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Fix typo
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chikuang committed May 16, 2024
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5 changes: 4 additions & 1 deletion README.Rmd
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Expand Up @@ -7,6 +7,8 @@ date: "*`r format(Sys.time(), '%B %d, %Y')`*"
output: github_document
---

\newcommand{\cov}{\mathbb{c}cov}

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
Expand Down Expand Up @@ -48,7 +50,8 @@ $\mathbf{\theta} \in \mathbb{R}^q$ is the unknown regression parameter vector,
response function $\eta(\mathbf{x}_i, \mathbf{\theta})$ can be a linear or nonlinear
function of $\mathbf{\theta}$, and the errors $\epsilon_i$ are assumed to be uncorrelated with mean zero and finite variance $\sigma^2$.

Let $\hat{\mathbf{\theta}}$ be an estimator of $\mathbf{\theta}$, such as the least squares estimator. Various optimal designs are defined by minimizing $\phi\left\( \mathbb{c}ov(\hat{\mathbf{\theta}}) \right\)$ over the design points
Let $\hat{\mathbf{\theta}}$ be an estimator of $\mathbf{\theta}$, such as the least squares estimator. Various optimal designs are defined by minimizing $\phi \left( \mathbb{c}ov(\hat{\mathbf{\theta}}) \right)$
over the design points
$\mathbf{x}_1, \ldots, \mathbf{x}_n$, where function $\phi(\cdot)$ can be determinant, trace, or other scalar functions. The resulting designs are called optimal exact designs (OEDs), which depend on the response function $\eta(\cdot,\cdot)$, the design space $S$, the estimator $\hat{\mathbf{\theta}}$, the scalar function $\phi(\cdot)$, and the number of points $n$.

Second order least-squares estimator is defined as
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4 changes: 2 additions & 2 deletions README.md
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@@ -1,4 +1,4 @@
SLSEDesign:Optimal designs using the second-order Least squares
SLSEDesign: Optimal designs using the second-order Least squares
estimator
================
*Chi-Kuang Yeh, Julie Zhou*
Expand Down Expand Up @@ -49,7 +49,7 @@ to be uncorrelated with mean zero and finite variance $\sigma^2$.

Let $\hat{\mathbf{\theta}}$ be an estimator of $\mathbf{\theta}$, such
as the least squares estimator. Various optimal designs are defined by
minimizing $\phi\left\( \mathbb{c}ov(\hat{\mathbf{\theta}}) \right\)$
minimizing $\phi \left( \mathbb{c}ov(\hat{\mathbf{\theta}}) \right)$
over the design points $\mathbf{x}_1, \ldots, \mathbf{x}_n$, where
function $\phi(\cdot)$ can be determinant, trace, or other scalar
functions. The resulting designs are called optimal exact designs
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