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Questions tagged [estimation]

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2 votes
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Prove that $T$ is a complete statistic and find a UMVUE for $p$

While preparing for my prelims, I came across this problem: Let $X_1, X_2,\cdots, X_n$ be a sequence of Bernoulli trials, $n \geq 4.$ It is given that, $X_1,X_2,X_3 \stackrel{\text{i.i.d.}}{\sim} Ber(\...
Wrik's user avatar
  • 21
0 votes
0 answers
9 views

How to deal with Bias Gradient Matrix for biased CRB(Cramér–Rao bound) calculation if the gradient matrix is m-by-n but $m \neq n$?

I am doing a model for collabrative localization and using the CRB(CramΓ©r–Rao bound) as the localization performance measurement. I want to consider interference caused by NLOS and clutter, therefore ...
Loco Citato's user avatar
0 votes
0 answers
14 views

Have I constructed the Neyman-orthogonal score correctly?

I am trying to construct a Neyman-orthogonal score for the Poisson m-estimator, using section 2.2 of Chernozhukov et al. (2018). Have I done this correctly? If so, can somebody please help me show/...
Nick Green's user avatar
0 votes
1 answer
34 views

Expectation of reciprocal residual sum of squares

Consider an IID sample $X_1 , \cdots, X_n \in \mathbb{R}^d$, then what can we say about the expectation of the reciprocal residuals when projecting onto every other point? That is can we compute $$ E \...
mather's user avatar
  • 31
2 votes
0 answers
29 views

Fitting a Multivariate Ornstein-Uhlenbeck Process to Data

I have multivariate time series data (100 dimensions or more) and wish to test the hypothesis that the dynamics follow a Langevin equation. A simple case is the Ornstein-Uhlenbeck process, how can one ...
ksheen's user avatar
  • 21
1 vote
0 answers
14 views

Conditional variance of random walk with given start points and ending points

If I have a random walk with 0 drift and I observe that $X_1 = x_1$ and $X_k = x_k$, bu I don't have all the points from $X_i$ for $i \in \{2, ..., k-1 \}$, how do I estimate them and given an CI? I ...
The One's user avatar
  • 225
0 votes
0 answers
27 views

Sampling distribution of the proportion of events

For categorical variables with $l \ge 2$ categories, what is the sampling distribution of the proportion of events in each category? These are obviously not independent, since they add up to 1. Does ...
Jessica's user avatar
  • 1,251
0 votes
0 answers
31 views

Bootstrap sampling to get monthly statistic from daily data

I have daily (iid) data for historic winter seasons: $d:$ (price, value, temperature, etc). The "value" is actually a concave up function of "price" and the other covariates. I'm ...
Sameer L's user avatar
1 vote
1 answer
31 views

Considering 96 observation for estimating the intercept (rule of thumb)

I remember Prof. Frank Harrell stated that in order to calculate the sample size using the rule of thumb, we must include 96 observations for just computing the intercept, hence the estimated sample ...
elisa's user avatar
  • 55
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0 answers
41 views

Unbiased Estimator of Nugget Effect

Question: I am trying the measure the nugget effect, which is parameterized by $(1-\lambda)$ in the following variance-covariance used to describe the multivariate normal distribution of my n-...
A Friendly Fish's user avatar
0 votes
0 answers
32 views

Notation to report the measurement of a parameter

The estimation of a parameter ($p$) is customary reported in Physics and other fields with, $ p = \hat{p} \pm \Delta p$, where $\hat{p}$ is an estimator, and $[\hat{p} - \Delta p, \hat{p} + \Delta p]$ ...
Diego Ravignani's user avatar
6 votes
1 answer
222 views

Estimating effects in the presence of a mediator

Suppose that one is interested to compare the effect of biological age versus "cognitive age" on a variety of outcomes. Cognitive age is measured by testing intelligence. The outcomes are a ...
Sam's user avatar
  • 755
1 vote
0 answers
86 views

Estimation in generalized additive models

I'm currently trying to learn about generalized additive models (GAMs) with the book Generalized Additive Models An Introduction with R by Simon N. Wood. However, I have some questions regarding the ...
Dude3400's user avatar
0 votes
0 answers
32 views

What is the difference between estimating parameters via MLE versus minimizing deviations from expectation?

