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seen Oct 17 at 9:58

Oct
17
awarded  Commentator
Oct
17
comment Conditions on ratio of $\frac{\sigma_{BIB}^2}{\sigma_{RB}^2}$
What do $Var_{RB}(\hat{\alpha}_i)$, $Var_{RB}(\hat{\alpha}_j)$, $Var_{BIB}(\hat{\alpha}_i)$ and $Var_{BIB}(\hat{\alpha}_j)$ equal?
Oct
9
comment Identifiability in linear regression and time series
Thus with X1 as the estimator, we cannot take a higher sample size to be sure we will estimate something close to the truth (given one sample of data), but for the mean of the normally distributed variables we can (this estimator is unbiased and consistent). Thus consistency is more "useful" when we want to be sure we are close to the truth for single dataset (albeit usually with a large sample size needed). Finally it is well known an estimator cannot be consistent if the model is not identifiable. Thus identifiability is required for a model if we want any estimator to be consistent.
Oct
9
comment Identifiability in linear regression and time series
Sorry @vman049 for not replying sooner. It is easier to think first of unbiasedness and consistency which relate to the expected value the estimator is close to the true value and the probability an estimator is close to the true value. You can have one without the other (see stats.stackexchange.com/questions/31036/…). Using the "unbiased not consistent" example in the first answer, we see the prob X1 is close to mu never gets closeer to 1 as n gets larger (it does not depend on n), even though it is unbiased.
Oct
3
comment Identifiability in linear regression and time series
Finally the first model is guaranteed to be identifiable if the minimum number of hyperplanes the covariate points lie on is 2 or greater - see Hennig Theorem 2.2.
Oct
3
comment Identifiability in linear regression and time series
Formally all of the covariate pairs $(x_{1},x_{2})$ lie on a 1-dimensional hyperplane (i.e. a line) in $\mathbb{R}^{3}$, and generally this model would not be identifiable if all your $n$ covariate points $(x_{1},...,x_{p})$ lie on the same $(p-1)$-dimensional hyperplane. Going back to the two column example, if just one of the entries in $\mathbf{x}_{2}$ were not equal to $c$ then this would yield information on the covariate-response relationship, and the model MAY be identifiable. See "Identifiability of Models for Clusterwise Linear Regression", Hennig (2000) for an in-depth look at this.
Oct
3
comment Identifiability in linear regression and time series
The first model would not be identifiable if $\mathbf{X}$ contains say a constant column: if you imagine $\mathbf{X}$ contains a column of 1's ($\mathbf{x_{1}}$ say), and a column ($\mathbf{x_{2}}$) whose entries are all the same (c say). Then if we picture $\mathbf{y},\mathbf{x_{1}}$, and $\mathbf{x_{2}}$ in $\mathbb{R}^{3}$ then all your $n$ triples $(y,x1,x2)=(y,1,c)$ lie on a line parallel to the y-axis regardless of what the $n$ values are for $\mathbf{y}$. Thus no information can be obtained on what happens to $\mathbf{y}$ as $\mathbf{x_{1}}$ and $\mathbf{x_{2}}$ change.
Jul
26
awarded  Scholar
Jul
26
accepted Observed information matrix is a consistent estimator of the expected information matrix?
Jul
25
answered Observed information matrix is a consistent estimator of the expected information matrix?
Jul
25
suggested suggested edit on Observed information matrix is a consistent estimator of the expected information matrix?
Jun
13
comment How to calculate sample size needed for comparing the “change from baseline” scores between two groups?
You are right in that the two groups are probably unrelated and so we can use a T-test for independent samples. If the first group represents baselines measurments and the second post-baselines measurments on the same people then we can use a dependent sample t-test.
Jan
22
comment Contrasts in mixed model
A correction to the above comment: The $L$ vector should sum to $0$, so if you use $L=(3/4,-1/4,-1/4,-1/4)$ then $L\beta=A-(A+B+C+D)/4$ which is group A versus the average of the other four groups.
Jan
22
comment Contrasts in mixed model
I would try $AvsAvg = L = (1,-1/3,-1/3,-1/3)$, so that if $\beta=(A,B,C,D)'$ then $L\beta=A-(B+C+D)/3$ which is the difference of group A versus the average of the other three groups.
Jan
22
answered Contrasts in mixed model
Jan
21
answered How to calculate sample size needed for comparing the “change from baseline” scores between two groups?
Jan
17
awarded  Teacher
Jan
17
answered Sample size calculation for t-test
Jan
14
comment Observed information matrix is a consistent estimator of the expected information matrix?
@Dapz Please accept my sincerest apologies for not replying to you until now - I made the mistake of assuming nobody would answer. Thank-you for your answer below - I have upvoted it since I can see it is most useful, however I need to spend a little time considering it. Thank-you for your time, and I will reply to your post below soon.
Jan
14
awarded  Supporter