Abstract This paper addresses the problem of Bayesian estimation of the parameters of Erlang distribution under squared error loss function by assuming different independent informative priors as well as joint priors for both shape and scale parameters. The motivation is to explore the most appropriate prior for Erlang distribution among different priors. A comparison of the Bayes estimates and...

This paper considers the problem of estimating a high-dimensional vector of parameters θ ∈ R from a noisy observation. The noise vector is i.i.d. Gaussian with known variance. For a squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector towards th...

This paper studies the problem of estimating the grahpon model – the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in recommender systems. The graphon model deals with a random graph of n vertices such that each pair of two vertices i and j are connected independently with p...

We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of multidimensional Brownian motion in R. Let ∼ x ∈ [0, 1] be a fractional feasible solution of a packing constraint Ax ≤ 1, A ∈ {0, 1} that maximizes a linear objective function. The independent randomized rounding method of Raghavan-Thompson rounds each varia...

Models of spatial interaction such as transport, migration, commuting and trade usually partition space into zones, to represent the receiving and sending end of the interaction. When zones encompass multiple locations, the partitioning causes an aggregation error (Hillsman and Rhoda 1978). The aggregation error increases with the size of zones. Aggregation errors can cause bias (Goodchild 1979...

In this paper we investigate the representation of integrals involving product Legendre Chi function, polylogarithm function and log function. We will show that in many cases these take an explicit form Riemann zeta Dirichlet Eta lambda other special functions. Some examples illustrating theorems be detailed.

Recent advances in the measurement of volatility have utilized high frequency intraday data to produce what are generally known as realised volatility estimates. It has been shown that forecasts generated from such estimates are of positive economic value in the context of portfolio allocation. This paper considers the link between the value of such forecasts and the loss function under which m...

Given a probability space (Ω,F , P ), a F -measurable random variable X , and a sub-σ-algebra G ⊂ F , it is well known that the conditional expectation E[X|G] is the optimal L-predictor (also known as “the least mean square error” predictor) of X among all the G-measurable random variables [8, 11]. In this paper, we provide necessary and sufficient conditions under which the conditional expecta...