Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least ...

learn more… | top users | synonyms (1)

0
votes
0answers
10 views

Bayes minimax estimator [closed]

I am having trouble finding bayes minimax estimator using least squares method. Can anyone clearly elaborate on this
2
votes
1answer
36 views

How to represent goodness of fit for multiple least squares fits

I have many sequences (~50) of time series data that I have fit to a non-linear model using a least squares fit. If I had a single sequence of time series data, and I fit a model to it using a least ...
1
vote
0answers
13 views

Using OLS with missing panel data

I am trying estimate the following model using OLS $$ Y_{t} = \beta_{0} + \beta_{1}X_{1t} + \beta_{2}X_{2t} + \epsilon_{t} $$ where $Y_{t}$ is the difference between two observed variables, $Y_{t} ...
0
votes
0answers
48 views

Finding the optimal threshold parameter

Assume we are penalizing the least squares by the hard thresholding penalty: $argmin_\theta 2^{-1}(z_2-\theta)^2 + p_\lambda(|\theta|)$ where $p_\lambda(|\theta|)$ is the hard thresholding penalty ...
2
votes
0answers
22 views

How to choose between different options in partial least square regression?

There seem to be several methods of performing partial least square regression. For example in pls pacakge in R, following are available: ...
0
votes
0answers
21 views

Multifactor Covariance Matrix

hanks for taking a look. I am struggling to understand a rather simple concept. I ran a simple linear regression of the form $$A= \alpha+ \beta X + E$$ $$C = \alpha +\beta X + E$$ Then i ...
1
vote
1answer
49 views

Identical observations in linear regression

I want to do a linear regression $Y = X\beta + e$, but some of the observations (rows in $X$) are identical (about 30 000 out of 50 000 remain after deleting all duplicates), so when I try to ...
0
votes
1answer
23 views

Least square estimation with quadratic fit. Any simple solution?

We consider the least square problem in the case where we got only one independant variable $x_i$ and only one dependant variable $y_i$. The number of observations is $n$. In the case of the linear ...
0
votes
0answers
32 views

Practical beginners resource for building a dynamic OLS model

I need to model the current account balance of a country. The regressors are the real effective exchange rate, the domestic GDP and the GDP of the world. I am using data for 30 years (in logs). It is ...
2
votes
1answer
28 views

Is OLS in Engle-Granger a valid method to use when finding the cointegrating vector?

In this post mpiktas showed that the sample correlation measure for two random walks (possible correlated) is a random variable and does not estimate the theoretical correlation. When trying to find a ...
0
votes
0answers
80 views

Interpreting regression coefficient - what units are fractions?

I am regressing a growth measure (in fraction form, between 0 and 1) on another fraction that lies between 0 and 1 (let's call the variable ``share"). The regression is performed using OLS. What is ...
1
vote
0answers
18 views

Preinititalising Neural Networks using Least Squares solution

I am attempting to train a neural network, to approximate an unknown function. The function domain and range is real valued vectors with 300 elements: all of which are between -1 and 1 (exclusive). ...
3
votes
1answer
41 views

OLS estimation for Nonlinear model

Consider the following model which may be nonlinear: $Y_{t} = f (X_{t}, \beta_{0}) + \mu_{t}, \hspace{0.2cm} t=1, ..., T$ If we assume that: $\mu_{t}$ i.i.d with mean = $0$ and ...
2
votes
0answers
41 views

Autocorrelation in DOLS: will HAC standard errors work?

I am currently estimating a cointegrating regression (DOLS), where my residuals have autocorrelation. Sometimes it is just in one or two lags, but sometimes it is more. My question is: Can I apply HAC ...
0
votes
0answers
23 views

What is the reverse of the between estimator called?

Between estimator is defined as running a regression of the form: $Y_i = C + B_0X_i + e_i$ On panel data, where Y is the cross sectional mean of Y, X is the cross sectional mean of X. As a result of ...
0
votes
0answers
23 views

All models (LPM, Logit, HGLM, etc.) yield same results — which to report?

I'm interested in people's opinions here on a modeling choice given this design. We have two years of data from students in a school district. An intervention was introduced in year two. We have a ...
0
votes
0answers
23 views

How to model “aggregate” dependent variable in case of variable transformation?

