This paper discusses the problem of estimating the population spectral distribution from high-dimensional data. We present a general estimation procedure that covers situations where the moments of this distribution fail to identify the model parameters. The main idea is to use generalized...

Large covariance or correlation matrix is frequently assumed to be sparse in that a number of the off-diagonal elements of the matrix are zero. This paper focuses on estimating the sparsity of a large population covariance matrix using a sample correlation matrix under multivariate normal...

Partial linear single-index model (PLSIM) is a flexible and applicable model when investigating the underlying relationship between the response and the multivariate covariates. Most previous studies on PLSIM concentrated on mean regression, based on least square or likelihood approach. In...

This paper aims at investigating model checking for parametric models with response missing at random which is a more general missing mechanism than missing completely at random. Different from existing approaches, two tests have normal distributions as the limiting null distributions no matter...

In estimation of the normal covariance matrix, finding a least favorable sequence of prior distributions has been an open question for a long time. This paper addresses the classical problem and accomplishes the specification of such a sequence, which establishes minimaxity of the best...

Variable selection in the Cox proportional hazards model (the Cox model) has manifested its importance in many microarray genetic studies. However, theoretical results on the procedures of variable selection in the Cox model with a high-dimensional feature space are rare because of its...

Many statistical data are imprecise due to factors such as measurement errors, computation errors, and lack of information. In such cases, data are better represented by intervals rather than by single numbers. Existing methods for analyzing interval-valued data include regressions in the metric...

We develop the panel-limited information maximum likelihood approach for estimating dynamic panel structural equation models. When there are dynamic effects and endogenous variables with individual effects at the same time, the LIML method for the filtered data does give not only a consistent...

This paper gives a comprehensive treatment of local uniqueness, asymptotics and numerics for intrinsic sample means on the circle. It turns out that local uniqueness as well as rates of convergence are governed by the distribution near the antipode. If the distribution is locally less than...

The weighted sum <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$S=w_1S_1+w_2S_2+\cdots +w_NS_N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>S</mi> <mo>=</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <msub> <mi>S</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>w</mi> <mi>N</mi> </msub> <msub> <mi>S</mi> <mi>N</mi> </msub> </mrow> </math> </EquationSource> </InlineEquation> is approximated by compound Poisson distribution. Here <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$S_i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>S</mi> <mi>i</mi> </msub> </math> </EquationSource> </InlineEquation> are sums of symmetric independent identically distributed discrete random variables, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$w_i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>w</mi> <mi>i</mi> </msub> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>