What is the difference between estimating parameters using MLE (or MAP with uniform priors): $$\theta^* = \arg \max_\theta p(X|\theta)$$ and estimating them according to which setting would engender ...
actinidia's user avatar
  • 145
4 votes
3 answers
117 views

What statistic best estimates the sample mean in case of missing data in a distribution?

I have samples of particles and am interested in the particle lengths. The problem is that the samples are assessed using image analysis. As the particles overlap, the measurements are incomplete and ...
Buck Thorn's user avatar
0 votes
0 answers
13 views

How to determin the theoretical prediction limit for a complex process?

how can we find out what is the theoretical prediction limit for a complex process? For example, for a coin toss (on average) the prediction limit is 50%, that is we cannot predict better than this ...
vzografos's user avatar
0 votes
0 answers
31 views

Prove that variance of log Exp is greater than variance of Exp log

In the context of variational inference, we move from estimating the gradient of: $\log E_{q \sim Q(z|x)} [ \frac{p(z,x)}{q(z|x)} ]$ to: $E_{q \sim Q(z|x)} [ \log \frac{p(z,x)}{q(z|x)} ]$, which is ...
user3180's user avatar
  • 591
0 votes
0 answers
25 views

How to aggregate the uncertainty around many predictions?

I have predicted trends for hundreds of time series. Each trend prediction comes with its own upper and lower bound at each time step. I would like to aggregate these trends and report them. Taking ...
Ress's user avatar
  • 417
1 vote
1 answer
28 views

Point estimate of exponential distribution [closed]

Let $X_1, ..., X_n \sim Exp(\lambda)$ What's the probability $p$ that $X > 1$ for $X \sim Exp(\lambda)$. $p$ should be $e^{-\lambda*1}$ I want to use only the following method for point estimate $p$...
popcorn's user avatar
  • 143
3 votes
1 answer
138 views

Estimate Standard Errors Effortlessly [closed]

I have an unobserved variable $𝑧_𝑖$, and three observed estimates of it: $𝑀_𝑖, π‘₯_𝑖, 𝑦_𝑖$. The errors $𝑀_π‘–βˆ’π‘§_𝑖,π‘₯_π‘–βˆ’π‘§_𝑖,𝑦_π‘–βˆ’π‘§_𝑖$ are zero mean, independent of each other and ...
ba yes's user avatar
  • 33
0 votes
0 answers
24 views

Estimating variance from several samples

If several samples are taken from a distribution, say Gaussian, each sample having size n1,n2,n3,... and the SD of the underlying distribution is estimated from each of the samples, how can those ...
Maciej Tomczak's user avatar
1 vote
0 answers
76 views

Estimating variance of a Gaussian distribution from the mean of absolute values of first differences in a sequential sample

Edited Question: This question is about estimating the variance (or $\text{SD}_0$) of a parent distribution from which a set of random independent samples is taken. The samples are taken in sequence ...
Maciej Tomczak's user avatar
2 votes
1 answer
41 views

For estimating weights in the Synthetic Control Method, what linear combination of the outcomes and symmetric matrix are used?

I am reading Synthetic Control Methods for Comparative Case Studies Paper, and on pg. 5 it states how to estimate Synthetic Control Weights. The following is a summary of the methods in the paper. I ...
user321627's user avatar
  • 4,438
0 votes
0 answers
26 views

Maximum Likelihood Estimation - Nested(?) Distributions

I am trying to estimate the parameters of an underlying Beta distribution using observations that arise from Geometric distributions that are conditional on the draws from the aforementioned Beta ...
WillTheGeek's user avatar
4 votes
2 answers
124 views

Must maximum likelihood method be applied on a simple random sample or on a realisation?