Background: I have a panel data set consisting of dependent variable $y_{i,t}$ and several independent variables $x_{j}$, where $i$ indicates observation (ID), $j$ serves as dependent variable index ...
0
votes
0answers
23 views

Tikhonov regularizes least square dual function

I'd like to find the dual problem for least squares with Tikhonov regularization. For now, I have the primal problem expressed as minimize $||Ax-b||_2^2 + \gamma||x||_2^2$. I'm introducing a dummy ...
2
votes
1answer
39 views

Intrumental variable for covariates

I am only interested in the causal and unbiased effect of x on y and I have used additional covariates in my model to control for other effects. I have a pretty decent instrument for my potentially ...
0
votes
0answers
27 views

What model to use? Heckman-Two-Stage? Tobit? OLS?

I am currently researching innovation with firm level data. I have a nice dataset, which allows to analyze the variable inno which is ...
0
votes
1answer
39 views

Can heteroskedastic residuals be justified by variance in dependent variable?

This is a very basic question and I hope it is not a duplicate. Im using a pooled regression model with a log-transformed dependent variable (electricity consumption meter values). The variance of ...
1
vote
0answers
35 views

Instrument variable that indirectly related to the error term. Valid?

I try to grasp the concept of instruments in 2SLS regressions. I have a variable that is correlated with an endogenous regressor (informative). I also believe that it is uncorrelated with the error ...
1
vote
1answer
54 views

How to determine if GLS improves on OLS?

I have a multiple regression model, which I can estimate either with OLS or GLS. The weights for the GLS are estimated exogenously (the dataset for the weights is different from the dataset for the ...
1
vote
0answers
19 views

Does it make sense to test for nonlinear moderation if my independent variable is insignificant?

Currently doing an OLS regression in Stata. I have 2 independent variables(also included square terms), dummy variables and 1 moderator variable. However, to the best of my knowledge, I have to ...
0
votes
0answers
26 views

General to specific: t-stat, Akaike, Schwarz, and Adjusted R-squared

Specifying a linear model from general to specific i find that removing regressors corresponding to insignificant coefficients actually makes the adjusted r-squared, the Akaike and the Schwarz stats ...
0
votes
0answers
17 views

Prediction interval with Weighted Least Squares Linear Regression

I have been looking for this kind of stuff on the internet for a while and I cannot find any answer. In the classical linear regression (without weights), one can compute the standard deviation and ...
0
votes
1answer
21 views

Testing OLS Model Prediction Accuracy?

How can I test the accuracy of my ordinary least squares model? Is it a simple comparison between the predicted values of my test set and their actual values (with perhaps a maximum threshold of ...
1
vote
1answer
41 views

Normality of data in OLS

I am trying to perform an OLS on time series for a project for college. The professor told me that I need my regressors to be normal in order to justify the use of a linear regression. His argument ...
0
votes
0answers
52 views

Why does the normality of the coefficient's probability distribution follow from the normality of the errors in OLS?

So suppose after a simpple OLS regression we want to know what the chance(P-value) is that the Beta coefficient is 0 . First we assume that many random processes caused the errors ($\epsilon\!_i$), ...
6
votes
1answer
96 views

Interpretation of Saturated Model vs. Model with Interaction and One Main Effect

Say that I have two regressions: 1) $Y_i = \alpha_0 + \alpha_1 X_i + \alpha_2 X_i*Z_i + \epsilon_i$ 2) $Y_i = \beta_0 + \beta_1 X_i + \beta_2 Z_i + \beta_3 X_i*Z_i + \epsilon_i$ $X_i$ and $Z_i$ are ...
4
votes
1answer
69 views

Stein's estimator vs James-Stein estimator

I read a lot of sources concerning stein's estimator and James-Stein estimator. Unfortunately, a lot of sources do not write the correct formulas of each estimator. And so I am now confused!! Kindly, ...
1
vote
1answer
15 views

F-test of joint significance vs multiple t-test for regression parameters? [duplicate]

In the context of linear regression, I don't understand why you need to perform an F-test for the H0 that all parameters are zero, instead of just looking at all the t-tests for each parameter. I ...
1
vote
2answers
60 views

Insignificance by confounding variables

I am confused about a result in my OLS regression. I am regressing health on both crime level and ubanization and a couple of commonly encountered covariates in the literature such as, for example, ...
4
votes
1answer
107 views

