  \mathbf{X} (\mathbf{X}^T \mathbf{X})^{-1}.
+\end{equation}
 
 This vignette is a detailed, self-contained simulation walkthrough that showcases
 `gmwmx2_new()` for an arbitrary design matrix `X` and response vector `y`. We build the

vignettes/estimate_linear_models_with_dependent_errors_and_missing_observations.Rmd

@@ -18,31 +18,36 @@ the presence of missing observations. Consider the model defined as:
 Missingness is modeled by a binary process \(\mathbf{Z} \in \{0,1\}^n\) with
 \(Z_i = 1\) indicating an observation and \(Z_i = 0\) a missing observation. The missingness process is independent of
 $\mathbf{Y}$ and follows the definition:
+
 \begin{equation}
   Z_i =
 \begin{cases}
     Z_{i-1}, & \text{with probability } \rho, \\
     W_i \sim \mathrm{Bernoulli}(\mu(\bm{\vartheta})), & \text{with probability } 1-\rho,
 \end{cases}
 \end{equation}
+
 with expectation $\mu(\boldsymbol{\vartheta}) = \mathbb{E}[Z_i] \in (0, 1]$ for
 all $i \in \{1, \ldots, n\}$, with covariance matrix
 $\boldsymbol{\Lambda}(\boldsymbol{\vartheta}) = \operatorname{var}\left(\mathbf{Z}\right)
 \in \mathbb{R}^{n\times n}$ whose structure is assumed known up to the
 parameter vector $\boldsymbol{\vartheta} \in \boldsymbol{\Upsilon} \subset \mathbb{R}^k$.
 The observed series is
+
 \[
   \tilde{\mathbf{Y}} = \mathbf{Y} \odot \mathbf{Z}.
 \]
 
 The design matrix with rows zeroed out for missing observations
 can be written as \(\tilde{\mathbf{X}} = \left(\mathbf{Z} \otimes \mathbf{1}^T\right) \odot \mathbf{X}\).
 The least‑squares estimator based on observed data is
+
 \[
   \hat{\boldsymbol{\beta}} =
   \left(\tilde{\mathbf{X}}^T \tilde{\mathbf{X}}\right)^{-1}\tilde{\mathbf{X}}^T \tilde{\mathbf{Y}},
 \]
 and we compute residuals
+
 \(\hat{\boldsymbol{\varepsilon}} = \tilde{\mathbf{Y}} - \tilde{\mathbf{X}}\hat{\boldsymbol{\beta}}\).
 
 We then estimate the parameters of the missingness process via maximum
@@ -66,7 +71,7 @@ $\hat{\boldsymbol{\beta}}$ is then obtained as:
 \begin{equation}
 \mu(\hat{\boldsymbol{\vartheta}})^{-2}(\mathbf{X}^{T}\mathbf{X})^{-1}
 \mathbf{X}^{T} \boldsymbol{\Sigma}(\hat{\boldsymbol{\gamma}}, \hat{\boldsymbol{\vartheta}})
-\mathbf{X} (\mathbf{X}^{T}\mathbf{X})^{-1}
+\mathbf{X} (\mathbf{X}^{T}\mathbf{X})^{-1}.
 \end{equation}