Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirrors the scientific discovery process. The learned structures can often decompo...

We prove the first fundamental theorem of invariant theory for the action of the special orthogonal group on m tuples of matrices by simultaneous conjugation. A basic relation between polynomial invariants is also studied.

Let Md(k) denote the space of d×d-matrices with coefficients in an algebraically closed field k. Let X be an orbit closure in the product [Md(k)] t equipped with the action of the general linear group GLd(k) by simultaneous conjugation. We show that X is regular at any point y such that the orbit of y has codimension one in X. The proof uses mainly the representation theory of associative algeb...

The generating function for words with several simultaneous maj weights is given. New maj-like Mahonian statistics result. Some applications to integer partitions are given.

In comparing two treatments with failure time observations, con®dence bands for the `̀ difference'' of two survival curves provide useful information about a global picture of the treatment difference over time. In this note, we propose a rather simple procedure for constructing such simultaneous con®dence intervals. Our technique can also be used in the one-sample case, which has been extensive...

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in the recent years, renewable energy sources are an important component of world energy consumption. gdp is one of the main measures of a country’s economic activity. most of the studies examine the impact of renewable energy consumption on gdp with single equation model and the others use dynamic panel data. since the granger causality analysis’s findings of this paper establish bidirectional...

This paper provides a selective survey of the panel macroeconometric techniques that focus on controlling the impact of “unobserved heterogeneity” across individuals and over time to obtain valid inference for “structures” that are common across individuals and over time. We consider issues of (i) estimating vector autoregressive models; (ii) testing of unit root or cointegration; (iii) statist...

Preparing the books to read every day is enjoyable for many people. However, there are still many people who also don't like reading. This is a problem. But, when you can support others to start reading, it will be better. One of the books that can be recommended for new readers is estimation of simultaneous equation models with error components structure lecture notes in economics and mathemat...

In this paper, short-run and long-run relationships between real interest rates in G-7 countries are analyzed. Using the model that follows the dynamic simultaneous equation models of Pesaran (1997) and Hsiao (1997), we find evidences of long-run relationships between the US real interest rate and the other six G-7 countries. However, the estimated parameters do not support the real interest ra...