Questions tagged [semiparametric]
Semiparametric probability models are a general class of models used for estimation and inference that contain a nonparametric component and a parametric component.
43 questions
2 votes
0 answers
34 views
Modeling Data Using a Hybrid Parametric and Non-Parametric Approach
I'm trying model a multivariate dataset using a hybrid of a Gaussian process and a parametric model. My dataset is a function of two variables, $m$ and $p$. I expect that the $m$-dependence is well ...
- 121
1 vote
0 answers
35 views
Influence function of expectation of conditional quantile [closed]
I am trying to derive the influence function of the estimand. $$Pr(Y<m) = E(I(Y<m)) = E(E(I(Y<m)|X))$$ where the distribution of Y is depend on the X P(Y) = P(Y|X)P(X) I appreciate your help!
- 11
2 votes
1 answer
577 views
Efficient influence function with interventions that depend on the natural value of the exposure
Figure A1 shows a SWIG with L being a confounder of the association between exposure X and outcome ...
- 926
1 vote
1 answer
134 views
How to generalise non-asymptotic Cramer-Rao lower bound for unbiased estimators in semiparametric models?
We all know the classic Cramer-Rao bound which specifies a lower bound of any unbiased estimator's variance in a parametric model. Note that this bound is non-asymptotic in a sense that it is valid ...
- 11
5 votes
0 answers
59 views
Are these two estimated regression coefficient asymptotically equivalent? If not, which one is more efficient?
Suppose I have $Y=\beta_1X_1+\beta_2X_1X_2+g(X_2)+u$, where $E(u|X_1,X_2)=0$ and $S=g(X_2)+e$ with $E(e|X_2)=0$. I have a random sample $\{Y_i,X_{1i},X_{2i},S_i\}_{i=1}^n$. Suppose I first use a ...
- 3,090
2 votes
0 answers
42 views
Semi-parameteric estimation
I am interested in the effect of certain interventions $T$ on my value of interest $Y$, my model is, $$Y = \tau f(T, X, Z) + g(X, Z), $$ where $f(T, X, Z) = T \times X + T \times Z$ , that is all the ...
- 1,647
4 votes
1 answer
155 views
Double Machine Learning: What kind of "naive" estimator do the authors use to get such a bias?
I am reading the double-machine learning paper by Chernozhukov et al. (2018), in Example 1.1. the authors consider the partially linear model: $$Y = D \theta_0 + g_0(X) + U, E[U|X, D] = 0\\ D = m_0(X) ...
- 741
0 votes
0 answers
88 views
Estimating Time-Varying Effects of Time-Invariant Covariates
In short, I have a time-invariant variable that I know has a time-varying effect on my outcomes of interest. I would like to estimate a plot this effect over time. What are some ways of going about ...
- 335
2 votes
0 answers
89 views
Deriving Influence Function for variance estimator
In chapter 2 of Tsiatis (2006), the following is stated After some straightforward algebra, we can express the estimator $\hat{\sigma}_n^2$ minus the estimand as $$(\hat{\sigma}_n^2 - \sigma_0^2) = ...
- 2,757
2 votes
1 answer
150 views
How to perform a linear regression to data which has transient behavior and saturation?
I am trying to linear-fit data in intermediate time scale (theoretically assumed to be linear) in the absence of the transient behavior in initial time and saturation after some time. For instance, ...
- 21
2 votes
1 answer
248 views
Method of Sieves with Data Driven Basis Functions
Consider a nonparametric regression problem with i.i.d. sampled data $(y_1,x_1), (y_2,x_2),\ldots, (y_n,x_n)$ and regression function $$y_i = g_0(x_i) + \varepsilon_i,\quad \mathbb E[\varepsilon_i | ...
- 2,565
0 votes
0 answers
117 views
Bandwidths in Nonparametric Estimation regarding local linear and local constant
I'm reading up on some nonparametric methods and I've gotten a bit confused regarding what will happen given a certain bandwidth. For example, if I consider the local linear least squares method and a ...
- 589
0 votes
1 answer
316 views
estimation method in GAM model
I created a GAM model with semiparametric with parametric and nonparametric covariates. In the parametric regression model there is an estimation method to determine the value of the beta coefficient. ...
- 31
0 votes
0 answers
58 views
Choosing variables for a semiparametric model
I am trying to create a semiparametric model for university (we were told it HAS to be semiparametric) and I have 11 response variables, some of them categorical and the rest continuous. In the simple ...
2 votes
0 answers
182 views
MCMC fitting of a Dirichlet Process or Polya Tree prior to the residuals in a (simple linear regression)/(2-independent-samples) problem
Consider a simple location-shift semi-parametric model with two mutually-independent samples (here $F$ is a cumulative distribution function (CDF) on $\mathbb{ R }$, the $C_i$ and $T_j$ are real-...
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