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I believe I have a very simple problem with missing data, but I'm a bit lost because all the materials I read seem to be focused on much more complicated cases.

I have a random variable $X$ which has a Binomial distribution with parameters $n$ and $p$ (i.e., $X\sim B(n,p)$), where $p$ is unknown ($n$ is known). I have $K$ independent samples of $X$, let them be $X_1,\dotsc,X_K$ but some of them are missing, in the sense that I observe the values $R_iX_i$, where $R_i\in\{0,1\}$. I know that $R_i = 0$ when $X_i< C$, for some known constant $C$, otherwise $R_i=1$. This means that my missing data are MNAR (Missing Not At Random), but I know the "mechanism" leading to their being missing, which I believe is what makes my case easier.

How can I estimate $p$? I'm also interested in finding a confidence interval for $p$.

References and links are much appreciated.

Thanks in advance.

I believe I have a very simple problem with missing data, but I'm a bit lost because all the materials I read seem to be focused on much more complicated cases.

I have a random variable $X$ which has a Binomial distribution with parameters $n$ and $p$ (i.e., $X\sim B(n,p)$), where $p$ is unknown ($n$ is known). I have $K$ independent samples of $X$, let them be $X_1,\dotsc,X_K$ but some of them are missing, in the sense that I observe the values $R_iX_i$, where $R_i\in\{0,1\}$. I know that $R_i = 0$ when $X_i< C$, for some known constant $C$, otherwise $R_i=1$. This means that my missing data are MNAR (Missing Not At Random), but I know the "mechanism" leading to their being missing, which I believe is what makes my case easier.

Edit: it's a case of left-censoring with Binomial data.

How can I estimate $p$? I'm also interested in finding a confidence interval for $p$.

References and links are much appreciated.

Thanks in advance.

I believe I have a very simple problem with missing data, but I'm a bit lost because all the materials I read seem to be focused on much more complicated cases.

I have a random variable $X$ which has a Binomial distribution with parameters $n$ and $p$ (i.e., $X\sim B(n,p)$), where $p$ is unknown ($n$ is known). I have $K$ samples of $X$, let them be $X_1,\dotsc,X_K$ but some of them are missing, in the sense that I observe the values $R_iX_i$, where $R_i\in\{0,1\}$. I know that $R_i = 0$ when $X_i< C$, for some known constant $C$, otherwise $R_i=1$. This means that my missing data are MNAR (Missing Not At Random), but I know the "mechanism" leading to their being missing, which I believe is what makes my case easier.

How can I estimate $p$? I'm also interested in finding a confidence interval for $p$.

References and links are much appreciated.

Thanks in advance.

I believe I have a very simple problem with missing data, but I'm a bit lost because all the materials I read seem to be focused on much more complicated cases.

I have a random variable $X$ which has a Binomial distribution with parameters $n$ and $p$ (i.e., $X\sim B(n,p)$), where $p$ is unknown ($n$ is known). I have $K$ independent samples of $X$, let them be $X_1,\dotsc,X_K$ but some of them are missing, in the sense that I observe the values $R_iX_i$, where $R_i\in\{0,1\}$. I know that $R_i = 0$ when $X_i< C$, for some known constant $C$, otherwise $R_i=1$. This means that my missing data are MNAR (Missing Not At Random), but I know the "mechanism" leading to their being missing, which I believe is what makes my case easier.

How can I estimate $p$? I'm also interested in finding a confidence interval for $p$.

References and links are much appreciated.

Thanks in advance.