# Questions tagged [restrictions]

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### Regression with unrestricted betas

Say for, instance, if I were to regress a unrestricted model such as: $$Y_it=\beta_0+V_{it}(\gamma_0+\gamma_1X_{it})+D\chi_{it}+\epsilon_{it}$$ In which I would be mainly interested in obtaining the ...
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### Multivariate normal distribution - hypothesis testing MLE

Suppose $X_{1}$, $X_{2}$,...,$X_{n}$ are i.i.d. observations from a multivariate normal distribution $N$($\mu$,$\Sigma$) where $\Sigma$ is known. Use the likelihood ratio procedure to produce a test ...
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### Reference Request - Bounded Discrete Multivariate Stochastic Processes

I would like to be referred to papers or textbooks about the dynamics of non-negative discrete stochastic processes under the constraint that all variables sum up to some constant. Appropriate ...
28 views

### Packages interfering with other packages on R? [closed]

I am working on a long R studio script for an experiment (more than 3000 lines) with different kinds of analyses that are not too complicated but combined there a lot of different kinds of analyses ...
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### SUR and cross equation restrictions in SAS

I am estimating a system of three equations using the option SUR in syslin procedure. Code: ...
67 views

### Maximum likelihood estimator when $\sum_{j} \theta_j = 1$. How to impose this condition? [duplicate]

I have a sample $x_1,\dots,x_n \stackrel{iid}{\sim}f(;\boldsymbol{\theta})$, where $\boldsymbol{\theta} = (\theta_1,\dots,\theta_d)$, and , $0<\theta_j<1$, $\sum_{j=1}^d\theta_j = 1$. I can ...
30 views

### Omission of variable in regression model

I am currently solving a question about the omission of variables in a regression model. The question says that $R^2$ decreases after two variables are omitted in the model; I understand this part. ...
207 views

### Significance of correlation with range restriction in x

Background Range restriction can happen in various study designs and it affects the results of bivariate correlation or in multiple regression, for example. In some cases the range restriction may be ...
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### How to find all models that meet the pre-specified restrictions

Let's say I have a large number of predictors (e.g. 2000) and I'm facing the problem of choosing the linear regression model under following assumptions: There are few predictors that have to be ...
52 views

### Hypothesis test testing for monotonic group mean change

I wonder if there is a statistical hypothesis test testing whether group average monotonically increases across groups? For example, I have four treatment groups, A, B, C and D. I would like to test ...
27 views

### How to optimize two related objective functions?

Suppose we have two functions which are somewhat related in that if one increases, the other decreases in a non-linear fashion. The decision variables for one function may or may not be present for ...
48 views

### Restriction in bayesian likelihood expression

I'm doing MCMC simulation but I'm confused in some part of my model. I dont know which of my likelihood expression is right. My model is as following. $\gamma$ = $(\gamma_{1},\cdots,\gamma_{K})$ and ...
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### How to test hypothesis with multiple 'or' restictions

I am seeking help to interpret a question and set up test procedures for a series of hypotheses (six in total, two of which I can answer). It is part of a weekly problem set we are given in class. The ...
46 views