I guess my trouble is not a big one but here it is: when one applies maximum likelihood, he considers the realization $(x_1, \dots, x_n)$ of a simple random sample (SRS), leading to ML Estimates. But ...
MysteryGuy's user avatar
2 votes
0 answers
35 views

Estimation of autocorrelation from unevenly sampled time series

Consider $n$ distinct time series $X^{(1)}, \ldots, X^{(n)}$, indexed by time (time ranging from 0 to 1), such that: each time series $X^{(i)}$ has a different number of observations, the time ...
Pohoua's user avatar
  • 2,628
1 vote
0 answers
32 views

Help with sequencing topics in undergrad stats course

For several years I sequenced my stats course so that estimation theory came before sampling theory. Seemed to make senseβ€”you need a couple of estimators in hand to talk about their distributions. But ...
1 vote
1 answer
34 views

Why can we get better asymptotic global estimators even for IID random variables?

Let $X_1,...,X_N$ be IID random variables sampled from a parametrised distribution $p_\theta$, and suppose my goal is to retrieve $\theta$ from these samples. We know that the MLE provides an ...
glS's user avatar
  • 383
0 votes
0 answers
26 views

How to make the profile likelihood model for estimation?

I tried to make the age estimation model using the chemical compound results from The soil. Initially, I used the multivariable regression model. However, the reviewer highly recommend using the ...
user21268575's user avatar
1 vote
0 answers
30 views

Extended Hidden Markov Models (HMM) parameter estimation

For simpler HMMs, we can use algorithms like Viterbi training (not decoding) or Baum Welch to estimate the parameters that best describe the observed data. How do we do the same when using a more ...
AlexS123's user avatar
0 votes
0 answers
96 views

Standard error for optimal solution of a convex optimization problem

Suppose I'm given a sample of IID pairs $\{(x_i, y_i)\}_{i=1}^n$ of non-negative numbers from some distribution $\mathcal{D}$ having a finite mean and covariance matrix. Moreover, I'm given a strictly ...
Alex Shtoff's user avatar
0 votes
0 answers
17 views

Denoising data with Rayleigh distribution assumption

Assume I have 3 random variables, $X$ (matrix of pixels of the noised images),$Y$ (matrix of pixels of the denoised unknown image),$Z$ (matrix of pixels of a noise with Rayleigh distribution), related ...
user2478159's user avatar
17 votes
5 answers
4k views

Is a product that has 4.9 stars from ten customers better than one that has 4.5 stars from a hundred customers?

In many areas, we encounter a situation where we compare averages of highly skewed statistics using two unequally sized samples. Typically, this happens when comparing items in an online store. For ...
0 votes
0 answers
27 views

Recovering normalized posterior distribution from log-posterior

For a Bayesian estimation problem that I am working on, where I update the log-posterior (many times based on data) instead of the posterior itself using Bayes rule. I find the following (rather ...
John Doe's user avatar
  • 195
0 votes
0 answers
9 views

What is the effect of sampling rate on parameter estimation when fitting a markov state model to timeseries data?

Let us say that I have some timeseries data, which can be described by a markov state model. And the time series has been sampled every $\Delta t$ time units. The sampling rate ($1/\Delta t$) must ...
ace_101's user avatar
0 votes
1 answer
38 views

Estimate of the intercept is off in a simulated AR(1) model

I've been working with a SARIMAX model for forecasting and found myself struggling to accurately interpret its long-term forecasts. To better understand the underlying mechanics and perhaps pinpoint ...
Quant In Spe's user avatar
3 votes
1 answer
40 views

Can we get the conditional bias of the estimator at a generic $x$?

Consider a standard ERM problem based on quadratic loss where we solve $$ \hat{f}_n\in \operatorname*{arg min}_{f\in \mathcal{F}} R_\text{tr}(f) $$ where $R_\text{tr}(f)=\frac{1}{n}\sum_{i=1}^n (Y_i-f(...
H.Y Duan's user avatar
  • 173
0 votes
0 answers
41 views

estimation in case of censorship

Suppose we want to estimate the if people agree to suppose additional funds to a project. So, the answer is whether yes (1) or no (0). If the true proportion is $p$, our goal is to estimate the value ...
Amin's user avatar
  • 693
4 votes
1 answer
104 views

Is it legit to estimate an AR(1) model for non-stationary time series?

