相关论文: Linear Estimation of Location and Scale Parameters…
In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when at least k of its coordinates are…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess…
Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic…
We study the structure of a uniformly randomly chosen partial order of width 2 on n elements. We show that under the appropriate scaling, the number of incomparable elements converges to the height of a one dimensional Brownian excursion at…
We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not…
We consider component-wise estimation of order restricted location/scale parameters of a general bivariate location/scale distribution under the generalized Pitman nearness criterion (GPN). We develop some general results that, in many…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution…
For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…
While the ordinary least squares estimator (OLSE) is still the most used estimator in linear regression models, other estimators can be more efficient when the error distribution is not Gaussian. In this paper, our goal is to evaluate this…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under…
The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of…
We use location model methodology to guide the least squares analysis of the Lasso problem of variable selection and inference. The nuisance parameter is taken to be an indicator for the selection of explanatory variables and the interest…
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…