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### How to compute bounding coefficients for McDiarmid's inequality?

I am trying to understand the proof in Sec. A2 of Gretton et al.. To make the question self-contained, I summarize below the key ingredients. At the end of the post, I state my question. Given a ...
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### Upper bounds on mixing times in MCMC for bayesian analysis in practice

I'm familiar with how, for a general markov chain with some transition kernel, the spectral gap and the log-Sobolev constant both provide an upper bound on mixing time. I also have heard people ...
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### Given a 1-Sided Lower Confidence Bound value, How to determine target failure rate

$R(t)$ = reliability = 1 - unreliability (probability that item is still operational for a given time t) unreliability = Cumulative Distribution Function (CDF) = (...
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### References on ARDL model

Please suggest books/references on ARDL model and ARDL bounds test approach to study.
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### If $\text{Var}(X) < \infty$, is $\text{Var}(XY) < \infty$ for $0 \le Y \le 1$?

I have a variable $X$ that I know has finite variance (and therefore also finite mean). Is it always true that its variance remains finite after scaling by $0 \le Y \le 1$? Note that $X$ and $Y$ are ...
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### Bounds of integration query

My question is for personal research. When finding the distribution of say Z=X+Y where X and Y are both exponentially distributed r.v's where X,Y > 0, I use the convolution method. I do the same for ...
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### Empirical Bernstein Bound for distributions outside range(0,1)

I'm working on using empirical Bernstein bounds to estimate the mean difference between 2 variables from different distribution. The algorithm samples from each variable until it detects a ...
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### Statistical methods for data where only a minimum/maximum value is known

Is there a branch of statistics that deals with data for which exact values are not known, but for each individual, we know either a maximum or minimum bound to the value? I suspect that my problem ...
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### Most likely event in a multinomial distribution setting

I'm looking at the following scenario: $k$ categories, distributed by a multinomial ($p_1,\dots,p_k$) such that $p_1 \ge \dots \ge p_k$. Draw $n$ samples. I'm interested in estimators/lower bounds ...
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### Bound on the variance of a product

Let $Z$ be a positive $\mathbb R$-valued random variable bounded above by $M>0$, and $H$ an $\mathbb R^d$-valued random variable (seen as a column vector) such that $\mathbb E[H_i^2]=1$. Define the ...
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### Perceptron Inseparable Case - Hinge loss

I am trying to understand the case where the perceptron algorithm can't find a perfect seperator. I am trying to understand how we bound the number of mistakes by using the hinge loss. My intuition ...
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### How to check if ARDL model is dynamically stable & bounds test, stata

I'm doing research on Spanish and Dutch GDP: the influence of domestic and foreign variables (industrial production, inflation, employment rate) on GDP. All variables are converted into growth rates, ...
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### Find expectation or lower bound of log erf

I need to find the expectation of $\log \Phi(x)=\log \left(\int_{-\infty}^x\frac{1}{2\pi}\exp(-\frac{1}{2}s^2)ds\right)$. (I realise this isn't quite the error function, but not sure what to call it). ...
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### Treatment Effect Bounds

My supervisor and I have run a randomized experiment in a developing country. Due to administrative problems there we unfortunately have the problem of non-response. This non-response is also not ...
Suppose that the random variable $X_T$ is $O_p(1)$ as $T \rightarrow \infty$. Does this imply that the random variable $\max\{0,X_T \}$ is $O_p(1)$?