Suppose ${X_{t}}$ is a non-stationary process. The goal is to estimate the following AR(1) model: $$X_{t}=\alpha +\beta X_{t-1}+\epsilon_t.$$ From classical time series analysis, we know that ...
Sane's user avatar
  • 489
7 votes
1 answer
383 views

Estimation of a uniform distribution corrupted by Gaussian noise

Problem definition I have a dataset composed by $m$ observations $y^{(1)},\dots,y^{(m)} \in \mathbb{R}^2$ generated as follow \begin{equation*}\begin{aligned} y &= z + v \newline z & \sim\...
matteogost's user avatar
0 votes
0 answers
37 views

Can I compare two estimates by their sample variance?

For example, to estimate the population mean $\mu$, I am given two sample mean $\bar{x}_1$ and $\bar{x}_2$ from two (independent) data sets of $N_1$ and $N_2$ observations respectively. Without access ...
Rokai's user avatar
  • 51
0 votes
0 answers
18 views

Estimating the parameters of a Process when only Charateristic function is known

<I asked a similar question earlier: Question> I am seeking guidance on methods for estimating the parameters of a process when the characteristic function is known but the distribution is not. ...
Starlord22's user avatar
0 votes
2 answers
53 views

Cramér-Rao bound when the samples come from two distributions

Is there a version of the CramΓ©r-Rao bound when samples are independent but not identically distributed? More specifically, I am considering a sample set that is divided in two subsets, each subset ...
Luis Mendo's user avatar
  • 1,099
0 votes
0 answers
30 views

Estimating the parameters when only characteristic function is known

Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data. To obtain VGSA, as explained in Carr et al. [2001], we take ...
Starlord22's user avatar
7 votes
3 answers
551 views

Unable to understand what confidence interval means

I seek to understand what confidence interval is with the aid of following example (which I know how to solve but do not understand the rationale behind it); Suppose it is known that the weight of ...
Quorthon's user avatar
  • 107
3 votes
1 answer
53 views

Cramér-Rao / Wolfowitz bound with nuisance parameter

Let $F$ be a distribution with two parameters, $\theta$ and $\phi$, whose values are non-random but unknown. Consider a sampling procedure in which $N$ samples $x_1, \ldots x_N$ are obtained from i.i....
Luis Mendo's user avatar
  • 1,099
1 vote
1 answer
27 views

How to manually evaluate a parameter estimate using the first few values of a time series?

I'm working on a problem (I paraphrase), Consider the $\text{AR}(2)$ model $$y_t=\alpha y_{t-1}-(1-\alpha)y_{t-2}+\epsilon_t, \hspace{1em} \epsilon_t\sim N(0,\sigma^2).$$ The conditional least ...
mjc's user avatar
  • 599
0 votes
2 answers
56 views

How to combine soft-max value from two or more neural networks

Consider a scenario where we have some input variable $X$ (maybe an image), which goes through several noisy path and we generate $K$ noisy observations: \begin{align} Y_i = X_i +Z_i, i \in \{1,\ldots,...
Boby's user avatar
  • 195
1 vote
1 answer
19 views

When using Weighted Estimating Equations (WEE) to estimate a linear regression model with missing data, what can do if missing probability is 1

When using Weighted Estimating Equations (WEE) to estimate a linear regression model with missing data. One way is to assume the missing at random and then compute the missing probability using some ...
Fangzhi Luo's user avatar
0 votes
0 answers
31 views

Maximum Likelihood Estimate not in Parameter Space

The observed value of mean of random variable from N($\theta$, 1) distribution is 2.3. If the parameter space is {0,1,2,3} then the maximum likelihood estimate of $\theta$ is? a) 1 b) 2 c) 2.3 d) 3 I ...
Rhea Agarwal's user avatar

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