Animals that are robust to environmental changes are desirable in the current dairy industry. Genetic differences in micro-environmental sensitivity can be studied through heterogeneity of residual variance between animals. However, residual variance between animals is usually assumed to be homogeneous in traditional genetic evaluations. The aim of this study was to investigate genetic heteroge...

In this work, a clear distinction is drawn between irreversibility associated with a finite mean driving force in a transport process and irreversibility associated with variance in the spatial and/or temporal distribution of this driving force. The portion of irreversibility associated with driving force variance is quantified via a newly defined dimensionless quantity, the equipartition facto...

The limiting distribution μ of the normalized number of key comparisons required by the Quicksort sorting algorithm is known to be the unique fixed point of a certain distributional transformation T—unique, that is, subject to the constraints of zero mean and finite variance. We show that a distribution is a fixed point of T if and only if it is the convolution of μ with a Cauchy distribution o...

This paper re-examines the performance of REITs, stocks, and fixed-income assets based on the preferences of risk-averse and risk-seeking investors using mean-variance and stochastic dominance approaches. Our findings indicate no first-order stochastic dominance and no arbitrage opportunity among these assets. However, our stochastic dominance results reveal that in order to maximize their expe...

The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees-of-freedom adjustment), applied to the fixed-effects estimator for panel data with serially uncorrelated errors, is inconsistent if the number of time periods T is fixed (and greater than 2) as the number of entities n increases. We provide a bias-adjusted HR estim...

The objective of this study was to identify the best random regression model using Legendre orthogonal polynomials to evaluate Alpine goats genetically and to estimate the parameters for test day milk yield. On the test day, we analyzed 20,710 records of milk yield of 667 goats from the Goat Sector of the Universidade Federal de Viçosa. The evaluated models had combinations of distinct fitting ...

We consider the problem of packing fixed-length patterns into a permutation, and develop a connection between the number of large patterns and the number of bonds in a permutation. Improving upon a result of Kaplansky and Wolfowitz, we obtain exact values for the expectation and variance for the number of large patterns in a random permutation. Finally, we are able to generalize the idea of bon...

Given constants s1, s2, . . . , sG, we consider variables X = ∑ sg1[g ∈ A] and Y = ∑ sg1[g ∈ B] as random variables with a joint distribution determined by taking (A,B) as uniformly random among set pairs in which A has fixed cardinality m, B has fixed cardinality n, and the intersection A ∩ B has fixed size q. Arguments about without-replacement sampling give the marginal mean and variance of ...

This paper concerns the instantaneous frequency (IF) of continuous-time, zero-mean, complexvalued, proper, mean-square differentiable nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for fixed time, which extends a result known for widesense stationary processes to nonstationary processes. For a fixed time the IF has either zero or infinite var...

We consider the exploration/exploitation problem in reinforcement learning. For exploitation, it is well known that the Bellman equation connects the value at any time-step to the expected value at subsequent time-steps. In this paper we consider a similar uncertainty Bellman equation (UBE), which connects the uncertainty at any time-step to the expected uncertainties at subsequent time-steps, ...