: One use of spectral analysis of time series is to determine if two different time series are realizations from the same process This thesis develops the theory behind Krishnaiah and Schuurmann's theoretical work reported in their report Approximations to the Distributions of the Traces of Complex Multivariate Beta and F Matrices We take the trace of a test statistic calculated from the spectral density matrices of the time series and test it The thesis applies the theory to two small sample simulations (Author)

Spectral Analysis of Time Series.

Summary. Quantile regression offers a more complete statistical model than mean regression and now has widespread applications. Consequently, we provide a review of this technique. We begin with an introduction to and motivation for quantile regression. We then discuss some typical application areas. Next we outline various approaches to estimation. We finish by briefly summarizing some recent research areas.

Quantile regression: applications and current research areas

SUMMARY Although nonparametric regression has traditionally focused on the estimation of conditional mean functions, nonparametric estimation of conditional quantile functions is often of substantial practical interest. We explore a class of quantile smoothing splines, defined as solutions to

/pdf/quantile-smoothing-splines-1tihfjip5f.pdf

Quantile smoothing splines

Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.

Fundamentals of Nonparametric Bayesian Inference

http://library.um.ac.id/free-contents/downloadpdf.php/buku/laws-of-small-numbers-extremes-and-rare-events-michael-falk-jurg-husler-rolf-dieter-reiss-42718.pdf

Laws of small numbers: extremes and rare events / Michael Falk, Jurg Husler, Rolf-Dieter Reiss

Let $(X_1, Z_1), (X_2, Z_2), \ldots, (X_n, Z_n)$ be iid as $(X, Z), Z$ taking values in $R^1$, and for $0 < p < 1$, let $\xi_p(x)$ denote the conditional $p$-quantile of $Z$ given $X = x,$ i.e., $P(Z \leq \xi_p(x)\mid X = x) = p$. In this paper, kernel and nearest-neighbor estimators of $\xi_p(x)$ are proposed. In order to study the asymptotics of these estimates, Bahadur-type representations of the sample conditional quantiles are obtained. These representations are used to examine the important issue of choosing the smoothing parameter by a local approach (for a fixed $x$) based on weak convergence of these estimators with varying $k$ in the $k$-nearest-neighbor method and with varying $h$ in the kernel method with bandwidth $h$. These weak convergence results lead to asymptotic linear models which motivate certain estimators.

/pdf/kernel-and-nearest-neighbor-estimation-of-a-conditional-vo8byeclxo.pdf

Kernel and Nearest-Neighbor Estimation of a Conditional Quantile

In data driven bandwidth selection procedures for density estimation such as least squares cross validation and biased cross validation, the choice of a single global bandwidth is too restrictive. It is however reasonable to assume that the bandwidth has a distribution of its own and that locally, depending on the data, the bandwidth may differ. In this approach, the bandwidth is assigned a prior distribution in the neighborhood around the point at which the density is being estimated. Assuming that the kernel function is a proper probability distribution, a Bayesian approach is employed to come up with a posterior type distribution of the bandwidth given the data. Finally, the mean of the posterior distribution is used to select the local bandwidth.

Bayesian approach to the choice of smoothing parameter in kernel density estimation

Foraging to the rhythm of ocean waves: porcelain crabs and barnacles synchronize feeding motions with flow oscillations

Estimation of spectral density of a stationary time series via an asymptotic representation of the periodogram

Let {(Xf, Zf), i > 1} be a sequence of independent and identically distri buted (i.i.d.) random vectors (r.v.) with a distribution function (d.f.) n(x9z), (x,z) e R2 ( ? (?oo, oo)2). Let F(x) = n(x, oo), xeR, and let G(z\x) be the conditional d.f. of Z given X = x, for zeR, xeR. A conditional quantile function (of Z given X = x) is defined by

Ashis K. Gangopadhyay

Papers

Kernel and Nearest-Neighbor Estimation of a Conditional Quantile

Bayesian approach to the choice of smoothing parameter in kernel density estimation

Foraging to the rhythm of ocean waves: porcelain crabs and barnacles synchronize feeding motions with flow oscillations

Estimation of spectral density of a stationary time series via an asymptotic representation of the periodogram

Bootstrap confidence intervals for conditional quantile functions