We consider the classical additive measurement-error model $X=Y+Z$, where the latent random variable $Y$ has unknown distribution $F_Y$ and the error $Z$ has a known distribution. We develop direct estimators for three functionals of $F_Y$: (i) $F_Y(x)$ at continuity points; (ii) interval probabilities $F_Y(y)-F_Y(x)$ when $x<y$ are continuity points; and (iii) the size of a jump at a prespecified discontinuity. We derive non-asymptotic bias and variance bounds, and establish asymptotic unbiasedness and consistency. Unlike previous work, we do not require $F_Y$ to admit a density, have a mixture representation, or satisfy global Sobolev smoothness assumptions. The framework accommodates arbitrary latent distributions, including those with both discrete and continuous components, and distributions with multiple jumps. These results rely on a link between Fourier inversion theorems and the algebraic structure of a class of estimators proposed in Mynbaev, Martins-Filho and Henderson (2022). A simulation study evaluates feasible tuning procedures and, where available, compares the finite-sample performance of the proposed estimators with existing methods.
This work constructs a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$.
A (computationally inefficient) adaptive estimator that, so long as $p$ is a mixture of $k$ symmetric log-concave densities, achieves error comparable with the optimal estimator that knows $p$ and has $\tilde\Theta(n/k)$ samples.
Given $[0,1]$-valued random variables $X_1,\dots,X_n$ such that $\mathbb{E}[X_i | X_1,\dots,X_{i-1}]= \mu$ for all $i$, we propose a new nonasymptotic confidence interval for $\mu$ that is obtained by inverting terminal e-values generated by a novel betting strategy. When the data are iid, its limiting width matches th...
Diego Martinez-Taboada, Aaditya Ramdas· 1 citation
Given probability distributions $\mu$ and $\nu$ on measure spaces $X$ and $Y$, and a closed set $S \subseteq X \times Y$, when is there a probability distribution on $X \times Y$ whose marginals are $\mu$ and $\nu$, and whose support is precisely $S$? We answer the question when the marginals are discrete, and when the...
Christopher Coscia, M. Tassy, P. Winkler· 0 citations
We study the stochastic differential equation $$d X_t=b(t,X_t)d t+\sqrt{2}d W_t$$ on $\mathbb R^d$, where $b$ is a time-dependent, divergence-free distributional drift of critical H\"older--Besov regularity $-1$, strengthened by an iterated-logarithmic correction. For every initial probability law, we construct a weak...
Let $X(t)$, $t\in K$, be a centred Gaussian process with continuous sample paths on a compact metric space $K$, and let $M=\min_{t\in K}X(t)$. Let $\sigma_*^2$ denote the minimum covariance energy associated with $X$, and assume that $\sigma_*^2>0$. Motivated by the results of \cite{chakrabarty2018asymptotic} for smoot...
E. Hashorva, Svyatoslav Novikov· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
