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The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this…
The Plackett--Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model's likelihood. In this paper, we…
The linear combination of Student's $t$ random variables (RVs) appears in many statistical applications. Unfortunately, the Student's $t$ distribution is not closed under convolution, thus, deriving an exact and general distribution for the…
Linear regression is widely used to model relationships between responses and predictors. In modern applications, one encounters data where the responses are non-Euclidean random objects situated in a metric space, paired with Euclidean…
The recent proliferation of computers and the internet have opened new opportunities for collecting and processing data. However, such data are often obtained without a well-planned probability survey design. Such non-probability based…
Maximum likelihood style estimators possesses a number of ideal characteristics, but require prior identification of the distribution of errors to ensure exact unbiasedness. Independent of the focus of the primary statistical analysis, the…
We propose a likelihood ratio statistic for forming hypothesis tests and confidence intervals for a nonparametrically estimated univariate regression function, based on the shape restriction of concavity (alternatively, convexity). Dealing…
We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when…
Bayesian Student-$t$ linear regression is a common robust alternative to the normal model, but its theoretical properties are not well understood. We aim to fill some gaps by providing analyses in two different asymptotic scenarios. The…
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…
A naive likelihood ratio (LR) estimation using the observed frequencies of events can overestimate LRs for infrequent data. One approach to avoid this problem is to use a frequency threshold and set the estimates to zero for frequencies…
Knowing the link between observed predictive variables and outcomes is crucial for making inference in any regression model. When this link is missing, partially or completely, classical estimation methods fail in recovering the true…
We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…
We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly…
Penalized methods are applied to quasi likelihood analysis for stochastic differential equation models. In this paper, we treat the quasi likelihood function and the associated statistical random field for which a polynomial type large…
In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…
The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove…
The choice of the prior distribution is a key aspect of Bayesian analysis. For the spatial regression setting a subjective prior choice for the parameters may not be trivial, from this perspective, using the objective Bayesian analysis…