عنوان

Edgeworth expansion and bootstrap approximation for M-estimators of linear regression parameters with increasing dimensions

شماره

TLpq303929612

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Edgeworth expansion and bootstrap approximation for M-estimators of linear regression parameters with increasing dimensions

نام عام مواد

[Thesis]

نام نخستين پديدآور

M. A. Tiro

نام ساير پديدآوران

S. N. D. Lahiri, H. A.

نام ناشر، پخش کننده و غيره

Iowa State University

تاریخ نشرو بخش و غیره

1991

نام خاص و کميت اثر

92

جزئيات پايان نامه و نوع درجه آن

Ph.D.

کسي که مدرک را اعطا کرده

Iowa State University

امتياز متن

1991

متن يادداشت

In this study, we consider two different inference problems in linear regression models. The first problem deals with the model usdy\sb j\ =\ x\sbsp{j}{\prime}\beta\ +\ \epsilon\sb jusd; j = 1,2, ...,n, where usdy\sb1,y\sb2usd, ...,usdy\sb nusd are observations; usd\epsilon\sb1,\epsilon\sb2usd, ...,usd\epsilon\sb nusd are independent and identically distributed random variables with a common distribution function; usdx\sb1,x\sb2usd, ...,usdx\sb nusd are known, nonrandom p-vectors; and usd\betausd is px1 vector of parameters. Edgeworth expansions for the standardized as well as studentized linear combinations of least squares estimators are obtained without assuming normal errors. The number of parameters p is allowed to increase with n and essentially under the condition p = usdO(n\sp{({1\over2}-\delta)})usd as usdn\to\inftyusd for any usd\delta > 0usd. These results extend the results of Qumsiyeh (1986). It is also shown that the bootstrap method is second order correct for the studentized statistics improving the results of Bickel and Freedman (1983). The second model is a p-population model given by usdY\sb{i}\ =\ X\sb iB\sb i\ +\ \epsilon\sb{i}usd; i = 1,2, ...,p, where usdY\sb iusd is the usdn\sb iusdx1 vector of observations from the usdi\sp{th}usd population; usd\epsilon\sb iusd is a usdn\sb iusdx1 random vector; usd\beta\sb iusd is the kx1 vector of parameters; and usdX\sb iusd is usdn\sb i{\rm x}kusd known nonrandom matrix. Here k is a fixed positive integer and usdn\sb i\geq 1usd denotes the usdi\sp{th}usd sample size for i = 1,2, ...,p. This is an extension of Ringland (1980) to a general regression model. Edgeworth expansions and bootstrap approximations of the M-estimator corresponding to some score function usd\psiusd of the linear regression parameters are obtained under some regularity conditions on usd\psiusd and on the error distribution function. This extends the results of Lahiri (1990) from fixed to increasing dimensionality. Results of this part remain valid under the condition usd{p\sp3\over N}\to 0usd as usdN\to\inftyusd, where N = is the number of observations.

موضوع مستند نشده

Pure sciences

موضوع مستند نشده

Statistics

مستند نام اشخاص تاييد نشده

M. A. Tiro

مستند نام اشخاص تاييد نشده

S. N. D. Lahiri, H. A.

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y