Making sense of the first difference regression model

There must be a fundamental error in my approach. Let's start by stating we have a simple regression with two variables $X_t$ and $Y_t$: $Y_t = BX_t + e_t$ Where $B$ is the coefficient and $e_t$ is ...
0
votes
2answers
74 views

Derivative of softmax and squared error

I'm trying to understand the derivatives w.r.t. the softmax arguments when used in conjunction with a squared loss (for example as the last layer of a neural network). I am using the following ...
3
votes
0answers
64 views

Derivation of Olsens LS Selectivity Correction

There are many estimation procedures that correct for sample selection. The most famous is Heckman's two-step selectivity correction (in two equations) that assumes bivariate normality of the error ...
1
vote
2answers
52 views

What does “special case of GMM” mean?

I was researching purchasing this text book: http://www.amazon.com/dp/0691010188/ref=wl_it_dp_o_pd_nS_ttl?_encoding=UTF8&colid=2QTISO1Y8TYVW&coliid=I3FUEFWL47AC4L In its description it talks ...
1
vote
1answer
32 views

A question on notation in the least squares method

I am reading some nice lecture notes on basic statistics, learning some basic topics on estimation of parameters. Reading the chapter about the method of least squares estimation I meet the following ...
2
votes
0answers
19 views

Pooled OLS with Common Shock

I have the following dataset: ...
4
votes
2answers
181 views

What is the interpretation of the covariance of regression coefficients?

The lm function in R can print out the estimated covariance of regression coefficients. What does this information give us? Can we now interpret the model better or diagnose issues that might be ...
2
votes
1answer
49 views

Common trends with Difference in differences

For OLS to have good properties, we should assume that $E(u|X)=0$. When using DiD, is it then this assumption which requires the so-called common trend assumption (need for the DiD to have good ...
10
votes
1answer
416 views

I have a line of best fit. I need data points that will not change my line of best fit

I'm giving a presentation about fitting lines. I have a simple linear function, $y=1x+b$. I'm trying to get scattered data points that I can put in a scatter plot that will keep my line of best fit ...
4
votes
1answer
32 views

R-squared value when using offset — how is it calculated?

I have a linear model with a test score variable as a dependent variable and a vector of covariates. I have an offset variable in the model. So the formula is= $$\text{score}_i = B_0 + B_xX_x + ...
5
votes
1answer
51 views

Least squares with exponential model

I'm trying to fit values from this model $$y(x)=ae^{−bx}+c$$ where a, b and c are 3 different parameters that I want to find with least squares. So using least squares I want to find the value of a, ...
5
votes
2answers
79 views

Fit exponential distribution with noise

I'm trying to fit an exponential with noise (which in this case is a constant $c$) like this one $$ y(x) = \alpha e^{- \alpha x} + c \text{ ,}$$ having $(x_i, y_i)$ values (So $\alpha$ and $c$ are ...
2
votes
1answer
51 views

Interaction between time-variant and time-invariant variable in FE model

I want to estimate the effect of several variables $x_{1,it}$, $x_{2,it}$, $\dots$ on $y_{it}$. All of these variables vary across countries $i$ and time $t$. I use OLS to estimate a model with ...
0
votes
0answers
23 views

How do I weight inputs to a regression model so that one figures into the model more than the other?

I have obtained a series of weights from a text mining algorithm. Unfortunately, my algorithm is not capable of doing certain tasks that are too similar without some sort of regression analysis, say ...
1
vote
0answers
36 views

Weighted Least Squares Normalization for Parameter Uncertainty

I want to fit a function $f(x_1,x_2..)$ to (noisy) data with unknown variance. For each datapoint, I have a weight $w_i$ which is proportional to the reliability of that particular datapoint. The real ...
1
vote
0answers
13 views

Different number of observations for two samples in pooled ols?

In a Pooled OLS regression, on stata, would it matter if my first sample had 100 observation (100 countries) and my second sample which is independent of the first sample, contains 120 observations ...
0
votes
0answers
50 views

Moving window forecasting in Python

I am looking to create some code that will out-of-sample forecast the HAR-RV model. The model itself is formulated as the following, and the betas are estimated through HAC-OLS or Newey-West. ...