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This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended…

We prove a general inequality on $\beta$-mixing coefficients of point processes depending uniquely on their $n$-th order intensity functions. We apply this inequality in the case of determinantal point processes and show that the rate of…

We study the fully entangled fraction (FEF) of arbitrary mixed states. New upper bounds of FEF are derived. These upper bounds make complements on the estimation of the value of FEF. For weakly mixed quantum states, an upper bound is shown…

The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…

Scientists and engineers are often interested in learning the number of subpopulations (or components) present in a data set. A common suggestion is to use a finite mixture model (FMM) with a prior on the number of components. Past work has…

Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…

Corresponding to $n$ independent non-negative random variables $X_1,...,X_n$, are values $M_1,...,M_n$, where each $M_i$ is the expected value of the maximum of $n$ independent copies of $X_i$. We obtain an upper bound to the expected value…

This work is concerned with the detection of a mixture distribution from a $\mathbb{R}$-valued sample. Given a sample $X_1,\dots,X_n$ and an even density $\phi$, our aim is to detect whether the sample distribution is $\phi(\cdot-\mu)$ for…

In this paper we extend the classical Glivenko-Cantelli theorem to real-valued empirical functions under dependence structures characterised by $\alpha$-mixing and $\beta$-mixing conditions. We investigate sufficient conditions ensuring…

Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a…

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with…

In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for…

Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture…

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We…

We give a new large deviation inequality for sums of random variables of the form $Z_k = f(X_k,X_t)$ for $k,t\in \mathbb{N}$, $t$ fixed, where the underlying process $X$ is $\beta$-mixing. The inequality can be used to derive concentration…

We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…